Copyright: © 2000-12 Theo Scheffers
Citation: © 2000-2012 HYGINIST Theo Scheffers


Getting Started (Summary)

HYGINIST is a decision making, statistical tool. It helps to assess the (bio)chemical exposure  in the workplace (the result of the complete working condition control regime) if you have collected a series discontinuous air exposure measurements.

This Help document explains the 6 transactions of HYGINIST. It tells you how to:

1.	perform:data entry and editing,

2.	examine the distribution shape,

3.	estimate the descriptive statistics: the measures of location and dispersion,

4.	extrapolate to unsampled periods and compliance test against a limit value,

5.	compare the exposure data with other sets of descriptive statistics,

6.	establish the minimum sample size for an unbiased estimate of long-term compliance control.

This Help further explains:

•	How to apply the HYGINIST statistical methods in working conditions control

•	The many aspects of the Lognormal distribution

•	Installing and running the program

•	Program operations

•	Register for regular use.

If, after installation, HYGINIST is started  then the following Splash screen and a Login box appear.

You may be asked to fill out your name and a password. See Annex C.5.1. on how to get a password.

If you entered your name and the password in the Login form, then the HYGINIST start page appears. This may take a few seconds, during which all forms and constants are loaded. Now  you can start  with the exposure data management and analysis.

I hope this program support your needs.

Please inform me by mail tscheffers@home.nl on your experience and don't forget checking regularly on the HYGINIST home page for updates of the program and the help file.

Regards

Theo Scheffers

Click here for a summary on the Goodness-of-fit methods used (2).

Click here for a summary on the Extrapolation methods used (3 & 4).


Goodness-of-fit (Summary)

The Getting started (Summary) mentioned the six transactions of HYGINIST, of which the second (2) is the goodness-of-fit. Sample air concentrations from similar exposure groups, will in fit the Lognormal model if:

•	you have practised good exposure assessment practise ,

•	sufficient data lie within the accuracy range of the measurement method,

•	the measurement method coefficient of variation CVt is smaller than the sample coefficient of variation ω/β, and

•	the grouping interval ∇C is small compared to the arithmetic standard deviation ω,

Goodness-of-fit with the shape of the Lognormal distribution is assessed by:

•	(2A) a visual inspection of the shape of the logarithmic transformed cumulative frequency distribution of the outcome on probability paper.

•	(2B) the W-test for Normality (Shapiro 1965), the most effective, complete sample test for shape.


Extrapolation (Summary)

The Getting started (Summary) mentioned the six transactions of HYGINIST, of which the third (3) and fourth (4) are to extrapolate from sample data to general results. HYGINIST deals with the common industrial hygiene practise to extrapolate from small (M<20), highly dispersive sample series to general results, proposing, in preference, unbiased statistical methods.

•	(3A) In complete samples unbiased estimators are calculated for the geometric mean EXP(μ), the geometric standard deviation EXP(σ), the arithmetic mean β and the arithmetic variance ω2 (Finney 1941, Laurent 1963).

•	(3B) If at least two results lie inside and one outside the range of accuracy, then the estimators GMg and GSDg are derived from the Lognormal probability plot and the least squares linear regression through the data points within the range of accuracy (Gupta 1952). The M-M' data outside the accuracy range, contribute for one half to the total degrees of freedom df=(M+M')\2-1, however, for at most twice the number of the uncensored data df<2M'.

(4A) From a series full reference period Time Weighted Average (TWA) measurements, the "long-term non-compliance probability" (NIOSH 1977, page 65) or the "acute health hazard" (Hawkins 1991 page 56) can be assessed using:

•	the standard Normal method (Leidel 1977),

•	the unbiased method (Wilks 1941), or

•	the Noncentral Student method (Tuggle 1982).

The standard Normal method is most efficient, but biased on the average and requires large sample size, small GSD's and very good Lognormal conformity. Wilks (for routine programs) and Tuggle (for first exposure assessment) have a higher sensitivity of in detecting non-compliance.

(4B) If the series exposure data are from within a reference period (e.g. grab or partial period, non consecutive measurements), then a TWA compliance probability and confidence upper limit can be estimated using:

•	the unbiased minimum variance method (Land 1971),

•	the approximate, consistent Student test (Jahr 1987) used in HYGINIST version 2.2.

(4C) From a series TWA measurements "The chronic health hazard" (Hawkins 1991 page 56) or the "Cumulative dose" (Seixas 1988) are assessed with the same methods as in (4B).

(4D) If Ceiling compliance is defined as no more than α% exceeding the limit using grab or partial period sampling, then the confidence δ can be calculated using the Noncentral Student method.


2. Exposure data management

HYGINIST evaluates two types of exposure data:

•	A series of M measurement results , or

•	A sample size M and the Lognormal statistical descriptive statistics GM and GSD.

The program always starts with the next window.

For context sensitive help move your cursor over the picture. Click your mouse if your cursor changes to a hand with index finger and you get context sensitive help.

this screen offers you the possibility to choose between:

•	'Entering raw data' by keyboard,

•	Entering the estimators of the Lognormal 'descriptive statistics' by keyboard,

•	Loading a raw data file from disk.

HYGINIST exposure data management further includes:

•	Instruction about the requirements that all exposure data should meet (par. 2.1),

•	Input of exposure data (par. 2.2),

•	Using the data grid (par. 2.3),

•	Error messages and handling (par. 2.4),

•	Save, show and edit data files (par. 2.5 through 2.8),

•	Exchange files with other database programs (par. 2.9),

•	At this moment it is not possible to import exposure data directly form a database or a spread sheet


2.1 Sample requirements

The numerical requirements on exposure values prevent random errors and the sample range (in numbers and numerical values) from influencing the validity and exceeding the range of accuracy.

Requirements are given for:

•	sample size (2.1.1)

•	measurement outcome (2.1.2)

•	Rounding and grouping interval (2.1.3)


2.1.1 Range of sample sizes

The sample size M is restricted to integer values between 2 and 2000. Two unequal and uncensored data are at least necessary to calculate a sample variance. The maximum of 2000 arises from the accuracy in calculating rankits (see B.1.1). Also with >2000 data the estimators GM and GSD differ hardly from their descriptive statistics EXP(μ) and EXP(σ). Three or more measurements makes it possible to examine the shape of the sample distribution. More on sample size see 2.2.1.1


2.1.2 Range of valid exposure data outcome

Sample measurement values are restricted:

     -	between c(1) ≥0.0000000001 and c(M) ≤10000000000.

     -	in the ratio of their extremes: 1.0001<c(M)/c(1) < 10000000000.

Sample measurements and the Lognormal descriptive statistics are further restricted in the range of the:

 -	geometric mean 0.0000000001≤GM ≤ 10000000000,

 -	geometric standard deviation 1<GSD ≤ 10000.

A GSD=1 indicate that all exposure data are equal. The presence of variance within a series measurements is a requirement for performing statistical analysis


2.1.3 Rounding and grouping interval

The measurement method or the coarse rounding of measurement outcome may overshadow the workplace variance and thus influence the shape of sample distribution and the validity of the evaluation. To prevent this the arithmetic standard deviation w should be much larger than the rounding and grouping interval ∇C.


2.2 Data entry

Choose between descriptive statistics or raw data (2.2.3).

If you click the option button 'Descriptive statistics' in frame 'Data type' then the frame 'Exposure data identification' appears:

In either ways it is possible to analyze:

•	a new series of measurement that you are going to enter in the program,

•	a series of measurement results that are exported from exposure databases,

•	literature or historical data from which only sample size and the estimators GM and GSD of the Lognormal descriptive statistics are reported.

You can enter exposure data :

•	by keyboard (2.2.1),

•	from a file in a directory (2.2.4).


2.2.1 Keyboard

Entering exposure data involves:

•	sample size (2.2.1.1),

•	the units of measurement (2.2.1.2),

•	the sampling duration of measurement (2.2.1.3),

•	characterization of the exposure by a name (2.2.2),

•	the choice between raw data and descriptive statistics entry (2.2.3).


2.2.1.1 Sample size

Enter the sample size. If more than two measurements are entered, then examining the shape of the sample distribution is possible.

If the goal of a HYGINIST session is the assessment of:

 -	The NIOSH non-compliance probability (see par.  5.1.2), or

 -	The minimum sample size for long-term control (see chapter 7),

and the descriptive statistics GM and GSD will be entered, then any integer between the limits is valid.

More on sample size see 2.2.1

Example 1	Reanalyzing exposure data by adapting the number of degrees of freedom


2.2.1.2 Sampling units of measurement

see 4.2.1.1


2.2.1.3 Sampling duration

See 4.2.1.2


2.2.2 Assign a name to the exposure data

Every file name should start with a character. The obligate name extension `.HYG` can be omitted. The name length may not exceed 255 characters

If a new file with raw data is created and saved with an existing name, then the data of that file are removed.

If only descriptive statistics will be entered, then using an existing name has no consequences for the raw data in that file.


2.2.3 Entering raw data

Click 'File' and than 'New *.HYG file' to start entering raw data.

The frame 'Exposure data identification' appears in which you can fill out :

•	a name for the data set (obligate)

•	A sample size (obligate)

•	Units of measurements

•	Sampling duration

If name and sample size are filled then two additional tabs appear at the top and a <Continue> button.

Click on tab 'Raw data' or on button 'Continue' to start entering individual measurement outcome (2.2.3.1).


2.2.3.1 Raw data (uncensored)

Fill first cell of the grid with a measurement result.

After pressing the <Enter> key a result is stored.

Press the <arrow down> key to go to the next cell.

You can enter positive values between 1D-10 and <1D+10.

Any value consists of at most 16 digits (double precision) and optional, a floating point and/or an exponent. The decimal point followed by an E or D, a + of - and one or two digits is recognized as an exponent. If no detection limit is introduced the operator is '='

After the last result is entered you can save the data (se Screen 10, par. 2.5). Next transaction is Show and Edit ( par. 2.8).

Example 2	Entering raw data


2.2.3.2 Censored data

Due to limitations of measurement methods, sampling results may indicate that the exposure lies outside the range of accuracy. The analytical outcome gives only an indication that the real exposure value is below or beyond a certain detction limit (the censor). Threat censored data as follows:

•	define an upper and/or lower limit (LL, UL) outside the range of accuracy (ll through ul), so that no outcome lie outside the range of accuracy and inside the limits (LL through ll and ul through UL);

•	give results outside the range of accuracy the value of the limit.

In the grid the operator of the outcome below the lower limit will change to '<' and the outcome beyond the upper limit will change to '>'

Example 3	Range of accuracy

You can enter the range of accuracy (= the detection limits) here or when examining the cumulative exposure distribution using the lognormal probability plot (see 3.1.2 Accuracy limits)


2.2.4 Loading a file

Choose an example  *.HYG for the HYGINIST program directory that you want to analyse.

Or browse to a data directory where you saved the *.HYG you want to analyse


2.2.4.1 Select a file from disk

Click '&File',  'Open *.HYG file' to load an existing raw data file.

The datagrid appears showing the outcome of the file.

You can fill out:

•	Units of measurements

•	the accuracy limits


2.2.4.2 Example files *.HYG

The program contains 36 files with industrial hygiene or quality control example data. More information on the example data files in Table 1. The name of the data files is mostly compiled from the authors name and the page number of the reference. The files in Table 1 are used throughout the text as examples. The descriptive statistics calculated for BOLEY62.HYG (see Example 57) and CHIP123.HYG will differ from those presented by the authors.

Table 1	Example data from different sources


2.2.5 Descriptive statistics

If you click the option button 'Descriptive statistics' in frame 'Data type'

then the frame 'Exposure data identification' appears:

In the frame 'Exposure data identification' you can fill out :

•	a name (obligate)

•	A sample size (obligate)

If name and sample size are entered then the frame 'Estimators of Lognormal geometric descriptive statistics' appears.

Now you can fill out:

•	a Geometric mean value between 0.0001≤ GM ≤ 10000

•	a Geometric standard deviation value between 1.001≤GSD≤1000

Entering estimators of the Lognormal descriptive statistics:

•	assumes the exposure data originate from a Lognormal distribution,

•	prohibits the evaluation of shape (chapter 3)

Example 4	Enter GM and GSD

Form more information on GM and GSD see B.2


2.3 Using the data grid


2.3.1 Append

In order to add outcome to the existing grid, click on tab <Start> and increase the sample size with the number of outcome you want to add.


2.3.2 Edit

Use the arrows up and down to move through the grid.


2.3.3 Delete
2.3.1 Append


2.4 Error messages and handling

still no text


2.5 Save

Browse to the data directory desired and save the raw data by entering a file name.

The HYGINIST extension is  *.HYG.


2.8.2 Editing raw data

Change the value of a result by clicking in the grid and selecting the value.

Now retype its value

If a series raw data from the current directory contains:

 -	values outside the range (1E-10  through 1E+10 ),

 -	just equals,

 -	too much variance,

a message box appears  with an error messages.

This offers you the possibility to correct a file (for example to introduce detection limit values in stead of zeros).

Example 5	Show raw data file


2.9 *.HYG file editors

Many software programs can create, read, write, expand, compress and edit *.HYG files. For example spread sheet programs like Lotus or Excel, database programs like Access and dBase , Text editors like Notepad, Editpad, word processing programs like Word and WordPerfect and many others ( e.g. SPSSPC, Basic, C). They can, like HYGINIST, process one column (field), numerical SDF or DELIMITED files with the extension *.HYG.

Example 6a	Making a *.HYG file using Word

Example 6b	Copying a *.HYG file form EXCEL

Example 7	Generating a Lognormal Monte Carlo *.HYG file using Basic

Example 8	Making a *.HYG file using dBase


3 Plot

The tab <Plot> includes:

 -	the examination of the Lognormal shape of a sample exposure data, and

 -	descriptive statistics estimation between limits of accuracy.

Table 4 in paragraph 3.4 helps the user to draw proper conclusions on the shape. A Lognormal shape is essential for an effective extrapolation to general results (Hawkins 1991 p58).

The tab "Plot" presents:

 -	a plot of the sample on Lognormal probability scale (Screen 17a, see par. 3.1),

 -	defining the accuracy range of the sample measurements (Screen 17bcd see par. 3.1.2)

 -	linear regression (Screen 17e, see 3.1.3)

 -	regression estimators for the descriptive statistics (Screen 17e, see 3.1.4)

 -	testing the shape (Screen 18, see par. 3.2),

 -	seven different transformations (Screen 19, see par. 3.3).

If at least three data entries are entered by the keyboard or loaded from a file, then this tab is visible.

The exposure data in example 9, example 10 and example 11, and the corresponding figures, are used throughout the manual to illustrate the different aspects on Lognormal extrapolation and inference in the following chapters.


3.1 Graphical examination

Graphical examination includes:

•	a rankit plot (Screen 17a, par.  3.1.1),

•	the assessment of the accuracy range (optional, Screen 17bcd, see  3.1.2),

•	a linear regression fit (Screen 17e, see  3.1.3) within the accuracy range,

•	the estimation of the descriptive statistics (Screen 17ef, see par. 3.1.4 and 3.1.5),

•	plots can be captured and saved, see  E.3


3.1.1 The rankit plot

In the picture box the ascending ordered concentrations are plotted against their expected places (see  B.1) within a normal distribution. The (un)transformed concentrations are displayed on the vertical Y-axis. For more information on normal probability plots see  B.1.1.

Screen 17a	Probability plot of exposure data on rankits scale

The median is displayed in Screen 17a if its value falls within the range of 5-95% of the vertical axis.

Rankit plots are made from all exposure data described in example 9, example 10 and example 11. Example 19 contains censored data files. How the rankit plot is used in the evaluation of shape is explained in paragraph 3.4.

Example 9	Description of rankit plots 1 through 4

 Figure 1 Ten TWA8 hours Dioxane (LEIDEL.67) 	Figure 2 45 TWA8 hours total hydrocarbons

 	among maintenance painters (Solv198)

 Figure 3 14 TWA8 hour Styrene on inlayers 	Figure 4 15 grab sample airborne

 working on different presses (POSTB11I)	chlorine concentrations (OWEN716)


3.1.2 Accuracy limits

With menu option "detection limits", upper and lower limits can be introduced and removed. A accuracy range prevents that outlier data that cannot be excluded from the sample, bias the estimation of the location and the variance. Using the data within the range of accuracy and the corresponding rankit values:

•	the shape is examined ( 3.1.3),

•	the descriptive statistics are estimated ( 3.1.4).

•	See par. 2.2.3.2 on how to enter censored exposure data.

Screen 17b 	Should accuracy limits be entered?

The range of accuracy is always limited:

•	All air sampling- and/or analytical methods do have a detection upper and lower limit. TWA8 hour PAS total dust measurements have an accuracy range of about 1.8 to 15 mg/m3 as will be shown in the examples. For aerosols and fibers PAS sampling accuracy limits are narrower than for  and gases.

•	Non-traceable errors in the strategy execution, the sampling, analysis and/or report procedure, or just by chance, can cause one or more of the extreme result(s) to behave like outliers. To prevent bias on the estimators without eliminating these data, upper and lower limits should be introduced.

Almost all Health and Safety organizations provide analytical methods for the determination of workplace air contaminants (AIHA, ISO, CEN, DFG, EPA, HSE, WHO etc.). They are often based on the manuals from OHSA (1985 and 1987) and NIOSH (Eller 1984). Voice (Dräger), Supelair (Supelco) and DOHS-Base (DOHSBase VOF) are data retrieval, Windows computer programs with industrial hygiene limit values and the detection range of the corresponding measurement methods.

A value of 1.1*C(M) is displayed as default upper limit in Window 17c.

A value of 0.9*C(M) is displayed as default upper limit in Window 17d.

Example 10	Upper limit

Example 11	Lower limit


3.1.2.1 Error messages

Tab "Plot" can display one of the following messages:

•	"Less than 2 data points are within the limits.".

•	"There is no variance between the limits": the relative difference of the highest and lowest value between the limits is below 10E-10.

•	"There is too much variance between the limits": the ratio of the highest and lowest value between the limits is more than 10E+10.

Click "OK" and fill in a valid limit to continue.


3.1.3 Linear regression

Screen 17e, displaying the linear regression line, is specifically made for:

 -	Graphically examining the goodness-of-fit,

 -	Selecting the most effective transformation,

 -	Making reports

Window 17e	Lognormal regression. 7 TWA8 hour ZnCl2 total dust on one worker

The linear regression line is calculated by using the method of least squares (Snedecor 1980 chapter 9).  If:

 -	at least one limit is entered, or

 -	the transformation is "untransformed",

then Window 17e shows the number of data pairs in the regression ("Regression through #### out of #### datapoints") in the left margin. For the Lognormal case the upper limit CU% can be estimated by:

Formula 3-1

With GMg and GSDg calculated using the Formula 4-10 and Formula 4-9.


3.1.4 Regression estimators for the descriptive statistics

If:

•	at least one limit is entered, and

•	the transformation is logarithmically or untransformed,

then Screen 17f shows in the right margin:

•	the number of data pairs in the regression ("Regression through #### out of #### datapoints"),

•	the censoring type ("Single" of "Double") to indicate that one or two limits are introduced,

•	the rankit estimators for location and variance based on the data pairs in the regression if the data are logarithmic transformed (GMg and GSDg) or untransformed (xcg and scg)

The use of the rankit regression estimators is recommended:

•	if a fixed background concentration exceeds the lower variance (see Leidel 1977 p103),

•	if the strategy used is based on it (Leidel 1977 p107, WHO 1984, Travis 1990),

•	in Reanalyzing historical references where it was used.

See B.3.1. for the algorithms of GMg and GSDg and their properties.

Example 12 Rankit versus direct estimators


3.1.5 Rankit estimators for Normal descriptive statistics

If you selected the option "untransformed" in Menu Transformation, then the rankit estimators for location and variance (xcg and scg respectively), based on the data pairs in the regression, are displayed.

Table 2	Rankit estimators for Normal descriptive statistics

Example 13	Normal distributions

Example 14 	Comparing xcg  and scg with estimators from literature

Figure 7	10 Chlorine TWA8 hour. Logarithmic transformed and uncensored (HAW104)

Figure 8	10 Chlorine TWA8 hour.  Untransformed and censored (HAW104)


3.2  Tests for normality

The W-test of Shapiro & Wilk (1965) for normality is the most effective one among the existing omnibus tests (see B.1.2). Shapiro (1990 p21), however, warned: "No single [goodness-of-fit] test statistic can give you as much information as a graphical display which shows the extent and types of departures from the hypothesized model".


3.2.1 The W-test for uncensored samples

The picture box displays the chance A(W) that the (transformed) complete sample is drawn from a normal distribution.

Test statistic W is calculated using Formula B-1 . W values vary between 0 and 1. The probability distribution A(W) results in a value for goodness-of-fit between the 0 and 100%. Increasing values for A(W) suggest an increasing conformity with the shape of the Normal distribution.

In Example 16 and Example 17 W-values are tabulated and its influence the final Lognormal conformity conclusion is shown.


3.2.2 Censored sample

In case of a censored, logarithmic transformed sample Screen number 18b appears.

Screen 18b	Goodness-of-fit for censored Lognormal sample

In the case of a censored non-Lognormal transformed sample Screen number 18c appears.


3.3 Other transformations

Try different transformations if the Lognormal shows a poor fit. It is not possible to combine two or more of the seven transformations. Different transformations will show similar figures if the variance is small (GSD<1.4).

Menu options  "Transformation"

Option	Comment

Double	Double logarithmic transformation, log{log(ci)}.

If c1≤1, then all results are multiplied with EXP(1)/c1 to keep log(ci) positive

Log	The natural logarithm of the result, log(ci), the standard transformation in HYGINIST

Sqrt	The square root, √(ci)

Untransformed	Untransformed, ci

Squared	Squaring, (ci)²

Exponential	The exponential transformation on base e=2.71828.., EXP(ci)=ec.

If c1>44, then all results are first multiplied by 1/c1 to prevent overflow

Reciprocal	Reciprocal transformation, 1/ci

Transformations 1 to 6 influence the skewness (asymmetry). The first two decrease the variance and stabilize distributions with high extremes. Transformations 4, 5 and 6 increase variance and stabilize a sample with low extremes. All transformations except the double logarithmic are independent of the location. In Table 3 some distributions and transformations are related.

Table 3	Type of distribution according to the goodness-of-fit with a transformation

Best transformation fit	Distribution type

Ci	Normal, Gaussian

log(Ci)	If s/x ≈ constant for every Ci, then Lognormal

Sqrt(Ci)	If s²≈ x for every Ci, then the Poisson distribution

1/Ci	If s ≈ x² for every Ci, then inverse normal

Figure 9 	5 TWA8 hour MDI during indoor spraying. 	 Figure 10	8 TWA20 min Ethyl Alcohol.

LogLog transformed (BILAN304)	 One worker, one shift, untransformed (LEIDEL56)

Example 15	Other transformations


3.4 Decision scheme

The following procedure, based on both industrial hygiene and statistical considerations, helps to decide if the Lognormal model is indeed the most effective model to describe this series exposure data (A.4.1 and proposition 1).

1	establish decision criteria, based on strategic 3.4.1 or compliance 3.4.2 considerations,

2	examine the assessment strategy, in particular on:

•	homogeneity in the population(s) under study (see A.2),

•	autocorrelation, if GSDTWA 8 hour<2 (Spear 1986, Francis 1989, Rappaport 1991),

3	examine the sample series on outliers and remove them from the sample if there are grounds for doing so (see B.3),

4	establish the accuracy range and set upper and/or lower limits in Screen 17bcd (see 3.1.2), if raw data exceed the accuracy range (see  B.4.3),

5	examine the conformity with the Lognormal distribution using Table 4,

6	test the results from 5 with the decision criteria in 1 and decide on the conformity.

If you decide that the conformity is not rejected, then continue with extrapolation and compliance testing.

Table 4	Lognormal goodness-of-fit decision scheme

Decide on situations not covered by Table 4, through an evaluation of the exposure assessment strategy.


3.4.1 Strategic considerations

Lognormal goodness-of-fit:

•	is of minor concern in range finding research,

•	should not be rejected in long-term compliance control and/or routine monitoring programs,

•	is important in first establishing similar exposure groups (see  A.2.3).

•	is important if the NIOSH method for long-term TWA control is used (see  5.1.2).

If the observed shape is not in compliance with the goal of the exposure assessment, then both sampling plan and the strategy should be reconsidered.


3.4.2 Compliance considerations

Goodness-of-fit is:

•	important if the limit H lies in the central region of the exposure distribution, that is:

•	C1≤H and CM≥0.1*H, or

•	GM<H and GM*GSD²>H.

•	less important if robust extrapolation distributions are used, like the (Noncentral) Student

•	of only academic importance if GSD<1.4, or

•	if limit H is an outlier in the exposure distribution, that is:

•	extremely high, GM≥H or CM/2≥H, or

•	extremely low, GM*GSD2≤H or CM≤0.1*H,

Figure 11 	15 Untransformed TWA8 hours	 Figure 12	Total dust 12 TWA8 hours

dust (HAW117)	 (BOLEY62)

Example 16	Conformity with the Lognormal model. 28 files with A(W)log>5%

Example 17	Conformity with the Lognormal model based on the graph. Complete files with A(W)log<5%


4 Sample characteristics

Tabs 3 ("Limits") and 4 ("Descriptives") makes it possible to:

•	overview all sample descriptive statistics (see 4.1)

•	change the environmental factors (see 4.2)


4.1 Descriptive statistics

This tab gives you an overview of different descriptive statistics. It is assumed the exposure data are sampled from a population that can be described using Lognormal descriptive statistics. All calculations are done using the sample estimators GM and GSD  of Lognormal descriptive statistics EXP(μ) and EXP(σ) respectively, and the number of degrees of freedom df. Window 20abc shows data from:

•	a complete sample ( 4.1.1),

•	a censored sample ( 4.1.2),

•	the entered values for M, GM and GSD ( 4.1.3)


4.1.1 Complete sample

This tab gives you an overview of different descriptive statistics calculated from GM, GSD and sample size M.

Table 5	Characteristics of the complete sample estimators of the Lognormal descriptive statistics

Example 18	Comparing samples with literature data


4.1.2 Censored sample

This tab gives you an overview of different descriptive statistics calculated from the regression estimators of GM and  GSD.

Table 6 Characteristics of the censored sample estimators of the lognormal distribution statistics

Example 19 df, GMg and GSDg of censored Lognormal samples


4.1.3 Entered values of GM and GSD

Not yet filled


4.2 Environmental factors

This tab is the control centre for extrapolation and inference.It offers the possibility to fill out or change

•	The units of measurement of both the concentration measured and the occupational exposure limit

•	The sampling period the samples represent

•	the occupational exposure limit H

•	The limit Hs' reference period T

•	The percentage U% of the distribution covered or the percentage α of the distribution not covered


4.2.1 Units of measurement
4.2.1 Exposure data identification

The series sampling results are characterized by their name, sample size and:

•	the units in which they are measured (see 4.2.1.1 samplining units)

•	the duration of the sampling (see 4.2.1.2 sampling duration)


4.2.1.1 Sampling units

Enter units of measurement (=dimension):

 -	to prevent errors in entering a limit value

 -	as an aid for the report facility,

The units in which the intensity of the exposure is measured or calculated. The sampling method decides on the denominator and the analytical methods on the numerator. Indicator tubes and direct readable devices for gasses and vapors often use 'parts per million' (ppm = ml/m3). For toxicological active gasses and  'weights per volume' (like mg/m3) as the dimension is mostly undesired. The use of these measures originates, however, from the analytical laboratory procedure. According to EN 689 (CEN 1995) the following dimensions for workplace atmosphere should be preferred:

•	gasses and vapors ml/m3 (ppm, independent of temperature and pressure) or mg/m3 at 20 °C and 101,3 kPa,

•	fibers/m3,

•	aerosols (suspended matter) mg/m3


4.2.1.2 Sampling duration

This is the time period the sampling measurements represent:

•	a few seconds air sampling period may represent instantaneous sampling (Ceiling),

•	10 to 20 minutes sampling may be used to test against a Short Term Exposure Limit (STEL)

•	a five hours sampling period is often sufficient for a full shift exposure assessment (TWA).


4.2.2 Exposure limit

The intensity of an agent over a reference period that is legally, health-based or otherwise accepted as admissible.


4.2.2.1 Value

Enter a value between 1E-10 and 1E+10 (0.0000000001 and  10000000000)


4.2.2.2 Reference period

The averaging period for which the limit value is defined


4.2.3 Percentiles


4.2.3.1 Confidence D

The confidence that the hypothesis is true

Enter a value between 0.01% and 99.99%

Normally 95% is chosen


4.2.3.2 Cover U

The fraction of the population distribution covered by the assessment

Use a value between 0.01% and 99.99%.

Normally 95% is chosen


4.3 Lognormal frequency distribution

Not yet filled


5 Extrapolation and compliance testing

The tabs <Upper Limit UTL> and <Mean UCL> calculate the effectiveness of workplace air exposure control measures by:

•	extrapolating the exposure data to general results,

•	testing exposure distribution against an industrial hygiene limit value.

Based on the exposure assessment goal and the required sample properties, Table 7 helps to choose the statistical method that is appropriate for extrapolation and compliance testing.

Table 7	Choosing the most appropriate method to generalize and test series sample exposure data.

Industrial Hygiene extrapolation and compliance testing deals with estimating:

•	The true fraction of the distribution beneath a certain value

•	The true value of a descriptive statistic, mostly the arithmetic mean

Remarks.

Calculations presented are performed exclusively with:

•	the estimators of EXP(μ) and EXP(σ) and the number of degrees of freedom df,

•	the industrial hygiene limit value H, the desired cover U%  and the desired confidence D%,

•	the Noncentral Student or special cases of this distribution (Owen 1968).

The theory of the Lognormal methods used in this chapter is described extensively by Land (1988 page. 87-106).


5.1 Long-term TWA control

To assess long-term compliance with hygiene limit H, 3 statistical extrapolation methods are presented and ranked  in the increasing probability that H is considered as being an element of the exposure distribution. Use table 7 to choose the appropriate method.

Table 8 combines the names found in literature for measures of long-term TWA extrapolation parameters, and the names (in bold) and symbols used in the screens 25 through 27.

Table 8	Names, parameters and estimators for assessing long-term TWA control

Upper and lower limits Ç δ (100-U)/2≤##% and Çδ (100+U)/2≤##% of the two-sided tolerance interval U% are calculated by introducing successively δ (100-U%)/2 and δ (100+U%)/2.


5.1.1 Comparing the 3 TWA extrapolation methods

To assess long-term compliance with hygiene limit H, 3 statistical extrapolation methods are presented and ranked (Screen 23a options 1, 2 & 3) in the increasing probability that H is considered as being an element of the exposure distribution. Use table 7 to choose the appropriate method.

The workplace air concentration distribution C in a homogeneous exposure situation is best described by the Lognormal distribution, If the population mean is μ and variance is σ², then the standard Normal deviate Z is the logarithm of C expressed in a standardized form:


5.1.2 Standard Normal (Leidel)

This generally accepted, long-term non-compliance probability method obtains its status from the recommendation of the USA's "National Institute of Occupational Safety and Health" (Leidel 1977). As is displayed in screen 25, its application is tied to such rigorous criteria on sample size, Lognormal fit and variance, that most industrial hygiene data sets cannot be evaluated using this method.

To estimate αC>H, Leidel (1977 page 69) replaced log(C)-μ and σ in formula 5-1 with the estimators LOG(H/GM) and LOG(GSD) respectively. The non-compliance probability test is based on the following statistic:

formula 5-2

Z is, under the null hypothesis, a deviate of the standard Normal distribution with probability AC>H:

formula 5-3

The standard Normal distribution is a special case of the Noncentral Student (Owen 1968) with df=infinite and noncentrality parameter Zδ=0. non-compliance probability AC>H in 5.3 is calculated from Z using:

input value Z	output AC>H=100 * AZ

ABS(Z)<1E-14	50 %

ABS(Z)<+5	the power series 26.2.11 of Abramowitz (1970). Accuracy ?A<1E-12%

5< ABS(Z) ≤37	the approximate fraction expansion AS 66 of Hill (1973). Accuracy ?A<1E-11%

<-8	100 %

-8 ≤ Z <37	1E-300 ≤AZ<+99.9999999999999 %

>37	0 %

The tolerance limit ÇU≥100-α% is derived from formula 5.2, by exponential transformation:

formula 5-4

The standard Normal tolerance factor Zα is calculated from α using:

Value of α	output Zα

ABS(α-50)<1E-4 %	0

>1E-4% and ≤99.9999%	Polynomials AS 111 of Beasley (1977), followed by the

inverse interpolation of Abramowitz1970 p954 Example 5).

Accuracy ?Z<5*1E-16

<1E-4 % or >99.9999%	Not accepted U% values in screen 21

Example 26	NIOSH tolerance limits and compliance probability

Example 27	Calculating standard normal tolerance limits from literature sources


5.1.3 Unbiased estimate of compliance (Wilks)

To improve the small sample bias of the NIOSH test statistic (see table 9) the unbiased method of Wilks was introduced in industrial hygiene (Scheffers 1987). The method has been developed in the quality control of large scale product lines with homogeneous conditions (e.g. chemical refineries, battery production; Proschan 1953 page 556), which is comparable with long-term non-compliance control in similar exposure groups. Screen 26 displays the unbiased estimation of the non-compliance probability and the corresponding tolerance limit.

The algorithm developed Wilks (1941) was proven mathematically correct by Proschan (1953). The unbiased non-compliance probability test against limit H is based on the following test statistic:

Formula 5-5

tdf follows, under the null hypothesis, the central student distribution. The right sided non-compliance probability At is the Student density distribution integrated from tdf to infinity:

Formula 5-6

The Student distribution is a special case of the Noncentral Student (Owen 1968) with noncentrality parameter Zδ=0. non-compliance probability AC>H in 5.3 is calculated from tdf and df using:

ABS(tdf)	df	output AC>H %=100 * At

_________________________________________________________________________________________

<1E-16	-	50 %

≥1E-16	≤30000	Power series of Owen (1968 page 465). Relative accuracy ?A/A=1E-4

≥1E-16	>30000	Normal approximate Algorithm 26.7.8 (Abramowitz 1970)

The corresponding tolerance limit ÇU≥100-α% is derived from formula 5.5 by logarithmic transformation:

Formula 5-7

The unbiased Student tolerance factor tα,df is calculated from α and df using:

Input α %	and df	output tα,df

________________________________________________________________________________________________

ABS(a-50)<0.00001 %	≥1	0

0.0001≤ α ≤99.9999%	1	Formula 5-8

0.0001≤ α ≤99.9999%	2	Formula 5-9

0.0001≤ α ≤99.9999%	≥3 and≥1000	Newton-Raphson iteration (Abramowitz 1970 3.9.5.)

on the power series of Owen (1968 page 465),

with the asymptotic expansion 26.7.5. (Abramowitz 1970)

as initiator. ?t/t<1E-6

0.0001≤ α ≤99.9999%	>1000	Asymptotic expansion 26.7.5. (Abramowitz 1970)

<0.0001% or >99.9999%	Any value	not accepted U% value in screen 21

The unbiased estimate is effective in al kind of similar exposure groups. With small but efficient sampling plans the effectiveness of control measures in a SEG can be assessed using control charts, examining goodness-of-fit and non-compliance probability calculations, just as is done in quality control for over decades (see e.g. Morrison 1958). Estimator ÇU≥##% overestimates the real CU≥##% on the average. For an unbiased estimate ÇU≥##%, see Owen (1968 page 461).

Example 28	Wilks tolerance limits and compliance probability

Figure 15	Vinylchloride Control chart in a SEG PVC operators TWA8 hours over 1987-1993

Figure 16	Lognormal probability distribution of 37 VCM TWA8hours

Example 29	Unbiased estimate of the long-term TWA control effectiveness

Example 30 	Different number of degrees of freedom


5.1.4 Noncentral Student, tolerance limits (Tuggle)

To improve the NIOSH decision scheme (Leidel 1977 figure 1.1 page 11) when GSD>2, the one-sided tolerance limit (OTL) method was introduced by Tuggle (1981, 1982). The Belgium Standard Institute  (BIN 1987) officially published an assessment strategy based on Tuggle's method. Screen 27 displays the confidence δ that <α% of the exposures is over limit H.

The confidence δ(Cα<100-U%>H) with a fixed non-compliance probability α<100-U% is estimated with the following test statistic (based on Tuggle 1982 formula B-2 page 345):

formula 5-10

Tdf,Zα is, under the null hypothesis, a deviate of the Noncentral Student distribution. The estimator D{Cα<100-U%>H} is calculated using Tdf,Zα the number of degrees of freedom df and the noncentrality parameter Zα, the deviate corresponding with the standard normal probability α=100-U%.

Input U, Tdf,Zα and/or   	df	output D(Cα<100-U%>H)

α<50%	-	Not accepted U%=100-α value in screen 21

50-a<10-14%	-	central Student formula 5.6

U<99.9999%	-	Not accepted U%=100-α value in screen 21

0<Tdf,Zα<10-16	-	50 %

Tdf,Za>10-16	<200	algorithms of Owen (1956 formula 3.9 & 1968 page 464)

Tdf,Za>10-16	>200	Normal approximate Algorithm 26.7.10 (Abramowitz 1970)

According to Leidel (1977 page 118) an employer should try to attain δ?95% confidence that workers exposure is with α?5% over the limit.

The upper or one-sided tolerance limit (UTL) Çα<100-U%,δ?U% is estimated using:

formula 5-11

The program calculates the one-sided upper tolerance limits (UTL) if the desired percentage U% is more than 50%. The UTL is the concentration under which U% of the population data lies with U% confidence.

The one-sided upper tolerance limit (UTL) is calculated as follows:

•	first a linear interpolation from D=0% to D=100% with GM/GSD as the initiating value and GSD as the multiplication constant

•	If the situation is reached that D(n+1)>100-U%>D(n), then an inverse linear approximation (General Falsi or False position; Abramowitz 1970 chapter 3.9.3) is performed. The accuracy of UTL is such that ABS[D(UTL)-U%)<0.01%.

If the desired confidence U% and the GSD are extreme high and the sample size is extreme low,  then the interpolation may take some time.

A non-iterative algorithm to calculate the inverse Noncentral Student based Cα<100-U%,δ?U% does not exist. The approximations of Patel (1982 chapter 7.11 page 204 Cornish-Fisher expansion), Johnson and Kotz (1970  30.5 page 194) and Owen (1968 page 468 a comparison of different algorithms) are, for common industrial hygiene values of M (small <10) and GSD (large >2), inaccurate. One-sided tolerance factors Tdf,α,δ for specific values of Zα and Zδ can be found in the tables of Resnikoff (1957), Ciba-Geigy (1980), Odeh (1980), Bezemer (1981), Tuggle (1982), Hawkins (1991 Table IV.1 page 136) and the charts in BIN (1987). There are small differences between the tolerance factors used by Tuggle and Hawkins (both from NBS 1966) and the tables of Odeh (1980). The latest is considered more accurate.

Example 31	Noncentral student tolerance limits


5.2 Dose assessment

The HYGINIST Tab "UCL" helps to assess the:

 -	TWAref per from a series grab samples and the chance of exceeding Href per ,

 -	the Lognormal arithmetic mean βlong term and the chance that it exceeds Href per, from a series TWAref per,

 -	the chance that the mean of a series TWAref per  exceeds Href per, on the average.

This is useful for:

•	the "Classification of exposure for an 8-hour TWA standard, based on grab or partial period, consecutive sample measurements" (Leidel 1977 page 55) and

•	the cumulative or average daily dose (Seixas 1988) or the chronic health hazard (Hawkins 1991).

If a limit value H aimes to protect against the effects of long term exposure (like carcinogenity or chronic toxicity) and a series of TWA8 hours  samples is collected stratified or at random over a long-term period (say three months) then dose assessment is the method of preference to test compliance against the limit value.

Table 10 displays the symbols and some of the names found in literature for the extrapolation parameters of the Lognormal arithmetic mean and the names (in bold) used in screen 24.

Table 10	Names, parameters and estimators of dose assessment

Upper and lower confidence limits Çβ, (100-U)/2=<% and Çβ, (100+U)/2##% of the arithmetic mean are calculated by introducing successively (100-U%)/2 and (100+U%)/2 in screen 21 .


5.2.1 uniform most powerful

A 'uniform most powerful' (=UMP) method to test an arithmetic mean of a Lognormal distribution against a limit value is developed by Land (1971, 1988 p89 & 103).

The use of the UMP is introduced in the industrial hygiene by Galbas (1975) and Bar-Shalom (1975, 1976), and supported by Leidel (1977 page 55) and Coenen (1978).

The UMP is the method of preference, because it is an unbiased estimator of the confidence limits of the aritmetic mean with minimum variance. However the UMP:

•	can only be solved analytically, for odd sample sizes.

•	is a rather laboreous calculation.

HYGINIST for Windows uses the procedure of Land (1988 6.1) to calculate the UMP estimator of:

•	the probability that the mean exceeds the limit

•	the Upper confidence limit of the mean

if:

•	Sample size is 3<M<1001

•	confidence 90%<D<99.75%

Example 32	The UMP test for the arithmetic mean of a Lognormal distribution


5.2.1.1 Nomograms

To test the sample based arithmetic mean against the hygiene limit H using nomograms follow the following procedure:

Plot the values of 10log(GSD) and:

•	10log(GM/H) in the nomograms of Bar-Shalom (1975 part II page 10 and 11), Bar-Shalom (1976 page 472) or Leidel (1977 page 58), for α=1% and α=5%, 10log(GSD)<0.5 (approximately GSD<3) and GM/H>.16,

•	GM/H in the nomograms of Coenen (1978 page 405), for α=5%, 0.05<10log(GSD)<0.95 (approximately 1.12<GSD<9) and GM/H>0.02 and M<1000.

The place in the nomogram leads to one of the following three conclusions:

•	there is non-compliance with the limit value H,

•	there is no decision possible; possible overexposure,

•	there is compliance with the limit value H.


5.2.2 Approximation

Screen 24b displays the:

 -	probability that the arithmetic mean β is above limit H for df?25 and GSD?1.64,

 -	confidence limits including the arithmetic mean β with confidence U%.

The approximate test of β against limit H is based on the following statistic (Jahr 1987, Armstrong 1992):

Formula 5-12

Deviate tdf is, under the null hypothesis, supposed to follow the Student distribution. Estimator Aβ>H of the right side chance αβ>H is calculated using tdf, df and the Student distribution. The corresponding upper confidence limit Çβ,U is derived from  by logarithmic transformation:

Formula 5-13

Example 33	Comparing different estimators of the confidence interval of the arithmetic mean


5.3 Ceiling control

There is no clear understanding on how to interpret a ceiling limit value (Leidel 1977  3.5 page 42). The strictest definition (not to be exceeded during any part of the working exposure. ACGIH 1993) does not leave room for statistical evaluation.

If, however, the ceiling is defined as a limit value Hshort period which may be exceeded at most kshort period times per shift or U% of the time in a shift and discontineous grab sample measurements ar taken, then an appropriate statistical method can be derived from the subjoined table 11.

Table 11 Methods to test Ceiling limits using TWAshort period


5.3.1 Binomial

If grab sample exposure data testing the Ceiling limit result in dichotomous outcome (Yes/No compliance), then the confidence D of the desired noncompliance probability δ(αC>H<100-U%)>D%, must be estimated using distribution free methods. For M<30 (the number of samples taken during the shift) use the exact cumulative binomial (Siegel 1956 page 37 formula 4.1 and 4.2):

formula 5.14

In which K is the number of samples exceeding the Ceiling and p the desired fraction grab samples that may not exceed the limit. For p<.05 and M*p<500 use the Poisson approximation (Snedecor 1980 7.14):

formula 5.15

For M>30 and p>.05, or for M*p>500 use the standard Normal approximation (Siegel 1956 page 40):

formula 5.16

with Z the standard Normal deviate. To estimate δ(M,k,p) use Z and the right-sided standard normal probability function of formula 5.3. If D<U%, then there is sufficient confidence that Ceiling noncompliance probability is below the desired percentage αC>H>100-U%. Because of the required large sample size, the Binomial method is only applied in situations where the sequence of controlling the work environment is large.

Example 36 Compliance with a ceiling limit value (distribution free)


5.3.2 Adapted Binomial

If in Ceiling compliance probability αC>H<100-U% control:

•	the exposure variability is Lognormally distributed and

•	sample size is small: M<1/p,

then the probability for noncompliance AC>H can be estimated using:

•	the standard normal 5.1.2  or

•	the unbiased method 5.1.3.

Next, the cumulative Binomial test of  5.3.1 can be performed using:

•	number of outcome over the limit k=INT(M*AC>H+1),

•	sample size M the largest of INT(1/AC>H) and M.

Leidel (1977 p65) used this method, to extrapolate to the unsampled periods in a confined population. The Lognormal Noncentral Student method described in the next section is a better alternative.

Example 37 Compiance with a ceiing limit value (distribution free)


5.3.3 Noncentral Student

If the TWAshort period is lognormally distributed and Ceiling compliance is defined as confidence δ=U% that the noncompliance probability α%<100-U%, then use the noncontral Student method (see 5.1.4). Control measures can be considered as effective for example if 100-δ=α<5%.

Example 38 Compliance with a ceiling limit value (Noncentral Student)


6 Comparing exposure data

This transaction compares the sample exposure estimators GM and GSD with:

•	estimators from a second sample,

•	true population descriptive statistics,

Valid reference data are the true Lognormal descriptive statistics EXP(μ) and EXP(σ), or the sample estimators GM and GSD and the sample size.

To compare more than two data sets, apply ANalysis Of VAriance on log-transformed exposure data (Snedecor 1980). ANOVA techniques are included in standard software like Microsoft® EXCEL.

The current developments in occupational health and safety care makes that:

•	more exposure data are collected in industrial hygiene (surveys, routine programs etc.),

•	(one or multi) year Health and Safety plans and engineering directives, plant lay-out, control measures ask for more quantified exposure information,

•	dose assessment becomes more important in occupational epidemiology.

This leads to an increasing need to collect, analyze and compare exposure data, not against limit H, but against other location and scale data:

•	in time (changing control measures, in longitudinal epidemiology),

•	between workplaces (different technical, organizational or behaviors control measures),

•	between exposure groups (differences in dose in epidemiology),

•	within exposure groups ({dis}homogeneity, identifying worst cases, time trends),

•	against true population values ("gold" standards).

This chapter explains with a lot of examples how this is done. For more information see chapter 6.1


6.1 Sample or population reference values

This transaction establishes differences and trends in exposure data when at least one of the following sets of reference values are known:

•	GSDref and size M2 of a second sample (see  6.2),

•	EXP(σ) (see 6.3.1),

•	EXP(μ) (see 6.3.2).

To compare GM's it is important to know if GSD's:

•	are equal (see  6.2.3.1), or

•	differ significantly (see  6.2.3.2).

Combining the exposure data from two samples is described in  6.2.4. To compare three or more data series see 6.4. To append the worksheet  in the <file name>.LOG file (for the report function see) press <file> and <print> after the calculations took place.

Location and scale are compared using the classical parametric Student methods and formulas (see Snedecor 1980, chapters 5 and 6). The subjoined table 12 combines names found in literature for inference statistics, and displays the used names (in bold) and symbols.


6.2 Two sample difference

Sample size Mref (see 6.2.1) and the estimators GSDref (see 6.2.2.) and GMref (see 6.2.3) of a second sample should be entered. It should be established first, however, that these data are from a Lognormal distribution. Use the raw data and the goodness-of-fit transaction described in chapter 3.


6.2.1 Reference sample size

The maximum size of the reference sample (Mref=30000) is more than is permitted in data entry from disk or by keyboard (see  2.2.1.1).


6.2.2 Difference in scale

The statistic for testing if both GSD`s originate from the population is (Snedecor 1980):

Formula 6-1

Under the null hypothesis follows F the variance ratio or Fisher distribution (Abramowitz 1970 26.6):

Formula 6-2

If the probalbility AGSD=GSDref  is below 5%, then it is normally accepted that the GSDs differ significantly.

Probability AGSD=GSDref in formula 6-2 is caculated as follows:

F	df1	df2	AGSD=GSDref=100*AF|df,df2 %

≤10-31	<∞	0 %

≥10+31	<∞	0 %

ABS(F-1)≤10-10	df1=df2	100 %

other values	odd	odd	Algorithm 26.6.8

other values	even	odd or (even & df1>df2)	Algorithm 26.6.4

other values	odd or (even & df1≤df2)	even	Algorithm 26.6.5

other values	df1*df2>32767	Normal approximate 26.6.15

All algorithms are from Abramowitz (1970)

Example 39


6.2.3 Differences in location

Comparing sample GM's:

•	is exclusively possible if sample GSDref  and size Mref are known,

•	is performed with different test statistics for GSD<>GSDref  and GSD=GSDref .

The option button frame "GSDs from the same population" demands your conclusion on the population base of both GSD's. Are they from one or from two different populations?

•	Compare GM's while GSD's are from same base ( 6.2.3.1)

•	Compare GM's while GSD's differ significantly ( 6.2.3.2)

The power to detect differences in GM's is larger if the GSD's are considered as from the same base.


6.2.3.1 Comparing GMs with matching GSDs

The statistic for testing if both GM`s originate from the population sample base is (Snedecor 1980, 6.9):

Formula 6-3

The weighted logarithmic standard deviation sw is calculated using:

Formula 6-4

Formula 6.3 follows, under the null hypothesis, the Student distribution. The two-sided probability A% is calculated using tdf and dft from formula 6.3, and the Student distribution (see formula 5.6).

Example 40


6.2.3.2. Comparing GMs while GSDs differ

The statistic for testing that both GM`s originate from the same population base is (Snedecor 1980, 6.11):

Formula 6-5

Formula 6.5 follows, under the null hypothesis, the Student distribution. The two-sided probability A% is calculated using tdf and dft from 6.5 and the Student distribution.

Example 41


6.2.4 Combining two samples

If two samples originate from the same population base and:

•	 the two samples are mutually independent, or

•	 the two samples were separated from one main sample,

then the number of degrees of freedom and the estimators GM and GSD of both samples can be combined into new estimators GMt and GSDt for that population base, using the next logical formulas:

Formula 6-6

Formula 6-7

If the two samples are mutually independent, then GSDs and GMs may not differ significantly. If the samples were separated from one main sample, then individual raw data may not be included in both samples.

Example 42	Comparing two GSDs


6.3 Differences with population descriptive statistics

Reasons to compare sample estimates with true values of EXP(μ) and EXP(σ) are:

the sample size van reference data are large or unknown (e.g M2≥100),

•	testing against program goals or golden standards in industrial hygiene,

•	finding the confidence range for EXP(μ) and EXP(σ), using trial and error.


6.3.1 EXP(s)
6.3.1 EXP(σ)

The test statistic that compares log(GSD)² with σ² is according to Snedecor (1980  5.11):

Formula A-8

The test statistic χ² follows, under the null hypothesis, a Chi-square distribution with a number of degrees of freedom df=M-1 (df=(M+M`)\2-1 or df=2M` for censored samples). For the theory on the confidence interval of GSD, see Land (1988 page 98-99).

Formula A-9

Calculating the chi-square probability distribution

ABS(χ)	Df	AGSD=σ

all values	<∞	if Qχ²,df<0.5, then AGSD=σ=200*Qχ²,df % else AGSD=σ=200*(1-Qχ²,df) %

<10-16	<∞	0 %

?24 and	?200 and even	Algorithm 26.4.4 (Abramowitz 1970)

?24 and	?200 and odd	Algorithm 26.4.5 (Abramowitz 1970)

>24 or	>200	Normal approximate Algorithm 26.4.14 (Abramowitz 1970)


6.3.2 EXP(m)
6.3.2 EXP(μ)

The test statistic that compares log(GM) with μ is according to Snedecor (1980, 5.7):

Formule 6-10

Formula 6.10 follows, under the null hypothesis, the Student distribution. The two-sided probability A% is calculated using tdf and dft from 6.10 and the Student distribution. The theory on the confidence interval of GM is described by Land (1988 page 93-95  3.1.2 and 3.2).

Example 43	Censored sample confidence limits


6.4 Comparing three or more samples

To compare three or more data series, use:

•	parametric analysis of variance (ANOVA) and regression analysis,

•	distribution free methods (Snedecor 1980 chapters 6 & 10.9, Siegel 1956 chapter 5) like:

•	Wilcoxon (two samples),

•	Kruskall-Wallis (non parametric ANOVA, three and more samples),

•	Page (1963, trend in three and more samples), and

•	Spearman or Kendall (rank correlation).

These methods are available in stat/graph packages like BMDP, GLIM, TRUE EPISTAT, SAS-PC, SPSSPC and BMDP.

Example 44	Regression analysis in exposure control chart


7. Sample size

The tabs <Upper Limit UTL> and <Mean UCL> may help to calculate the smallest sample size for which a series TWA measurements will estimate compliance (AC>H≤α) or non-compliance (AC>H≥100-α) using the unbiased method of Wilks, the upper confidence limit .

The sample size M2 is calculated using:

•	 the desired percentage U%=100-α,

•	 the industrial hygiene limit value H ,

•	 the estimators GM and GSD or GMg and GSDg and the proportion results within the accuracy range (screen 20b),

•	 the inverse algorithm of the standard normal and the unbiased Student .

Values for GM, H and GSD can be derived from:

•	calculations on emission and ventilation (A.2.1),

•	exposure assessment programs or inventories done before ( A.3),

•	data from literature.

The standard normal estimator AZ  (formula 5.3) and the unbiased Student estimator At,df=1 of formula 5.5, are compared with the desired the non-compliance probability αC>H=100-U%. If H/GM>1, U%>50 and

Formula 7-1

are true, then a minimal sample size M2=1,2,3,...? for the unbiased estimate of the compliance probability α exist.

If a value of df2 exist, then the smallest sample size M2 for an unbiased estimation of the compliance probability in a complete sample (M'=M) can be calculated using the formula 7.2 or 7.3 dependent if the sample is censored:

Formula 7-2

In a censored sample (with M' the number of results within the accuracy range):

Formula 7-3

Because df2, M' and M are known, M2 can be derived iteratively. For GM/H<1 this routine is also useful to calculate the sample size for an unbiased estimate of AC>H≥95% for being in non-compliance on the average.

The following situations are :

•	7.1 Compliance for every sample size.

•	7.2 Compliance for a specified number of samples.

•	7.3 Compliance for only a large number of samples.

•	7.4 Non-compliance for every sample size.


7.1 Stop sampling

Tab 34a displays the situation when At,df=1<α, so in which compliance is reached for every sample size M>1.

In this special case the Wilks test statistic is:

formula 7-4

Because the Student distribution is only defined for integer values of df, the confidence of compliance with the limit value is higher than expected on the average even for df=1. In statistical terms it is not possible to conclude "Stop measurement program, the confidence is sufficient!". This is the domain of the experienced industrial hygienist, but this situation could justify such a decision.

From screen 34a it can be concluded that if:

 -	the ratio GM/H<.25,

 -	the variance GSD?1.20 and

 -	the desired noncompliance probability α=5%

then the exposure will be considered as in compliance on the average for every sample size. The upper line in table 1 of Scheffers (1987) provides, for different values of GSD, the ratio GM/H for which sampling is less useful.


7.2 Two through 100 degrees of freedom

Tab 34c displays the increase of M2 and the decrease At,df=i. It stops at the first integer value of M2 for which At,df=i<α or if df≥99

Tab 34b displays one of three messages:

 -	if M2<M, then: "even for a smaller sample size than the current."

 -	if M2<M, then: "for the current sample size."

 -	if M2>M, then: "if sample size increases."

The minimal degrees of freedom df2 is calculated using:

formula 7-5


7.3 More than 100 degrees of freedom

In practise it seems of little value to perform more than 100 measurements to show noncompliance with a limit value. The money involved which such a program could better be used to improve the working conditions. Screen 34c displays a situation that At,df<α for 99<df<∞.

The minimal degrees of freedom df2 is calculated using:

formula 7-6

For GSD=1.20 and GM/H>0.7344, more than M2=50 samples are necessary to establish the desired probability α unbiased on the average. The bottom line of table 1 in Scheffers (1987) provides, for different GSD's, ratio GM/H values for which sampling is not useful. for 99<df<∞.


7.4 Noncompliance
7.4 Non-compliance

Tab 34d shows the state of being in permanent noncompliance: At,df>α  for df→∞.

formula 7-7

This situation is in noncompliance, even if the sample size is infinite. You can estimate that for α=5%, EXP(σ)=3.00 and EXP(μ)/H>0.1642 there is no sample size M2 that estimates α unbiased. The bottom line of table 1 of Scheffers (1987) provides for different GSD's, the EXP(μ)/H ratios over which measuring is ineffective.


A EXPOSURE ASSESSMENT
A.	EXPOSURE ASSESSMENT

HYGINIST is an instrument for the quantitative exposure assessment:

•	Sample exposure data and the Lognormal distribution are used to draw general conclusions on exposure range, compliance with hygiene limits and inference with reference exposure characteristics.

This qualitative annex describes four aspects of exposure assessment:

•	its place within the process "effective control of occupational exposure risks" (A.1),

•	domains in which it can be utilized (A.2),

•	different exposure assessment strategies (A.3)

•	the extrapolation of sample data (A.4).

In Annex B the quantitative aspects of exposure assessment are discussed


A.1 Effective control of exposure

The evaluation of exposure is part of the effective control of occupational exposure risk factors (working conditions). This is in many countries (IOHA Conference 1992) a part of Health & Safety control regulation and legislation. Effective working condition control can be pictured as a nine step process.

Table 13	Effective control of occupational exposure risks

+----------+   +------------+

|         1|   | Limit     2|

| hygienic +-->| Value      +--+  +--------------+

| hazards  |   +------------+  +->|  Exposure   4|yes/unknown

+--|-------+   +------------+  |  |  compliance  +---+

   |   |       | Exposure  3+--+  +------|-------+   |

   |   |       +-----|------+            |           |   +-------------+     +------------+

   |   |             |         +---------+no         |   |            8| yes | Effective 9|

   |   |       +-----+------+  |  +--------------+   +-->| Sustainment +--->| Control     |

   |   |       |           5|<-+  |mental &     7+---|   |             |     |            |

   |   |       | Control    +---->|physical      |   |   +-------------+     +------------+

   |   +------>| measures   |     |resistance    |   |           |no               no |

   |           |            |     +--------------+   |           |                    |

   |           |            |     +--------------+   |           |                    |

   |           |            +---->|Co-exposure  6+---+           |                    |

   |           +-----|------+     +--------------+               |                    |

   |                 |                                           |                    |

   +-----------------+----------------------<--------------------+                    |

   +-----------------------------------------<----------------------------------------+

1	Hazards. The static, innate health and safety aspects of an occupational agent (physical, chemical, biological and mental).

2	Limit value. The intensity of an agent over a reference period that is legally, health-based or otherwise accepted as admissible.

3	Exposure. The, at large, conductible and dynamic intensity of the occupational agent in the workplace, caused by the plant, the organization and the conduct of the employees.

4	Testing the exposure against a limit value. This leads to the decision:

•	no, additional control measures are necessary,

•	yes, exposure is in compliance with the limit,

•	unknown, the limit is not suitable to test the exposure (co-exposure, restricted resistance).

5	Control measures. The technical, organizational and  restriction of emission or immission.

6	Co-exposure. The controllable, but static interaction with other occupational agents.

7	Mental and physical resistance of an individual or a group. The result of:

•	innate health, unequally distributed in the population,

•	homeostasis, the tendency to maintain the internal stability in a physiological system,

•	health perception, the dynamic vision of a person on its health and/or on public health, and

•	health risks perception, the dynamic vision of a person or a community of hygiene hazards possibly threatening health.

8	Sustainment. Testing total exposure in similar exposure groups against the physical and mental resistance by means of health examination or epidemiological analysis. This leads to the decision:

•	yes, there is a state of effective control,

•	no, supplementary control measures are necessary.

In both cases this may increase the knowledge about hygiene hazards.

9	Effective control. A state of control in which:

•	employer and employees are cognizant with and give sufficient credit to industrial hygiene risks and control measures,

•	exposure is in compliance with the limit values,

•	technical and  measurements are in compliance with the current industry state of the art and comparable with what's usual practise in this branch of industry,

•	occupation related complaints, effects and absenteeism and the industrial hygiene risk complies with the socially accepted level,

•	knowledge is generated about how to control occupational exposure risks effectively.


A.2 Domains utilising exposure assessment
A.2 Domains utilizing exposure assessment

The evaluation of exposure in workplace atmosphere is practiced in Process safety, Industrial hygiene, health surveillance, Occupational medicine and Occupational epidemiology. In  table 14, the application of exposure assessment is sorted by sampling plan and domain (Corn 1985, CEN 1995).

In the red colored fields of table 14 HYGINIST is useful for:

 -	the assessment of homogeneity in sample data (see chapter 3),

 -	the extrapolation to general results (see chapter 5),

 -	inference between two samples (see chapter 6),

 -	assessment of minimum sample size (see chapter 7).

The classification of exposure for a TWA8 hour standard (column 2 of table 14) is explained in detail by Leidel (1977) and many others and is therefore not included in the program.


A.2.1 Process safety

To control the state of a production installation (i.e. reactors, appendages, seals, gaskets, extrusions, sampling points, logistics) and to detect unwanted emissions, the chemical industry utilizes routine measurement programs on fixed places and with a fixed sequences, mostly with directly readable instruments. The grab samples are directly compared to the limit value. For  there is a legal framework for continuous or sequential sampling (EG directive 78/610/EEG, PB L 197/12 of July 22, 1978).


A.2.2 Industrial/Occupational hygiene

Industrial (US) or occupational (GB) hygiene, in its classic form, deals with the working conditions at the workplace: the spot where employees meet hardware and materials. The aim is to keep risks in compliance with the current standards in order to guarantee workers a safe and healthy stay in the work environment not only during a (fraction of the) work shift but even during a lifetime. The method is to recognize, evaluate and control the agents at the workplace.

Industrial hygiene is a mature applied science: You can find basic or complete professional information of almost every present-day problem in the peer review or other literature that is produced since the forties and that can be found in hardcopy, on-line or compact disk databanks. The recognition of chemical agents risk is described by e.g. Roach (1977), Leidel (1977 chapter 2), Clayton (1978 p29-112), Oostendorp (1985ab), Boleij (1987), Guest (1993), Hawkins (1991), Mulhausen (1998) . The statistical aspects of the evaluation of workplace exposure can be found throughout the complete text.


A.2.3 Health surveillance in similar exposure groups

In chemical process industry the evaluation of exposure is often conducted among similar exposure groups (Mulhausen 1998, Hawkins 1991 page 5, Damiano 1987, Corn 1979). Its aim is:

•	assessment of long-term risk of overexposure,

•	administration of exposure history.

In occupational settings the activity pattern of groups of employees is often similar throughout the year, despite the sometimes significant between-worker-variability during short observation periods (Rappaport 1993). Within a SEG the distribution of activities among the workers throughout the year should only be determined by chance. The statistical aspects of assessing exposure and risk in similar exposure groups can be found throughout the complete text.

HYGINIST strongly supports the quantitative aspects of SEG health surveillance programs as described in the appendices of AIHA's strategy for occupational exposure assessment (Hawkins 1991):

 -	II, descriptive statistics and plotting probability,

 -	III, arithmetic means tests,

 -	IV, tolerance limit test.


A.2.4 Occupational medicine

Exposure data are sometimes used in assessing the sustainment (see table 13) of a healthy individual or in employees with a limited mental and/or physical resistance against the total of occupational exposure. According to Rempel (1990 page 435): "The principal tool for preventing work related illness should be the industrial hygiene exposure assessment (primary prevention). Unfortunately, even in the best situations, work related illness occurs. Medical surveillance in the workplace functions as a backup to exposure assessment, as a 'safety net' to catch illness early and activate interventions to prevent it from progressing (secondary prevention)." Statistical evaluation of exposure data will be of limited use in this domain.


A.2.5 Occupational epidemiology

Occupational epidemiology (Monson 1980, Smith 1987, Checkoway 1989, Harris 1993) applies exposure assessment in similar exposure groups, to find:

•	dose-response relations between exposure and health (biometrics, blood and urine values, lung function, mortality and morbidity rates),

•	no-effect or accepted risk levels for industrial hygiene limit value assessment.

Table 15	Scheme for health based limit value setting in similar exposure groups


A.3 Existing exposure assessment strategies

In recent decades strategies have been developed for the long-term exposure assessment (e.g. AIHA, BIN, CEFIC, CONCAWE, EH42, Leidel 1977, TrgA 402, VDI 2450, WGD, WHO, CEN 689, Guest). In general these strategies all include four steps:

•	what are the hazards (agents, routes of entry, exposure duration and frequency),

•	what is the exposure (identifying similar place/group/time situations),

•	what are worst-cases (ranking hazard and exposure),

•	which of the ranked worst cases is in non-compliance with the limit value(s) ?

They all provide some sort of evaluation to generalize measurements performed.

In the last few decades the industrial hygiene world is flooded with alternative exposure assessment sampling strategies and statistical methods to analyze sample data. Some of these methods provide only  concepts and do not even claim to improve the power of exposure control over the classical methods with fundamental basic concepts. They are ignored here.


A.4 Extrapolation

The methods to generalize the measurement results in the assessment strategies are based on:

•	the experience of "experts" (CEFIC, CONCAWE, TRgA 402, WGD),

•	distribution free statistical analysis (VDI 2450),

•	the Lognormal distribution (AIHA, BIN, CEN 689, EH42, NIOSH, WHO)

•	other parametric distributions (Berry 1973, Owen 1980).

HYGINIST is based on the Lognormal distribution. The statistical aspects are explained throughout the manual. Other parametric distributions are explained only superficially (see B.4.2). Stellingwerf commented (1984, letter to the editor) the power and other statistical aspects of the first two methods.

Depending on sampling duration and limit value reference period, two types of extrapolation to unsampled periods (general results) can be distinguished:

•	In number: the measured periods are considered as a fraction of the total number of exposure periods,

•	In time: the sampling durations are considered as a fraction of the total exposure reference period (see Example 47).

For extrapolation in numbers the sampling duration should be equal to the limit value's reference period.


A.4.1 The Lognormal evaluation

Most assessment strategies are based on Lognormally distributed workplace air concentrations (among others BIN, Bar-Shalom, EH42, Leidel, Rappaport, Tuggle, WHO, CEN 689).

According to Esmen (1977) and many others population, mutually independent, industrial hygiene measurements are best represented by the Lognormal distribution (see Figure 21). `Best` means, according to Esmen (1977), that the estimator is unbiased or consistent and efficient. `Best` also means that the estimator has the highest probability among the existing estimators. (Gamma, Weibull, Normal, exponential, Nonparametric).

Much knowledge and experience on the Lognormal distribution, extrapolation and inference has been gathered within the biometrics (Gaddum 1945), econometrics, technometrics, survival analysis, meteorology and geology (Shimizu 1988). Industrial hygiene has learned and is still learning from these applied sciences.

Figure 21	A family of Lognormal distributions with mean M and standard deviation s

Example 48	Lognormal


A.4.2 Other parametrical distributions
A.4.2 Other parametric distributions

The Lognormal distribution Λ can be approximated by a linear combination of Normal distributions (Shimizu 1988a page 9):

with Λ the Lognormal L(μ,σ) and η the Normal N(μ,σ) distribution. If σ<0.2→0, then the last three terms tend to zero and the Lognormal distribution is approximately normally distributed.

Berry (1973, cited by Leidel 1977 page 103) finds, for certain contaminants in food and drinking water, the Gamma distribution more suitable than the Lognormal. He further expands this for samples with a high proportion of censored data. This method is not further applied in industrial hygiene.

The three parameters, Lognormal Delta distribution is effective in a stationary process with a constant low level background concentration (Owen 1980, Leidel 1977 104). In contrast to the statistical point of view, the three parameter Lognormal distribution is in industrial hygiene a special case of the two parameter distribution (with δ=0) because a random and a fixed exposure level are considered.

According to Shapiro (1991 p8, 15) many of the distributions applied are mutually dependent:

 -	the exponential distribution is a special case of both the Gamma (Chi-square with 2 degrees of freedom) and the Weibull distribution,

 -	the Weibull becomes an "extreme value distribution" through logarithmic transformation,

 -	the Lognormal distribution can be approximated with a Weibull or an exponential distribution.

In conclusion there is no evidence and there are no good reasons to use other distributions in stead of the Lognormal in the industrial hygiene exposure assessment.


B THE LOGNORMAL DISTRIBUTION

The statistical evaluation of industrial hygiene sample exposure data is tied to different, implicit and explicit, conventions. Which convention or alternative HYGINIST uses, is made explicit  in table 16 and is explained in the chapters mentioned in the last column.

With good Statistics , population characteristics like Goodness-of-fit, location, range, and inference can be estimated from a sample, in a reliable and reproducible way. It is the task of the industrial hygienist to develop a reliable exposure assessment strategy and to choose the right statistical methods. Therefore, good exposure assessment requires both industrial hygiene and statistical skills.

Proposition 1:

•	Quantifying workplace air exposure in similar exposure groups is most effective with a random or stratified sampling strategy and with Lognormal extrapolation.

HYGINIST evaluates the following situations:

 -	A complete sample to a complete population (B.2),

 -	A censored sample to a complete population (B.3.),

 - 	A complete or censored sample to a confined population (B.4.2.).

Proposition 2:

•	Lognormal extrapolation is possible if the expert industrial hygienist decides that the model is acceptable., based on:

•	the population description,

•	the measurement strategy,

•	the effectiveness of the measurement method, and

•	the goodness-of-fit,

This proposition makes a heavy appeal on the experience and expertise of the industrial hygienist. A scheme which helps to decide on conformity with Lognormality based on statistical grounds is presented in par. 3.4 . In non-experimental research, like industrial hygiene and occupational epidemiology, elements are not randomized over the populations (Miettinen, 1985) and thus the variance in observations on elements can be in part non stochastic. The bias in population selection, exposure assessment strategy and the measurement method will distort the conclusions. Checking on selection is more than just goodness-of-fit control: it means auditing the complete design of the investigation.

Proposition 3:

•	Unbiased estimators and unbiased extrapolation methods should be preferred.

This proposition deals with the industrial hygiene habit of general extrapolation from small samples (M<10). A perfect estimator is unbiased with minimum, and normally distributed, variance. The inaccuracy of maximum likelihood estimators in small samples leads to more errors of the first kind (incorrectly accepting compliance). This should be considered as more serious than the lower efficiency (with the chance of incorrectly accepting non-compliance) of unbiased estimators.

Proposition 4

•	If data are censored, estimating the descriptive statistics from the rankits plot is the method of preference.

Eliminating censored data or using a fraction of the detection limit as their value is replaced by a more effective method (see B.3)

Proposition 5:

•	It is general practice in industrial hygiene to perform statistical extrapolation to general results.

The extent of the extrapolation and associated degrees of freedom is further elaborated in B.4.

Proposition 6:

•	In censored samples the number of results outside the accuracy range contributes for one half to the number of degrees of freedom with a maximum equal to of the number of the uncensored results.

This proposition is a compromise between extremes (see B.4.3).

Proposition 7:

•	Extrapolation to a one-sided 95% confidence level is just tradition.

Almost every application of statistics uses 95% as default for inference and extrapolation (see 4.2).

Proposition 8:

•	Student-t based statistics should be preferred in industrial hygiene statistical inference and extrapolation.

The Student distribution is asymptotically normal, sufficiently robust to guard against violating the normal model (Boneau 1960, Heeren 1987) and relatively easy to calculate.


B.1 Goodness-of-fit

Following Geary (1947) one could say that "Lognormality is a myth. There never was and will never be, a Lognormal distribution.". Exposure data are only best represented by the Lognormal model (see B.4.1). Shapiro (1990 page 5) states that the reason to study the shape of a distribution is ".... whether or not it is reasonable to approximate the data with the model, not whether the data came from the hypothesized distribution". Thus studying goodness-of-fit of industrial hygiene exposure data is functional (Hawkins 1991 page 58), it can be done in samples of at least 3 exposure data and in two different ways:

 -	graphically, with a probability plot (B.1.1),

 -	quantitatively, with a test on Lognormality (B.1.2).

For both it is true that the effectiveness increases with sample size. The interested reader in "distributional assumption testing" is referred to Shapiro (1990).


B.1.1 Graphical

The examination of Lognormal shape with probability paper has a long tradition in industrial hygiene (Oldham 1953, Leidel 1977 page 102) and other quality control situations (Morrison 1958, Snedecor 1980 4.13). In probability paper the standard normal deviates or their probabilities (the expected values) are located on the horizontal axis and the logarithmically transformed, observed exposure data ci in ascending order are located on the vertical axis. In the ideal case the crosshairs form a straight line through the (non existing) origin (see Figure 22. The decision that the sample data are from a (Log)normal distribution is subjective in this case.

Figure 22	Lognormal probability plot on 24 TWA8 hours methyl methacrylate (LEIDL104)

Rankits Ri or `Normal Order Statistics` are estimators of standard Normal deviates (Fisher 1938 p 25, Teichroew 1956, Harter 1961 and 1970). The algorithm for calculating exact rankit values is rather laborious (Royston 1982b). HYGINIST uses 'read data statements' for M<21 (from Teichroew 1956 page 416 rounded at the fifth decimal) and for sample size of 21 through 2000 the polynomials of Royston (1982b, NSCOR2) are used.

see example 49


B.1.2 Shapiro's W-test (uncensored)

"The one major drawback of the probability plotting technique .... is the lack of objectivity"  (Shapiro 1990 page 21). Statistical tests on shape are more objective, because of their reproducibility. However, the classical tests on skewness and kurtosis (Fisher 1938, Geary 1947) are only useful for samples of at least 50 measurements (see Hawkins 1991 page 58). These tests are now overshadowed by the omnibus test (= combined test on kurtosis and skewness) of Shapiro (1965).

The W-test of Shapiro (1965) estimates the effectiveness of the linear regression through the rankits (Schneider 1986 page 182). This special case of the analysis of variance test uses the following algorithm:

B-1

The coefficients Si in formula B-1 are established using:

•	S1=1/sqrt(2) for M=3,

•	Royston's polynomials (1995, AS R94) for M>4 and M≤2000.

The one sided probability distribution A(W) is (Royston 1995, AS R94) is calculated using:

•	the exact W-distribution for M=3,

•	a transformation to a standard Normal approximation for 3<M≤2000.

The power of the W-test is strongest against short-tailed (platykurtic) and skew distributions and weakest  against symmetric moderately long tailed (leptokurtic) distributions (Royston  1992).

The significance level of A(W)<5% can be used to reject the Lognormal null hypothesis for M< 31. The effectiveness of the W-test decreases if results are rounded in grouping intervals ΔC (Pearson 1977). The W-test needs to be adapted (Royston 1989) if ΔC>0.1*ω (with ω= the arithmetic standard deviation see formula B-18).


B.1.3 Shapiro's W-test (censored sample)

For one-sided censored samples a adapted W-test is developed by Royston (1993,1995).

The censoring must be:

•	less the 80% and

•	the sample size more than 20.

This test, extended to two sided censored samples, is included in HYGINIST for Windows. It was not available in HYGINIST version 2.2 and earlier.

The less effective Monte Carlo based test for Lognormality of Waters (1991) is easily expanded towards censored samples but this will lead to a mounting number of tables.


B.2 Parametric descriptive statistics (complete sample)

The Lognormal probability density function is completely described by its descriptive statistics μ and σ2 (Shimizu 1988 page 2):

B-2

Table 17 displays the symbols used for the population parameters and sample estimators, and refers to the formulas and pages where the algorithms are displayed.

Descriptive statistics are measures for:

•	location (modus, median, geometric and arithmetic mean, fractions, extreme values) (B.2.2 & B.2.4),

•	variance (arithmetic and geometric standard deviation, range) (B.2.3 & B2.5), and

•	shape (degrees of freedom, GSD, the higher moments of the normal distribution like kurtosis and skewness).

Descriptive statistics are normally divided in two groups:

•	parametric descriptive statistics, which can describe completely a continuous probability density function: the (Log)normal mean  and standard deviation s, the Weibull variance and shape,  the Chi-square shape df (Shapiro 1991 page 6 & 8),

•	distribution free descriptive statistics, which are independent of the shape and thus characterize the probability density function only in part: the extremes, median, modus, fractions and the number of results above or below the industrial hygiene limit value.

The relation between the four measures of location of the Lognormal distribution is:

Modus < Median = Geometric mean Exp(μ) < Arithmetic mean β.

See example 50


B.2.1 Mean and standard deviation

All estimators of EXP(μ) and EXP(σ) use the following formulas for mean and standard deviation:

B-3

B-4

both with:

B-5


B.2.2 Location (1). The geometric mean

The geometric mean EXP(μ):

•	 is a measure of source strength (Seixas 1988, Rock 1982),

•	 has a unit dimension of intensity or concentration,

•	 can take every real value over zero,

•	 is identical to the median.

If an estimator of EXP(μ) exceeds a corresponding hygienic limit value H, then at least one result of the sample exceeds limit H.

There are four sample estimators:

•	the maximum likelihood (see B.2.2.3)

•	The unbiased (see B.2.2.1)

•	The median

•	The rankit estimator

For the confidence limits around GM see  B.2.2.2

Notes:

•	GM in B.6 is biased but consistent: for limited sample size it overestimates  EXP(μ) on the average. See B.2.2.1.

•	If the sample include undetectables then GM is estimated using rankit regression B.3.1.

•	GM is necessary for the calculation of:

•	tests on the limit value (chapter 5),

•	inference statistics (chapter 6) and

•	sample size calculations (chapter 7)


B.2.2.1 The unbiased estimator

The bias of the Geometric Mean estimator GM  (see B.6) is exactly known (Laurent 1963 formula 1):

Formula B-7

The average overestimation EXP(σ2/2M) decreases with increasing sample size M. For σ2 about unity, a common value for the variance, and M≤10 the bias is ≥5%. An unbiased estimator of EXP(μ) with minimum variance was developed by Laurent (1963, see Shimizu 1988 page 29). Laurent's algorithm (1963, formula 7), however, is a Bessel function of the first kind and order (M-3)/2, and is difficult to calculate with values for the descriptive statistics which are relevant in industrial hygiene.

The following algorithm is more effective in industrial hygiene. The bias function EXP(-σ2/2M) is first expanded in a Taylor series (Abramowitz 1970 formula 4.2.1.):

 	Formula B-8

In the Taylor series the unbiased and efficient estimator of the numerator σ2k is (Laurent 1963 formula 4):

Formula B-9

The ratio of the two Gamma functions G[(M-1)/2] and G[k+(M-1)/2] can be expanded and easily programmed in a series using formula 6.1.22 of Abramowitz (1970):

Formula B-10

Substitution of formula B-10 in formula B-9 and then in the numerator of formula B-8 results in an unbiased estimator for EXP(μ) with minimum variance:

Formula B-11

The accuracy of BASIC is such (see D.3) that formula B-11 is calculable for GSD/M²<6. Because M²≥4 (by definition) and GSD's are mostly smaller than 24 (see B.2.3), formula B-11 is effective in industrial hygiene practice. Depending on the values of s and M, Φ(t) needs up to thirty terms before a constant value is reached.

Click here for the censored sample.


B.2.2.2 Confidence limits

LOG(GM)/μ follows, under the null hypothesis, the Student distribution (Snedecor 1980, 4.9). The upper and lower limits, including EXP(μ) with confidence U%, are calculated using (Land 1988 page 93 3.1 and 3.2):

Formula B-12

where tU%,df is the deviate of the Student distribution with df degrees of freedom and U% is the desired percentage of the confidence limit, mostly 5% and/or 95%. The two-sided confidence interval is the fraction between two confidence limits.


B.2.2.3 The maximum likelihood estimator

The most commonly used estimator for the Geometric Mean EXP(μ) for a sample without undetectables is the antilog of the sum of the logarithms of the results ci, divided by the sample size M:

Formula B-6

withx defined as in formula B.3.

Click here for the censored sample rankit estimator of the Geometric Mean.


B.2.3 Variance (1). The geometric standard deviation

The geometric standard deviation EXP(σ) is a parameter:

•	of scale and shape (see Figure 21 in Shimizu 1988a p10, Shapiro 1991 p6),

•	without a dimension,

•	larger than unity (by definition).

If all sample data are equal, then the estimator of EXP(σ) equals unity and is useless.

According to Leidel (1977 page 73) group GSDs commonly occur in the range 1.5 to 2.5. In Dutch series Buringh (1989, 1991) found GSD values between 1.4 and 3.5. For the estimation of the sample size Corn (1985 p 176) uses a EXP(σ) between 2.2 and 2.5. Kromhout (1993) reports a median GSD=2.41 in 45 studies yielding almost 20000 measurements. GSDs seem to have been increasing the last few decades, especially in chemical industry (Kromhout 1993). A change in organizing work (from fixed post operations to team structure) is a possible explanation.

Some windows in this manual will show the value GSD=EXP(1)=2.71828 as an example.


B.2.3.1 The unbiased estimator

The unbiased estimator of EXP(σ) with minimum variance is the antilog of the standard deviation of the logarithms of the results:

Formula B-13

with s as defined in formula B.4.

For confidence limits of the GSD see B.2.3.2

Click here for the censored sample rankit estimator of the GSD.


B.2.3.2 Confidence limits

The variance ratio s2/σ2 follows, under the null hypothesis (s=σ), the Chi-square distribution (Abramowitz 1970  26.4). The limits, including EXP(σ) with confidence U%, are calculated using (Land 1988 page 98 4.1.2.):

Formula B-14

where χU%,df is the square root of the Chi-square distribution with df degrees of freedom.


B.2.4 Location (2). The arithmetic mean

The arithmetic mean β (first moment):

•	has the units of measurement of  concentration (or intensity),

•	can take every real value over zero (by definition).

In the Lognormal distribution β is a function of EXP(μ) and EXP(σ):

B-15

The arithmetic mean β of a series:

•	grab sample measurements within a reference period is a measure for the TWAreference period,

•	more days TWA8 hour measurements is a measure for the mean dose of accumulating agents (Seixas 1988) like asbestos, silica, cadmium et cetera.

There are four sample estimators:

•	The maximum likelihood (see B.2.4.5)

•	The unbiased (see B.2.4.1)

•	the minimal mean square error (see B.2.4.2)

•	The linear (see B.2.4.3)

Confidence limits around the arithmetic mean estimator are calculated in B.2.4.4


B.2.4.1 The unbiased estimator

The 'uniformly minimum variance unbiased' estimator (UMVU; Shimizu 1988b p 29, Finney 1941) of the arithmetic mean AM of the Lognormal distribution can be derived, in the same way as was done for GMu, in a Taylor series expansion (see Shimizu 1988b p30 & 31 formula 2.3. & 2.6.):

Formula B-16

Although well known in industrial hygiene (Oldham 1953, Galbas 1975, Bar-Shalom 1975 part II page 47; 1976 page 472, Leidel 1977, Owen 1980) its use is inhibited because of the believed possible deterrent to its users (Dewell 1993) and/or misinterpretation (Selvin 1989).

The superior characteristics of formula 5.16 over other estimators (e.g. the maximum likelihood and direct estimators) are described by Kuo-Hsing Chang (1990) and Attfield (1992, 1993). formula B-16 converges much more quickly to a constant value than formula B-11. For s2>.1 the relative increase in the 7e or 8e term is, for all values of MD2, less than 1E-8. In BASIC, formula B-16 is programmable in a small subroutine.

Click here for the censored sample.


B.2.4.2 The minimal mean square error estimate

The estimator with the smallest mean square error among the estimators (Zhou 1998) is:

Formula B-28

This estimator can only be applied for sample sizes of at least four.


B.2.4.3 The linear estimator

The most simple, method to estimate the arithmetic mean of the Lognormal distribution uses Formula B-3  with xi=ci. This estimator of the mean is consistent, which means unbiased for infinite sample size.


B.2.4.4 Confidence limits

Exact confidence limits for the aritmetic mean can be:

•	established (Armstrong 1992, see Example 33) using tables (Land 1975).

•	calculated using the procedure of Land (1988 6.1)

HYGINIST calculates the exact limits using the procedure of Land (1988 6.1) but provides also also the approximate method that was used in HYGINIST version 2.2 and earlier.

See example 33 to compare different estimators of the confidence limits of the arithmetic mean.

The approximate method of Jahr has severe limitations. It uses the Student-t distribution.

The figures 23 and 24 show however that the distribution of AM is skewed and cannot be described with the Normal distribution. For a sample size of 50  (Figure 23 ) AM can be described with al Lognormal distribution but for the lowest sample size possible (M=2, Figure 24) the AM distribution is even more skewed.

Figure 23 Rankit plot of 2000 AM values.	Figure 24	Rankit plot of 2000 AM values.

Monte Carlo Lognormal. Sample size 50	Monte Carlo Lognormal. Sample size 2


B.2.4.5 The maximum likelihood estimator


B.2.5 Variance (2). The relative, arithmetic standard deviation

The variance (the second moment) of the Lognormal distribution is (Finney 1941 formula 4, Mehran 1973, Shimizu 1988b p9 formula 4.3 and Attfield 1992):

Formula B-17

The unbiased estimator with minimum variance is (Finney 1941 formula 15, Shimizu 1988b p31 formula 2.7):

Formula B-18

with φ(t) as formula B-16. The relative, arithmetic standard deviation (Shimizu 1988 page 10) is:

Formula B-19

formula B-19 is independent of the location and is also called the sample coefficient of variation (Shimizu 1988b formula 4.10). Its estimator w/AM is the ratio of formula B-18 and formula B-16. w and w/AM are used in the comparison with the:

•	measurement coefficient of variation CVt,

•	the grouping interval dC.

If CVt and dC/AM are of the same order of magnitude as w/AM, then the Lognormal shape of the exposure variability will be camouflaged.

The most simple method to estimate the standard error of the Lognormal distribution  uses the  formula B-4 . However with xi=ci not xi=log(ci ).

Click here for the censored sample.


B.3 Parametric descriptive statistics (censored sample)

Censoring (Hald 1949) is a situation in which a part of the sample data has an unknown or a fixed value. Type I corresponds with censoring with accuracy limits (Schneider 1986 page 2). Methods based on censored samples have the advantage of resistance to outliers (Snedecor 1980 page 135): A small percentage of outliers, produced by gross mistakes in measuring, recording and copying, will hardly bias the estimators.

See:

•	B.3.1 on how Lognormal descriptive statistics are calculated using linear regression through the outcome within the detection range see

•	B.3.2 on how the other descriptive statistics are calculated

Censoring greatly complicates extrapolation and inference (Schneider 1986 p 177). With asymmetric (one sided) censoring, a case that is often seen in industrial hygiene, the estimators of the descriptive statistics μ and σ become mutually dependent. The precision of censored based estimators and estimates depends on (Schneider 1986  4.7):

•	 the sample size,

•	 the symmetry of censoring.

Figure 25  500 Rivet heads (HALD151)


B.3.1 Censored sample estimators for EXP(m)

In the case of a censored sample the program estimates μ from the linear regression through the uncensored data M' in the rankits plot. GMg is the regression line median, corresponding to the 50%-tile on the x-axis (Rj=0):

Formula 21

In formula formula B-21 ll and ul are the lowest and highest uncensored data rank and M' is the number of results between the accuracy limits. Formula B.21 is identical with the linear, alternative estimators of Gupta (1952  5.2. formulas 31 through 35) and Sarhan (1962 p208 formulas 10C.2.1 and 10C.2.2). See Example 14, 21 and 44 on the rankit estimators for mean and variance of strontium in milk.

Example 52	Comparing untransformed linear estimators

For uncensored samples the rankit estimator is as effective as the classical estimators (see B.2). They are more effective than classical solution where results below the detection lower limit LL receive the value .5*LL (Hornung 1990, Hawkins 1991 p 104). Example 53 suggest that the rankits estimators should be preferred in industrial hygiene.


B.3.2 Censored sample estimators for EXP(s)
B.3.1 Censored sample estimator for EXP(s)

In the case of a censored sample the program estimates the Geometric Standard Deviation EXP(σ) from the linear regression through the uncensored data M' in the rankits plot. Log(GSDg) is the regression slope (Prescott 1970, section 5):

Formula 20

In formula B-20  ll and ul are the lowest and highest uncensored data rank and M' is the number of results between the accuracy limits. The formulas B.20 and B.21 are identical with the linear, alternative estimators of Gupta (1952  5.2. formulas 31 through 35) and Sarhan (1962 p208 formulas 10C.2.1 and 10C.2.2). See Example 14, 21 and 44 on the rankit estimators for mean and variance of strontium in milk.

Example 52	Comparing untransformed linear estimators

For uncensored samples these rankit estimators are as effective as the classical estimators (see B.2).

They are more effective than classical solution where results below the detection lower limit LL receive the value .5*LL (Hornung 1990, Hawkins 1991 p 104).

Example 53 suggest that the rankits estimators should be preferred in industrial hygiene.


B.3.3 GMu, AM, and w² (censored)

In a censored sample, the descriptive statistics GMu , AMu and w² are calculated using GMg in B.3.1 , GSDg in B.3.2 and the degrees of freedom df of B.4.3.

Figure 27	Mice survival time (GUPTA271, Schneider 1986 p 69 & 88)

Example 53	Performance of estimators of censored sample descriptive statistics


B.4 Degrees of freedom

Degrees of freedom df are defined as the mutually independent variables of the sample in the population. If the statistical uncertainty (e.g. the extrapolation space) increases, the number of degrees of freedom decreases.

In a one dimensional sample df is established by:

 -	the number of measurements M (see B.4.1),

 -	the population size (expanded B.4.1 or confined B.4.2).

More complex are situations with:

 -	censored data (see B.4.3),

 -	when samples with unequal GSDs are compared (see 6.2.3.2).

HYGINIST calculates the number of degrees of freedom for the censored and the non-censored case  as follows:

    If DetecNumAantal < M Then

        Nu = (M + DetecNumAantal)  2 - 1

        If Nu > 2 * DetecNumAantal Then Nu = 2 * DetecNumAantal

    Else

        Nu = M - 1

    End If

With:

M is sample size

DetecNumAantal is the uncensored number of measurements

Nu is the Number of degrees of freedom

The choice of the estimators of the descriptive statistics and the extrapolation methods (see chapter 5) are, in part, determined by the size of df.


B.4.1 General results

df equals the number of sampling periods minus unity (M-1) if:

•	the total exposure duration ô is much larger (up to infinity) than the total sampled time (ô>>t*M, t= sampling duration), the TWA situation,

•	the number of consecutive exposure periods Mτ is much larger (up to infinity) than the number of the sampled periods M (Mτ >> M), in the long-term compliance control situation.

Most exposure assessment strategies use df=M-1 and thus extrapolate implicit to general results.


B.4.2 Confined population

If the reference period τ of a limit value (e.g. TWA8 hour, TWA40 hour for lead, τ=480 hours or Mτ=60 shifts of TWA8 hour in a period of 3 months for asbestos) can be divided in Mô consecutive sampling periods (of e.g. t=1 minute, t=15 minutes or t=8 hours) and M non consecutive periods are sampled during time t (with M<<Mτ, Leidel 1977 p38), then the non-sampled periods over which extrapolation should be carried out is confined Mτ-M. The number of degrees of freedom in this case is (Juda 1967):

The last term in formula formula B-22 determines that df=M-1 for Mτ →∞ and df=∞; if M→Mτ. The influence of a confined population on df is relevant, if both Mτ and M are small; roughly if M<20 and Mτ<3*M+1

Example 54	Degrees of freedom in confined populations


B.4.3 Censored

There is no convention in industrial hygiene on how results outside the accuracy range of (1) the sampling procedure and (2) the analytical method, should contribute to the degrees of freedom. The following methods are found (with no justification given for the choices made):

•	Perkins (1990) establishes the arithmetic mean of a large, censored sample with the uncensored data only (df=M`-1).

•	Schneider (1986 page 190) uses the uncensored data when sample size is small (df=M`-1).

•	Schneider (1986 page 200 & 201) estimated tolerance limits (=percentile values), independent of sample size (df ≡ ∞) on 96 locomotives of which 59 were type I censored (large samples are considered as asymptotic normally distributed).

•	Hornung (1990 method 2 & 3) and Hawkins (1991 p104) use both censored and uncensored data (df=M-1),

•	The most liberal is the NIOSH method for non-compliance probability in long-term exposure situations (Leidel 1977 page 65) which is independent of sample size and accuracy range (df ≡ ∞),

If:

•	sample data show enough variance (e.g. GSD>1.4)

•	the standard deviation w>>ΔC overshadows the grouping interval, and

•	limit H lies inside the accuracy range,

then censored data can be considered as data of equal value in a continuous distribution and thus, at least in part, mutually independent (see proposition 6):

with M` the results within the accuracy range. This method is rather conservative taking into account that, for NIOHS` method of non-compliance probability in long-term exposure situations (Leidel 1977 page 65), no considerations on df have to be made (see screen 25 par.. 5.1.2). For Nonparametric (distribution free) methods dealing with censored data is more simple:

 -	In the one sample binomial test and Poisson test with the hygienic limit inside the accuracy range, the results outside the accuracy range are considered as independent (df=M-1),

 -	When the Wilcoxon rank test is applied to compare two samples and one sample contains nondetectable values, they are considered as equals and independent (df1=M1-1),

HYGINIST calculates the number of degrees of freedom for the censored and the non-censored case  as follows:

    If DetecNumAantal < M Then

        Nu = (M + DetecNumAantal)  2 - 1

        If Nu > 2 * DetecNumAantal Then Nu = 2 * DetecNumAantal

    Else

        Nu = M - 1

    End If

With:

M is sample size

DetecNumAantal is the uncensored number of measurements

Nu is the Number of degrees of freedom

Example 55	Degrees of freedom in censored samples


B.5 Sample size

In estimating exposure the following theoretical minima for the sample size exist:

 -	location, source strength, EXP(μ), β: one measurement,

 -	variance, scale, EXP(σ), w: two measurements,

 -	shape, kurtosis, goodness-of-fit: 3 measurements.

Most industrial hygienists will establish their sampling plan based on:

 -	the goal of the exposure assessment (see A.2),

 -	the measurement accuracy,

 -	the expected difference between concentration C and limit value H,

 -	organizational and financial considerations.

For every exposure application and domain (see A.2), sample size considerations are made in literature (Leidel 1977, page 120, The need for an action level; Leidel 1977, page 82, and Dewell 1989 accuracy based; Hawkins 1991, page 51, and Esmen 1992, long-term compliance control; Hawkins 1991, page 59; Schneider 1988, chapter 7, censored samples; Leidel 1977, pages 34 & 71, worst-case employee, cumulative binomial; Buhring 1989 and Hawkins 1991, page 59, variance based; Rappaport 1987, Ammo dose based, criticised by Evans 1988; Corn 1985, page 176 and Tait 1992).

In general the sample size should increase if:

 -	the population under study is large,

 -	the desired confidence increases,

 -	the exposure variability is large,

 -	the difference between C and H is small,

 -	CVt is large.


B.5.1 Sample size using Wilks method

HYGINIST calculates the minimum sample size for long term compliance control and general exposure assessment based on the expected values for EXP(μ) and EXP(σ) and limit value H. Like Hawkins (1991 page 51) the robust Student distribution is used (see chapter 7). If formula 7-1 is true, then also:

Formula 24

is true. Rearranging formula 5.24 so that df2 becomes a function of the other parameters results in:

Formula 25


B.6 GSD and CVt

Part of the sample variance may be explained by the non-systematic measurement error CVt. Based on the relation between EXP(σ) and the arithmetic mean β and variance ω² (Leidel 1977, table M-1):

A relative adjustment factor R can be derived using w2=wt2-se2 with:

•	wt² the total arithmetic variance of the sample data  (see formula B-16),

•	se2 the variance caused by measurement error and, according to Leidel (1977 p50 NOTE), se2=(CVt*H)².

AM and wt² are the unbiased estimators of the arithmetic mean β and the arithmetic standard deviation ω (see formulas 5.16 and 5.18). If wt<CVt*H, then the square root of a negative number is extracted in the denominator and formula 5.27 becomes incalculable. In Example 56 values of GSDadj and wadj/AMadj are calculated for relevant values of GSD, M, and CVt. For M>10 or GSD>2.71828 the influence of random measurement errors CVt<.35 is irrelevant. The same applies for MD2, GSDD1.4 and CVt<.1.

Example 56	Adjusting GSDs and w/AM for different values of M and CVt

Example 57	CVt influence on GSD in example data


C How to get the program (running)

Follow the next steps to get a copy of HYGINIST running on your computer:

•	C.1 Download HYGINZIP.EXE and HYGINHLP.EXE from the internet,

•	C.2 Extract the HYGINIST setup files from HYGINZIP.EXE ,

•	C.3 Remove earlier versions of HYGINIST for Windows from your computer,

•	C.4 Install  the program in your computer, add HYGINWIN.HLP.

•	C.4 Start  the program .

Other items included here are:

•	Register the program for continuous use,

•	Stop execution.


C.1 Download from the HYGINIST homepage

•	Go to the HYGINIST internet homepage http://www.tsac.nl

•	Click in the frame on the left on download and subsequently in the frame on the right on HYGINZIP.EXE

•	Now save HYGINZIP.EXE in a temporary directory and

•	Wait while file is downloaded in the directory for temporary files on your system.

To do this in real press on http://www.tsac.nl.

Continue with extracting the HYGINIST setup files from HYGINZIP.EXE


C.1.1 The HYGINIST internet site


C.1.2 Download frame on the HYGINIST internet site

Download both HYGINZIP.EXE and HYGINHLP.EXE


C.1.3 Choose between direct executing or downloading

Choose if you want the zipped install program to be saved on your system (preferred!) or to be extracted from the internet.


C.1.4 Saving HYGINZIP.EXE


C.1.5 Downloading HYGINZIP.EXE in your computer

If you have chosen to save it on your system choose a directory


C.2 Extracting HYGINZIP.EXE

If an earlier version of HYGINIST is still installed then remove it first.

Now start the self-extracting program  HYGINZIP.EXE from the directory where was saved.

It does the following:

•	it will extracts the files into a directory

•	Accept the suggestion or choose an alternative

•	Keep the directory  name in mind.

•	The number of extracted files is given

Continue with installing HYGINIST for Windows

If a HYGINIST for Windows (development) version was allready installed on this system remove it first.


C.2.1 Unzip

It will come with a suggestion to place the extracted files in a directory for temporary files

Accept the suggested directory (advised!) or browse to another.

Then press Unzip to extract


C.3 Remove earlier version from HYGINIST for windows
Uninstall or remove (earlier versions of) HYGINIST

If you have already installed a development version of HYGINIST for Windows or you want to remove the HYGINIST program from your system, then click in ascending order:

•	Start,

•	Preferences,

•	Configuration,

•	Software,

•	Scroll to HYGINIST,

•	Click Add/Remove.

All installed HYGINIST components are now removed.

The remove is finished. Now continue with the installation.


C.4 Automatic installation on a hard disk

Browse with the explorer to the directory containing the extracted HYGINZIP.EXE files or:

•	Click Start in the lower left corner and then click on Run,

•	Browse to the directory containing the extracted files,

Now click on SETUP.EXE to start the installation.

The Installation starts with the following message window:

Close all programs before you continue.

Now click the large button in the upper left corner to install the program in the default directory.

You can change the standard  (sub)directory C:\Program files\HYGINIST by clicking the "Change Directory" button on the right site.

All HYGINIST files are copied to the destination directories.

An program Icon to start HYGINIST is set under 'Start', 'Programs'.

The installation of the program is completed successfully!

Now add the Helpfile to the HYGINIST program.

Double click on the downloaded selfextracting file HYGINHLP.EXE and the next message box will appear.

Browse to to the HYGINIST directory and press unzip to extract the 2 files.

You now can start HYGINIST on your system


C.5 Start the program

You start HYGINIST for Windows by clicking 'Start', 'Programs'.

Now click on the HYGINIST [image] Icon.

If there is no Icon in your menu or on your desktop then do the following:

•	By default HYGINIST for Windows is installed in the directory C:\Program files\HYGINIST\

•	If you haven't accepted the default directory and don't know were HYGINIST was installed then search  HYGINIST for Windows using the Explorer. If HYINIST is found then (double)click on HYGINWIN.EXE.

If this is the first time the program is started after installation took place, then the HYGINIST Login screen appears. If you already filled out Login form then only the Splash screen is displayed for a few seconds before the exposure data management screen appears.


Explorer


Start, Programs


HYGINIST Icons


C.5.1 Enter name and password

A login screen appear. The name of the system user of the computer is displayed

If you have received your password in reply to your registration then fill out:

•	your name

•	 and the password

Press <OK> if you entered all available information.

If the information is correct the program

<Yes> to get a password or <Esc> for direct use of an unregistered version


C.5.2 How to get a password

If you don't know the password or pressed the <Enter> key before filled it out, then the next  message box appears:

•	If you want to have a password because you will be using HYGINIST regularly, then press <Yes>. Your email program will be activated in oder to request a pasword.

•	The HYGINIST help file will be activated and you will be instructed in how to obtain a password.

•	If you have a valid password but you entered before you could fill out the Password textbox then press <No>

•	If you just wat to see how the program works then press <Cancel>

•	Do you want to know the license agreement then press <Help>


C.5.3 Use as unregistered shareware
C.5.3 Use as unregistered freeware


C.6 Stop and Exit the program

Click  your cursor on the upper right corner [x] or the menu option exit.


C.6.1 MenuExit

The HYGINIST program stops and asks you if you want to exit.


C.6.2 Exit Button


E PROGRAM OPERATION

This chapter provides detailed information on:

•	operating the program,

•	screen lay-out,

•	report making,

•	on line help.


E.1 Operating the program

In the next table the most important key functions and commands are explained.

<key>	Comment	See further

<Pause>	Screen fixation. Press any key to continue	-

string<Enter>	Type and enter text (file name, dimension; W 8 characters)	E.1.4, E.1.4.1 & E.1.4.2

digits<Enter> 	Type and enter a number 	E.1.4, E.1.4.1 & E.1.4.2

(sample size, exposure data, limit value, desired percentage)

<Delete>	Delete typed or imported characters from the left hand side of the cursor	E.1.4

<Backspace>	Delete typed or imported characters from the right hand side of the cursor	E.1.4

<Prt Sc>	Sends current screen to clipboard	E.3

←,↑,→,↓	Stirs reverse video block 	2.2.4.1


E.1.4 Entering characters or numbers

Text or numbers entered by keyboard, are completed if the object in which the are placed losses the focus.

•	Comma's <,> in a series characters or digits are replaced automatically by a decimal point <.>

•	Use <Backspace> or <Del> to remove undesired characters or digits.

•	Text (name data file or dimension) may exceed 8 characters, however the text may be less visible. Upper and lower case characters are both accepted.


E.1.4.2 Numbers

The decimal sign differs between and within the US and Europe. Comma's <,> in a series digits are replaced automatically by a decimal point <.>

Numbers <10000 and ≥ 0.1 are displayed with 9 digits at most, with a fixed decimal point.

####.#####

Any number between 10000 and 1D+100 or between 1D-100 and 0.1 is displayed with at most 8 digits and with a fixed decimal point combined with an exponent `D±NN`. The real value of the number is the mantissa multiplied by 10 raised to the ±NN power.

  ##.######D±NN

Numbers ≥ D+100 or ≤1D-100 who do not exceed the extremes, are displayed with at most 7 digits and with a fixed decimal point combined with an exponent `D±NNN`. The real value of the outcome is, the mantissa multiplied by 10 raised to the ± NNN power.

  ##.#####D±NNN


E.2  Help

HYGINIST informs you you on several ways what the program does and can do.

•	consult the manual

•	context sensitive help

•	tooltips

•	Internet


Help manual


Context sensitive help

If you are somewhere in the program and need help on the transaction you are preforming or you want to perform  just press the f1 key


Tool tips

Tooltips are the yellow text balloons explaning the content of an object


Internet

Visit the HYGINIST homepage


E.3 Report facility

All HYGINIST screens are easily incorporated in text editor programs. Since standard text and picture processing programs have extended facilities to manipulate text and figures in reports HYGINIST screens are only made available for these programs


E.3.1 The *.LOG report file
E.3.1 *.LOG report text file

If Report is displayed in the menu bar, then you can append the information of the current screen to the TEXT data file *.LOG.

If HYGINIST.LOG does not exist in the current directory, then it is created automatically.

To report exact figures, use HYGINIST.LOG. The file can be imported in any word processing program.


E.3.2 Capture graphics

You can copy bitmaps of all tabs and the 'log-Normal frequency distrbution' using the follwing keys on your keyboard:

•	the 'Print Screen' button

•	the combination of 'Alt' + 'Print Screen'.

If you then open a picture editor program (like Paint, Photo Editor etc.) or a professional word-processing program, you can paste, edit, select and save the full screen ('Print Screen') or only HYGINIST window ('Alt' + 'Print Screen').


E.3.3 Printer


F References

F.1 Computer program and quantitative evaluation

F.2 The example data in Table 1

F.3 Further readings


F.1 Computer program and quantitative evaluation

F.1.1 English references

F.1.2 Non English references


F.1.1 English references

Abramowitz M., Stegun I.A.  Handbook of mathematical functions. New York: Dover Publications Inc. (1964) 5e edition 1970.

ACGIH  Protection of the sensitive individual; papers of a symposium, Cicinnati, Nov 1981. Ann. Am. Conf. Ind. Hyg. 3 (1982).

ACGIH  1993-1994 Treshold Limit Values for chemical substances and physical agents and Biological Exposure Indices Cincinnatti 1993.

d`Agostino R.B.  An omnibus test of Normality for moderate and large size samples. Biometrika 58 (1971) 341-348.

d`Agostino R.B.  Small sample probability points for the D test of Normality. Biometrika 59 (1972) 219-221.

Armstrong B.G.  Confidence intervals for the arithmetic means of Lognormally distributed exposures. Am. Ind. Hyg. Assoc. J. 53 (1992) 481-485.

Attfield M.D., Hewett P.  Exact expressions for the bias and the variance of estimators of the mean of a Lognormal distribution. Am. Ind. Hyg. Assoc. J. 53 (1992) 432-435.

Attfield M.D., Hewett P.  Letter to the editor. Am. Ind. Hyg. Assoc. J. 54 (1993) A-86.

Bar-Shalom Y., et al  Handbook of statistical tests for evaluating exposure to air contaminants. HEW Publication No. (NIOSH) 75-147 Washington: U.S. Department of Health, Education and Welfare (1975).

Bar-Shalom Y., Segall A., Budenaers D.  Decision and estimation procedures for air contaminants. Am. Ind. Hyg. Assoc. J. 37 (1976) 469-473.

Beasley J.D., Springer S.G.  The percentage points of the Normal distribution. Applied Statistics 26 (1977) 118-121.

Berry G., Day, N.E.  The statistical analysis of the results of sampling an environment for contaminant when most samples contain an undetectable level. Am. J. of Epidemiology 97 (1973) 160-166.

Boneau C.A.  The effects of violations of assumptions underlying the t test. Psychological Bulletin 57 (1960) 49-64.

Brief R.S., Scale R.A.  Occupational exposure limits for novel work schedules. Am. Ind. Hyg. Assoc. J. 36 (1975) 467-469.

Brief R.S., Scala R.A.  Occupational Health Aspects of Unusual Work Schedules: A Review of Exxon Experiences. Am. Ind. Hyg. Assoc. J. 47 (1986) 199-202.

Buring E., Lanting R.  Working paper on monitoring strategies in the United Kingdom, Federal Republic of Germany and United States of America. Labour Inspectory S 69. Voorburg 1989.

Buringh E., Lanting R.  Exposure variability in the workplace: Its implications for the assessment of compliance. Am. Ind. Hyg. Assoc. J. 52 (1991) 6-13.

CEFIC  Report on occupational exposure limits and monitoring strategy. Conseil Européen des Federations de l`industrie Chemique. Brussel (no publication year mentioned, probably 1984).

CEN/T 137  Workplace atmospheres - Guidance for the assessment of exposure to chemical agents for comparison with limit values and measurement strategy. EN 689. Brussels (1995).

CEN/T 137  Workplace atmospheres - General requirements for the performance of procedures for measurement of chemical agents Draft prEN 482. Brussels (1995).

Checkoway H., Pearce N., Crawford-Brown D.J.  Research methods in occupational epidemiology. Monographs in epidemiology and biostatistics. Oxford university press 13 (1989).

Cicollela A., Servais M., Vincent R., Wild P.  STARTREX (STAtistique, Resultats, TRaitement EXploitation) Logiciel de traitement des données d'exposition aux substances chimiques. Developpé par: Institut National de Recherche et de Sécurité (1993).

Clayton G.D., Clayton F.E.  Patty's industrial hygiene and toxicology. Third revised edition. Volume I General principals. John Wiley & Sons (1978).

CONCAWE  Review of strategies for the evaluation of employee exposures to substances hazardous to health. CONCAWE's Industrial Hygiene Subgroup. Report no. 87/57 The Hague October 1987.

Corn M.  Strategies of air sampling. Scand. j. Work Environm. Health 11 (1985) 173-180.

Crow E.L.  Minimum variance unbiased estimators of the ratio of means of two Lognormal variates and of two gamma variates. Commun. Statist.-Theor. Meth. A6 (1977) 967-975.

Damiano, J.  A guideline for managing the industrial hygiene sampling function.  Am. Ind. Hyg. Assoc. J. 50 (1989) 366-371.

Dewell P.  Some applications of statistics in occupational hygiene. BOSH Technical Handbook Series No. 1 (1989).

Dewell P.  Letter to the editor. Am. Ind. Hyg. Assoc. J. 54 (1993) A85-A86.

EG  The council of the european communities. Council directive of 16 december 1988 (88/642/EEC). Official Journal of the European Communities No L 356/74. 24.12.88.

Eide I.  The application of 8-hour occupational exposure limits to non-standard work schedules off-shore, Ann. Occup. Hyg. 34 (1990) 13-17.

Eller P.M.  Manual of analytical methods Third edition U.S. Department of Health and Human services NIOSH Cincinnati (1984 with updates).

Esmen N.A, Hammad Y.Y.  Log-normality of environmental sampling data. J. Environ. Sci. Health. 162 (1977) 29-41.

Esmen N.A.  A distribution-free double-sampling method for exposure assessment. Appl. Occup. Environ. Hyg. 7 (1992) 613-621.

Evans J.S., Hawkins N.C.  The distribution of Student's t-statistics for small samples from Lognormal exposure distributions Am. Ind. Hyg. Assoc. J. 49 (1988) 512-515.

Filiben J.J.  The probability plot correlation coefficient test for Normality. Technometrics 17 (1975) 111-117.

Finney D.J.  On the distribution of a variate whose logarithm is Normally distributed. J. Royal Statistical Society Suppl., 7 (1941) 155-161.

Fisher R.A., Yeates F.  Statistical tables for biological, agricultural and medical research. New York: Hafner (1938) 6e edition 1963 Table 20.

Francis M., et al  The effect of autocorrelation on the estimation of workers' daily exposure. Am. Ind. Hyg. Assoc. J. 50 (1989) 37-43.

Gaddum, J.H.  Lognormal distributions. Nature 156 (1945) 463-366.

Gerlach B.  A correlation-type goodness-of-fit test for normality with censored sampling. Math. Operationsforsch. Statist., Ser. Statistics 11 (1980) 207-218.

Gupta A.K.  Estimation of the mean and the standard deviation of a Normal population from a censored sample. Biometrika 39 (1952) 260-273.

Geary R.C.  Testing for Normality. Biometrika 34 (1947) 209-242.

Gustafson T.L.  TRUE EPISTAT Manual. Fourth edition. Epistat services. Texas (1991).

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Hald A.  Statistical Theory with engineering applications. par..  6.9.: The truncated Normal Distribution. Wiley (1952) 144-151.

Hall I.J., Sampson C.B.  One-sided tolerance limits for a Normal population based on censored samples. J. Statist. Comput. Simul. 2 (1973) p 317-324.

Harter H.L.  Expected values of Normal order statistics. Biometrika 48 (1961) 151-165.

Harter H.L.  Order statistics and their use in testing and estimation. Vol 2: Estimates based on order statistics of samples from various populations. Chapter III: Expected values of order statistics of samples from various populations. par..  1: Normal population. Washington U.S. Government Printing Office (1970) 25-29.

Harris R.L.  Guideline for collection of industrial hygiene exposure assessment data for epidemiologic use. Chemical Manufacturers Association (1993) 36p.

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Hawkins N.C., Jayjock M.A., Lynch J.  A rationale and a framework for establishing the quality of human exposure assessments. Am. Ind. Hyg. Assoc. J. 53 (1992) 34-41.

Heeren T., d'Agostino R.  Robustness of the two independent samples t-test when applied to ordinal scaled data. Statistics in medicine 6 (1987) 79-90.

Hickey J.L., Reist P.C.  Application of occupational exposure limits to unusual Work Schedules. A. Ind. Hyg. Assoc. J. 38 (1977) 613-621.

Hill I.D.  The Normal integral. Applied Statistics 22 (1973) 424-427.

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HSE  Monitoring strategies for toxic substances. Health & Safety Executive. Guidance note EH 42. Environmental Hygiene 42 (1989) 1-12.

HSE  Methods for the Determination of Hazardous Substances. MDHS ... Health and Safety Executive. i.e.: Methods for the Determination of Hazardous Substances. MDHS 67: Total (and speciated) chromium in chromium plating mists. Health and Safety Executive, february 1990

ISO  International Standard: Workplace Air - Determination of ...., ISO,...., Genève. i.e.: International Standard: Workplace Air - Determination of particulate lead and lead compounds - Flame atomic absorption spectrometric method. ISO 8518, december 1990.

Jahr J.  Calculations for workplace measurements and other data with a Lognormal distribution. Staub. Reinhaltung der Luft. 47 (1987) 153-156.

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Laurent A.G.  The Lognormal distribution and the translation method: Description and estimation problems. Am. Stat. Assoc. J. 58 (1963) 231-235.

Leidel N.A., Bush K.A.  Statistical Methods for the determination of non-compliance with Occupational Health Standards (1975a). HEW Publication No. (NIOSH) 75-159 Cincinnati: U.S. Department of Health, Education and Welfare.

Leidel N.A., Bush K.A., Crouse W. E.  Exposure measurement action level and occupational environmental variability (1975b). HEW Publication No. (NIOSH) 76-131 Cincinnati: U.S. Department of Health, Education and Welfare.

Leidel N.A., Bush K.A., Lynch J.R.  Occupational exposure sampling strategy manual. DHEW, NIOSH publ. 137, (1977) Cincinnati: U.S. Department of Health, Education and Welfare.

Mietinnen O.S.  Theoretical epidemiology: principles of occurrence research. New York: John Wiley & Sons (1985)

Mehran F.  Variance of the MVUE for the Lognormal mean.  JASA 68 (1973) 726-727.

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NIOSH  Manual of Analytical Methods, third edition. U.S. Department of Health and Human Services.

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Oldham P.D.  On estimating the arithmetic means of Lognormally-distributed populations. Biometrics 39 (1965) 235-239.

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Page E.B.  Ordered hypotheses for multiple treatments: a significance test for linear ranks. American Statistical Association Journal (1963) 216-230

Patel J.K., Read C.B.  Handbook of the Normal distribution. Chapter 7: Normal approximations to distributions. Statistics: textbooks and monographs. Vol 40 (1982) 168-223.

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Proschan F.  Confidence and tolerance intervals for the Normal distribution. Am. Stat. Assoc. J. 48 (1953) 550-564.

Rappaport S.M.  Assessment of long-term exposure to toxic substances in air. Ann. Occup. Hyg. 35 (1991) 61-121.

Rappaport S.M., Selvin S.  A method for evaluating the mean exposure from a Lognormal distribution. Am. Ind Hyg. Assoc. J. 48 (1987) 374-379.

Rappaport S.M., Spear R.C. Physiological damping of exposure variability during brief periods. Ann. Occup. Hyg. 32 (1988) 21-33.

Rappaport S.M., Kromhout H., Symanski E.  Variation of exposure between workers in homogeneous exposure groups. Am. Ind. Hyg. Assoc. J. 54 (1993) 654-662.

Rempel D.  Occupational Medicine. Medical surveillance in the workplace. Philadelphia (1990) 435.

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Rock J.C.  A comparison between OSHA-compliance criteria and action-level decision criteria. Am. Ind. Hyg. Assoc. J. 43 (1982) 297-313.

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Royston J.P.  Expected Normal order statistics (exact and approximate). Applied Statistics 31 (1982b) 161-165.

Royston J.P.  The W-test for Normality. Applied Statistics 31 (1982c) 176-180.

Royston J.P.  Correcting the Shapiro-wilk W for ties. J. Stat. Comput. Simul. 31 (1989) 237-249.

Royston P.  Estimating departure from Normality. Statistics in Medicine 10 (1991) 1283-1293.

Royston P.  Estimation, reference ranges and goodness of fit for the three-parameter log-normal distribution. Statistics in Medicine 11 (1992a) 897-912.

Royston P.  Approximating the Shapiro-Wilk W-test for non-Normality.  Statistics and Computing 2 (1992b) 117-119.

Royston P.  A toolkit for testing for non-normality in complete and censored samples.  The Statistician 42 (1993) 37-43.

Royston J.P.  Remark AS  R94. A remark on Algorithm AS 181: The W-test for Normality. Applied Statistics 44 (1995) 547-551.

Sarhan A.E., Greenberg B.G.  Estimation of location and scale parameters by order statistics from single and double censored samples, Part 1, The Normal distribution up to samples of size 10. Ann. Math. Statist. 27 (1956) 427-451.

Sarhan A.E., Greenberg B.G.  Contributions to Order Statistics. New York: John Wiley (1962). Chapter 10. Normal Distributions.

Scheffers T.M.L., Jongeneelen F.J., Bragt P.C.  Development of effect-specific limit values (ESLVs) for solvent mixtures in painting. Ann. Occup. Hyg. 29 (1985) 191-199.

Schneider H.  Truncated and censored samples from Normal populations. Statistics: textbooks and monographs. Vol 70 (1986).

Schneider H.  Simple and highly efficient estimators for censored Normal samples. Biometrika (1984) 412-414.

Selvin S., Rappaport S.M.  A note on the estimation of the mean value from a Lognormal distribution. Am. Ind Hyg. Assoc. J. 50 (1989) 627-630.

Seixas N.A., Robins T.G., Moulton L.W.  The use of the geometric and arithmetic mean exposures in occupational epidemiology. Am. J. Ind Medicine 14 (1988) 465-477.

Shapiro S.S., Wilk M.B.  An analysis of variance test for Normality. Biometrika 52 (1965) 591-611.

Shapiro S.S., Wilk M.B., Chen H.J.  A comparative study of various tests for Normality. Am. Stat. Assoc. J. 63 (1968) 1343-1372.

Shapiro S.S., Francia R.S.  An approximate analysis of variance test for Normality. J. Am. Stat. Assoc. 67 (1972) 215-216.

Shapiro S.S., Brain C.W.  A review of distributional testing procedures and development of a censored sample distributional test. In Statistical distributions in scientific work Editors C. Taillie et. al. Reidel Publshing Compagny 5 (1981) 1-24.

Shapiro S.S.  How to test Normality and other distributional assumptions. -2nd ed. Volume 3 in The ASQC basic references in quality control: Statistical techniques Editors S.S. Shapiro and E.F. Mykytka. The American Society for Quality Control (1990).

Shimizu K., Crow E.L.  History, Genesis, and Properties. In: STATISTICS: Textbooks and Monographs Volume 88 Lognormal Distributions. Edited by Edwin L. Crow and Kunio Shimizu. New York: Marcel Dekker (1988a) 1-25.

Shimizu K.  Point Estimation. In: STATISTICS: Textbooks and Monographs Volume 88 Lognormal Distributions.  Edited by Edwin L. Crow and Kunio Shimizu. New York: Marcel Dekker (1988b) 27-86.

Siegel S.  Nonparametric statistics for the behavioral sciences. McGraw-Hill New York (1956).

Smith T.J.  Exposure assessment for occupational epidemiology. Am. J. Ind Medicine 12 (1987) 249-268.

Snedecor G.W., Cochran W.G.  Statistical methods. The Iowa State University press. (1980) 7e edition.

Spear R.C., Selvin S., Francis M.  The influence of averaging time on the distribution of exposures. Am. Ind. Hyg. Assoc. J. 47 (1980) 365-386.

SPSS  SPSS/PC+? Update for V3.0 and V3.1 for the IBM PC/XT/AT and PS/2. Chicago (1989).

Stellingwerf J.  Time dependent aspects in the european communities directives of asbestos and lead. Letter to the editor. Br. J. Ind. Med. 41 (1984) 354-356.

Tait K.  The workplace exposure assessment expert system (WORKSPERT). Am. Ind. Hyg. Assoc. J 53 (1992) 84-98.

Teichroew D.  Tables of expected values of order statistics and products of order statistics for samples of size twenty and less from the Normal distribution. Annals of Mathematical Statistics 27 (1956) 410-425.

Thomas A.A.  Skin Absorption: a potential contributing factor to the BEI (biological exposure index). Appl. Ind. Hyg. 1 (1986) 87-90.

Travis C.C., Land M.L.  Estimating the mean of data sets with nondetectable values. Environ. Sci Technol. 24 (1990) 961-962.

Tuggle R.M.  The NIOSH decision scheme. Am. Ind. Hyg. Assoc. J 42 (1981) 493-498.

Tuggle R.M.  Assessment of occupational exposure using one-sided tolerance limits. Am. Ind. Hyg. Assoc. J 43 (1982) 338-346.

Verrill S., Johnson R.A.  The asymptotic equivalence of some modified Shapiro-Wilk statistics - complete and censored sample cases. The Annals of Statistics 15 (1987) 413-419.

Waters M.A.  A measure of goodness-of-fit for the Lognormal model applied to occupational exposures. Am. Ind. Hyg. Assoc. J. 52 (1991) 493-502.

 WHO  Health effects of combined exposures in the work environment. Report of a WHO Expert Committee. Technical Report Series 662. World Health Organization Geneva (1981).

WHO  Evaluation of exposure to airborne particles in the work environment. WHO offset publication no 80. World Health Organization Geneva (1984).

Wilks S.S.  Determination of sample sizes for setting tolerance limits. Ann. Math. Statistics 12 (1941) 91-96.


F.1.2 Non English references

Bezemer P.D.  Referentiewaarden. Een verkenning voor het bepalen van `normale waarden`. Proefschrift VU 1981.

BIN  Strategie voor het meten van stoffen met een tijdgewogen grenswaarde. Belgisch Instituut voor Normalisatie NBN T96-002. juni 1987.

Boleij J., Heederik D., Kromhout H.  Karakterisering van blootstelling aan chemische stoffen in de werkomgeving. Wageningen: Pudoc 1987.

Buringh E., Huygen C.  Concept voorlichtingsblad meetstrategie 4. Frequentieverdeling van meetgegevens. Toetsing en schatting. TNO-MT Rapport R 88/251b Delft 1989.

Ciba-Geigy  Wissenschaftliche Tabellen Geigy. Basel (1980).

Coenen W.  Zur Frage des Vertrauensbereiches bei Mittelwerten der Staubkonzentration. Staub Reinhalt. Luft 26 (1966) 216-221.

Coenen W., Riediger G.  Die Schatzung des zeitlichen Konzentrationsmittelwertes gefährlicher Arbeidsstoffe in de Luft bei stichprobenartigen Messungen.  Staub- Reinhaltung der Luft 38 (1978) 402-409.

DFG  Analytischen Methoden zur Prüfung gesundheitsschadlicher Arbeitsstoffe. Band 1/3, Luftanalysen. Deutsche Forschungsgemeinschaft.

DFG  idem, Band 2/3, Analysen in biologischen Material.

Galbas H.G.  Schätz- und Testmethoden für den Erwartungswert einer Lognormal verteilten Grundgesamtheit. Staub- Reinhaltung der Luft 35 (1975) 448-452.

Heederik D., et al  Meetstrategieën voor chemische belasting ten behoeve van risico-analyze. NVvA symposium verslag. Den Haag: Nederlandse Vereniging voor Arbeidshygiëne (1987).

Jonge H. de  Inleiding tot de medische statistiek. Deel 1. Fundamentele begrippen en technieken verdelingsvrije methoden. Nederlands Instituut voor Praeventieve Geneeskunde, Leiden (1963).

Jonge H. de  Inleiding tot de medische statistiek. Deel 2. Klassieke methoden. Nederlands Instituut voor Praeventieve Geneeskunde, Leiden (1964).

Juda J., Budzinski K.,  Bestimmung des Toleranzbereiches des Mittelwertes bei den Messungen der Staubkomzentration. Staub Reinhaltung der Luft 27 (1967) 176-179.

Manz A., Manz J.  Praktische Beispiele für die Toxicologische Bewertung der Gesamtwirkung verschiedener gesundheitsgefahrdender Stoffe in der Luft am Arbeitsplatz. Zentralblatt für Arbeitsmedizin, Arbeitsschutz, Prophylaxe und Eergonomie 37 (1987) 278-284.

NNI  Luchtkwaliteit - Werkplek atmosphere. Bepaling van de concentratie aan ...., NVN, .... Delft. Bijvoorbeeld: Luchtkwaliteit - Werkplek atmosphere. Bepaling van de concentratie aan arseen in stof door middel van atomaire-absorptiespectrometrie na actieve monsterneming op een membraanfilter. Nederlandse Voornorm, NVN 2951, juni 1990.

Oostendorp Y., Kromhout H.  Protokol voor algemeen chemisch werkplekonderzoek. Landbouw Hogeschool Wageningen Vakgroep, Luchthygiëne en -verontreiniging. Wageningen juli 1985a.

Oostendorp Y., Kromhout H.  Model voor werkplekonderzoek naar de blootstelling aan chemische stoffen. Landbouw Hogeschool Wageningen, Vakgroep Luchthygiëne en -verontreiniging. R-154. Wageningen November 1985b.

Scheffers T.  EPO: een arbeidshygiënisch en gezondheidskundig informatie systeem van werknemers met een beroepsmatige blootstelling aan chemische stoffen. In: Meetstrategieën voor chemische belasting ten behoeve van risico-analyze. NVvA symposium verslag. Redactie D.H. Heederik. Nederlandse Vereniging voor Arbeidshygiëne, Den Haag (1987). 77-89.

Scheffers T.  HYGINIST, handleiding bij het computerprogramma. NVvA Den Haag 1990, 100 blz. (inclusief computerprogramma).

Scheffers T., et al  DOHS-Base. Een databestand met arbeidshygiënische grenswaarden en meetmethoden voor de Nederlandse arbeidshygiënist. Een publikatie van de werkgroep Grenswaarden en Meetmethoden van de Nederlandse Vereniging voor Arbeidshygiëne (Eerste uitgave, januari 1992) 1-43.

Stresemann E.  Die allergologische Bedeutung von Stoffen der MAK-Werte-Liste. Zentralblatt für Arbeitsmedizin, Arbeitsschutz, Prophylaxe und Eergonomie 38 (1988) 389-393.

TRgA 402  Messung und Beurteilung von Konzentrationen gefährlicher Arbeitsstoffe in der Luft; Anwendung von Maximalen Arbeidsplatzkonzentrationen (MAK). Bundesarbeitsblatt 11 (1984) 55-61.

VDI 2450  Messen von Emission, Transmission und Immision luftverunreinigender stoffe. Methoden zur behandlung einzelner Variabeln. Quantile. Verein Deutscher Ingenieure (1979).


F.2 The example data in Table 1

Albrecht W.N., Burr G.A., Neumeister C.E.  Sampling and analytical method for workplace monitoring of aspartame in air. Applied Industrial Hygiene 4 (1989) 217-221. Table II Weight-out.

Bar-Shalom Y., et al  Handbook of Statistical Tests for Evaluating Exposure to air contaminants. HEW Publication No. (NIOSH) 75-147 Washington: U.S. Department of Health, Education and Welfare (1975) I-25.

Bilan R.A., Haflidson W.O., McVittie D.J.  Assessment of isocyanate exposure during spray application of polyurethane foam Am. Ind. Hyg. Assoc. J. 50 (1989) 303-306. Table 1 sprayer.

Boleij J., Heederik D., Kromhout H.  Karakterisering van blootstelling aan chemische stoffen in de werkomgeving. Pudoc Wageningen (1987) 62 & 84.

Booher L.E.  Lead exposure in a ship overhaul facility during paint removal. Am. Ind. Hyg. Assoc. J. 49 (1988) 123.

Cohen A.C.  Three-Parameter estimation. In: STATISTICS: Textbooks and Monographs Volume 88 Lognormal Distributions.  Edited by Edwin L. Crow and Kunio Shimizu. New York: Marcel Dekker (1988) 113-137.

Conover W.J.  Practical Nonparametric Statistics. Texas Tech University. John Wiley & Sons (1980) 195, 365.

Dewell P.  Some applications of statistics in occupational hygiene. BOSH Technical Handbook Series No. 1 (1989) 24, 42 and 44.

Gupta A.K.  Estimation of the mean and the standard deviation of a Normal population from a censored sample. Biometrika 39 (1952) 271.

Gustafson T.L.  TRUE EPISTAT Manual chapter 6. Epistat services Texas (1989) 17.

Hald, A.  Statistical Theory with engineering applications. par..  6.9.: The truncated Normal Distribution. Wiley (1952) 151.

Hawkins N.C., Norwood S.K., Rock J.C. (ed.)  A strategy for Occupational Exposure Assessment. Akron (Ohio): AIHA (1991) 104, 105 and 110.

Leidel N.A., Bush K.A., Lynch J.R.  Occupational exposure sampling strategy manual. DHEW NIOSH-137 (1977) 56, 61, 63, 67, 103 and 104.

Owen W.J., DeRouen T.A.  Estimation of the mean for Lognormal data containing zeroes and left-censored values, with applications to the measurement of worker exposure to air contaminants. Biometrics 36 (1980) 707-719.

Post W.K.  Schatten van blootstellingen: Een onderzoek naar het nut van kwalitatieve blootstellingsschattingen en de (on)zin van indicatieve metingen. LUWageningen Rapport Gezondheidsleer 382 (1989) bijlage 11 vervolg, Styreen, funktie inlegger.

Potts D.L., Craft B.F.  Occupational exposure of Veterinarians to waste anaesthetic gases. Applied Industrial Hygiene 3 (1988) 134.

Sarhan A.E., Greenberg B.G.  Contributions to Order Statistics. New York: John Wiley (1962) 212.

Scheffers T.M.L., Jongeneelen F.J., Bragt P.C.  Actual health-related hazard from solvents to maintenance painters. Ann. Occup. Hyg. 29 (1985) 198.

Schneider H.  Truncated and censored samples from Normal populations (Statistics, textbooks and monographs ; vol 70) New York: Marcel Dekker (1986) 69 and 88 {a 10Log transformation of the data of Gupta (1952)}, 70 and 224.

Swaen G.M.H., Bloemen L.J.N., Twisk J., Scheffers T., Slangen J.J.M., Sturmans F.  Mortality of workers exposed to acrylonitril JOM 34 (1992) 801-809.


F.3 Further readings

AIHA  Quality assurance manual for industrial hygiene chemistry. American Industrial Hygiene Association. Prepared by the Analytical Chemistry Committee of the AIHA. (1988).

Aitchison J., Brown J.A.C.  The Lognormal distribution. Cambridge University Press (1957) Edition 1976.

Ali M.M., Chan L.K.  On Gupta's estimates of the parameter of the Normal distribution. Biometrika 51 (1964) 498-501.

Cohen A.C.  Simplified estimators for the Normal distribution when samples are single censored or truncated. Technometrics 1 (1959) 217-237.

Corn M., Esmen N.A.  Workplace exposure zones for classification of employee exposures to physical and chemical agents. Am. Ind. Hyg. Assoc. J. 40 (1979) 47-57.

Hall I.J., Sampson C.B.  One-sided tolerance limits for a Normal population based on censored samples. J. Statist. Comput. Simul. 2 (1973) p 317-324.

Hering S.V.  Air sampling instruments for evaluation of atmospheric contaminants. 7th edition. Am Conf. Governm. Ind. Hygienists Cincinnati (1989).

Hertig B.A. Work in hot environments: Threshold Limit Values and proposed standards. In: Industrial Environmental Health, The Worker and the Community. New York: Academic Press (1975) 219-231.

Kennedy W.J. Gentle J.E.  Statistical computing. Chapter 5: Approximating probabilities and percentage points in selected probability distributions. Statistics: textbooks and monographs. Vol 33 (1981) 61-132.

Kromhout H., et al  Agreement between qualitative exposure estimate and quantitative exposure measurements. Am. J. Ind. Medicine 12 (1987) 551-562.

Lewis H., et al  Aerodynamics of the human microenvironment. Lancet 1 (1969) 1273-1277.

Myers R.A., Pepin P.  The robustness of Lognormal-based estimators of abundance. Biometrics 46 (1990) 1185-1192.

Pirsig R.M.  Zen and the art of motorcycle maintenance. An inquiry into values (1974).

SKC  Guide to air sampling standards, Blandford Forum, UK, (1991).

Selvin S.  A graphical estimate of the population mean from censored Normal data. Applied Statistics 25 (1976) 8-11.

Theune J.A.  Comparison of power for the d'Agostino and the Wilk-Shapiro test of Normality for small and moderate samples. Statistica Neerlandica 27 (1973) 163-169.

Thöne H.,  A table for estimating the mean of a Lognormal distribution. Am. Stat. Assoc. J. 64 (1969) 632-636.

Zielhuis R.L., Wibowo A.A.E.  Standard setting in occupational health: Philosophical issues. Am. J. Ind. Med. 16 (1989) 569-598.


G Symbols and abbreviations

Greek letters α,β,γ,δ... are population parameters.

Latin letters A,D.... are sample estimates.

Symbol	name	description

α	alpha	Change, probability,

A	Sample estimator of chance á

Agem	Arithmetic mean of a series probabilities

A(W)	Probability distribution of Shapiro's W-test (1965)

AM	Finney's estimator of β

AMam	Direct, simple or arithmetic estimator of β

AMml	Maximum likelihood estimator of β

β	beta	Arithmetic mean of the Lognormal distribution. First moment

BLU	Best linear unbiased estimators (Schneider 1986 p57)

ci	Measured concentration in workplace air in period i

Ci	True concentration in the workplace air in period i

CT	True concentration in workplace air in reference period T

C(δ,α)	Calculated concentration overlying at least U% of the Lognormal distribution

Ç(δ,α)	Estimator of C(δ,α)

CI	Confidence Interval (two sided upper and lower limit)

CVt	Sampling an analytical measurement coefficient of variation (Leidel 1997 p78)

δ	delta	Confidence, reliability

ΔC	Grouping interval

D	Sample estimator of the confidence δ

d	Noncentrality parameter

df	Degrees of freedom

E()	epsilon	The expectation, the theoretical arithmetic mean of the probability distribution

EXP()	De exponential distribution with base e=2.71828...

EXP(μ)	Geometric mean of the Lognormal distribution

EXP(σ)	Geometric standard deviation of the Lognormal distribution

F	Deviate of the Fisher or variance ratio distribution

GM	Direct sample estimator of EXP(μ)

GMU	Unbiased sample estimator of EXP(μ)

GMG	Regression sample estimator of EXP(μ)

GSD	Unbiased sample estimator of EXP(σ)

GSDG	Regression sample estimator of EXP(σ)

H	Industrial hygiene limit value

SEG	Similar exposure group

INT()	Integer, a function to establish the value before the decimal point

Λ(μ,σ²)	Lambda	Lognormal distribution with descriptive statistics EXP(μ) and EXP(σ)

LCL	Lower confidence limit of a descriptive statistic

UTL	Lower tolerance limit of a distribution

LOG()	The natural logarithm with base e=2.71828...

μ	mu	The mean of a Normal distribution

M	The total sample size (censored and uncensored data)

M'	The number of results within the detection limits

Mτ	The population size (confined or expanded)

ML	Maximum likelihood

MM	Method of moments (Schneider 1986 p39)

MML	Modified maximum likelihood (Schneider 1986 p97)

N(0,1)	Standard Normal distribution with μ=0 and σ=1

OTL	One-sided tolerance limit

Π	Product of a series results

Ri	Rankit, normal order statistic, standard normal order expectations

RML	Restricted maximum likelihood (Schneider 1986 p100)

RSD	see CVt and ω/AM

σ	sigma	Standard deviation of the normal distribution

s	Sample estimator of σ

Si	Coefficient for the normal W-test

Σ	Sum of a series results

SQR()	The square root

t	Deviate of the Student distribution

ti	A sampled period within reference period T

tj	An unsampled period within reference period T

T	The duration of the reference period

Tσi	The sum of all sampled periods within the reference period T

Td	Deviate of the Noncentral Student distribution

ô	tau	The sum of all reference periods T

TI	Tolerance Interval (two sided upper and lower limit)

TWA	The arithmetic, time weighted average concentration within the reference period

U%	The desired percentage for confidence and tolerance limits

UCL	Upper confidence limit of a descriptive statistic

UTL	Upper tolerance limit of a distribution

W	The probability density function of the analysis of variance test for Normality (Shapiro 1965)

ω2	Variance of the Lognormal distribution. Second moment

ω/AM	The relative arithmetic standard deviation

xi	log(ci)	The natural logarithm of concentration ci

Direct estimator of the arithmetic mean μ of the Normal distribution

χ	Chi	Square root of the deviate of the Chi-square distribution

Z	Deviate of the standard Normal distribution  N(0,1).


H Terms and definitions

The explanations are based on Kendall (1982) or subsequently the most suitable term in literature. References between ().

•	Accuracy, the difference between the measurement and the truth (Hawkins 1991), the extent in which calculations or estimations, the true value approximate

•	Asymptotic unbiased or consistent estimator, an estimator which expectation equals the parameter by infinite sample size

•	Autocorrelation, the phenomenon that observations in a series are dependent upon the preceding

•	Averaging time, a period of time for which the measuring procedure yields a single result (prEN 482)

•	Bias, systematic error (Hawkins 1991 156). Consistent deviation of the results from the true value (ISO 6879)

•	Censored distribution, a distribution with a known fraction of observations outside the detection range (Hald 1949)

•	Confidence δ of one sided tolerance; (1-δ) the probability of accepting the desired compliance probability correctly (Tuggle 1982)

•	Confidence (in relation to a fraction), the chance that the tolerance interval contains the desired fraction of the population

•	Confidence (in relation to the parameter), the chance that the confidence interval contains the parameter of estimation

•	Consistent estimate, see Asymptotic unbiased estimator

•	Degrees of freedom, the mutually independent, number of elements in a sample from the distribution

•	Descriptive statistic, a number representing a probability distribution

•	Dispersion, variance (Sarhan)

•	Effectivity, Effectiveness the combined minimum of systematic (bias, accuracy) and random errors (efficiency, variance, precision). Increases if the systematic error of the first and second kind and the random error decrease

•	Efficiency, according to Fisher (1921) an estimator is efficient if his population variance is the smallest (Kendall)

•	Error of the second kind, accepting an invalid hypothesis. Also specificity (rejecting compliance)

•	Error of the first kind, rejecting a valid hypothesis. Also sensitivity (detecting non-compliance)

•	Error, see effectivity

•	Estimate, the value of the estimator (Kendall)

•	Estimator, a rule or method to estimate a constant in the population (Kendall)

•	Expectation, the arithmetic mean of a probability distribution

•	Extrapolation, to estimate the value a variable outside its tabulated or observed range

•	Fraction, the number of elements of a population with a given property, divided by the size of the population

•	Similar exposure group, a group of persons performing the same tasks and with a random exposure variability which overshadows the systematic in-between person variability (ad hoc).

•	A group of workers with identical probabilities of exposure to a single environmental agent (Hawkins 1991 page 5).

•	A group of employees who experience agent exposures similar enough that monitoring of any worker in the group provides data useful for predicting exposures of the remaining workers  (Hawkins 1991 page 160).

•	Inference, the process of deriving from assumed premises either the strict logical conclusion or one that is to some degree probable (The Random House college dictionary)

•	Interpolation, to insert, estimate or find an intermediate term (in a sequence)

•	Kurtosis, the fourth moment

•	Location, mean (Sarhan)

•	Lognormal descriptive statistics, location and variance parameters describing a Lognormal distribution

•	Maximum likelihood, one of the methods that provides estimators of the parameters of a parent population from samples. ML estimators fulfil certain criteria for consistency, efficiency and sufficiency. In fact ML estimators are consistent, tend to Normality for large sample size, have minimum variance in the limit at least, and provide sufficient statistics where such exist (Kendall 1947 volume II par..  17.22)

•	Median, the most central result or, in case that sample size is even, the arithmetic mean of the untransformed two most central data.

•	Minimum variance estimate, a method of calculating an estimator with the characteristic of maximum efficiency

•	Modus, the value in a distribution with the highest frequency.

•	Monomorphic group, A group of workers whose individual mean exposures compromise a single log-normal distribution. Term introduced by Rappaport (1991 page 66) but should be avoided. See Similar exposure group.

•	Mutually independent, in opposite with autocorrelation

•	non-compliance probability, the population fraction measurements over the industrial hygiene limit value

•	Occupational exposure assessment, comparing exposure with the limit value (prEN 689)

•	Omnibus, term used by d'Agostino (1971) to characterise tests on shape that combine aspects of both skewness and kurtosis

•	Performance, general requirements on the effectiveness of the exposure assessment (prEN 482)

•	Periodic measurements, the regular check if exposure conditions have changed (prEN 689)

•	Population, collection of elements on which the conclusions of the statistical evaluation are related to

•	Power, the chance of rejecting a unvalued null hypothesis

•	Precision, random error

•	Precision, the size of the deviation from the mean of the observations (Hawkins 1991 163) the closeness of agreement between the results obtained by applying the method several times under prescribed conditions (prEN 482)

•	Random drawing, taking an element from a population with a method that is independent of all properties of the element

•	Range of accuracy, the values for which the measurements are considered to be reliable

•	Reliability, see confidence

•	Robust, the property of a test that it works well for a wide variety of population types (Snedecor 1980 p 135)

•	Rankit, the expectation of the standard normal ordering (Fisher 1938)

•	Reference period, the specified period of time stated for the limit value of a specific agent (prEN 689)

•	Sample, a series drawings from a population

•	Scale, variation

•	Selectivity, degree of independence from interferents (prEN 482)

•	Skewed distribution, an asymmetrical distribution (Kendall)

•	Sustainment, the capacity of individuals or groups to bear exposure

•	Truncated distribution, a distribution with an unknown proportion result outside the measurement reach (Hald 1949)

•	Upper tolerance limit, the upper boundary containing at least the desired fraction of the population

•	Unbiased estimator, an estimator with the characteristic that the expectation equals the parameter for every sample size

•	Workplace, the defined area or areas in which the work activities are carried out.


Accuracy

The difference between the measurement and the truth (Hawkins 1991), the extent in which calculations or estimations, the true value approximate


Asymptotic unbiased

Asymptotic unbiased or consistent estimator: An estimator which expectation equals the parameter by infinite sample size


Autocorrelation

the phenomenon that observations in a series are dependent upon the preceding


Averaging time

a period of time for which the measuring procedure yields a single result (prEN 482)


Bias

systematic error (Hawkins 1991 156). Consistent deviation of the results from the true value (ISO 6879)


Censored distribution

A distribution with a known fraction of observations outside the detection range (Hald 1949)


Confidence d of one sided tolerance

(1-δ) the probability of accepting the desired compliance probability correctly (Tuggle 1982)


Confidence (in relation to a fraction)

The chance that the tolerance interval contains the desired fraction of the population


Confidence (in relation to the parameter)

Confidence (in relation to the parameter), the chance that the confidence interval contains the parameter of estimation


Consistent

•	Consistent estimate, see Asymptotic unbiased estimator


Degrees of freedom

The mutually independent, number of elements in a sample from the distribution.


Descriptive statistic

A number representing a probability distribution


Detection range

see range of accuracy


Dispersion

Variance (Sarhan)


Effectivity, Effectiveness

The combined minimum of systematic (bias, accuracy) and random errors (efficiency, variance, precision). Increases if the systematic error of the first and second kind and the random error decrease


Efficiency

According to Fisher (1921) an estimator is efficient if his population variance is the smallest (Kendall)


Error of the second kind

Accepting an invalid hypothesis. Also specificity (rejecting compliance)


Error of the first kind

Rejecting a valid hypothesis. Also sensitivity (detecting non-compliance)


Error

See effectivity


Estimate

The value of the estimator (Kendall)


Estimator

A rule or method to estimate a constant in the population (Kendall)


Degrees of freedom

The number of degrees of freedom for the censored and non-censored case are calculated using:

    If DetecNumAantal < M Then

        Nu = (M + DetecNumAantal)  2 - 1

        If Nu > 2 * DetecNumAantal Then Nu = 2 * DetecNumAantal

    Else

        Nu = M - 1

    End If

With:

M is sample size

DetecNumAantal is the uncensored number of measurements

Nu is the Number of degrees of freedom


Expectation

The arithmetic mean of a probability distribution


Extrapolation

•	To estimate the value of a variable outside its tabulated or observed range


Fraction

The number of elements of a population with a given property, divided by the size of the population


HEG

•	A group of workers with identical probabilities of exposure to a single environmental agent (Hawkins 1991 page 5).

•	A group of employees who experience agent exposures similar enough that monitoring of any worker in the group provides data useful for predicting exposures of the remaining workers  (Hawkins 1991 page 160).

see also Similar Exposure Group


Inference

The process of deriving from assumed premises either the strict logical conclusion or one that is to some degree probable (The Random House college dictionary)


Interpolation

To insert, estimate or find an intermediate term (in a sequence)


Kurtosis

The fourth moment


Location

Mean (Sarhan), the first moment


Lognormal descriptive statistics

Location and variance parameters describing a Lognormal distribution


Maximum likelihood

One of the methods that provides estimators of the parameters of a parent population from samples. ML estimators fulfil certain criteria for consistency, efficiency and sufficiency. In fact ML estimators are consistent, tend to Normality for large sample size, have minimum variance in the limit at least, and provide sufficient statistics where such exist (Kendall 1947 volume II par..  17.22)


Median

The most central result or, in case that sample size is even, the arithmetic mean of the untransformed two most central data


Minimum variance estimate

A method of calculating an estimator with the characteristic of maximum efficiency


Modus

The value in a distribution with the highest frequency.


Monomorphic group

A group of workers whose individual mean exposures compromise a single lognormal distribution. Term introduced by Rappaport (1991 page 66) but should be avoided. See Similar exposure group.


Mutually independent

In opposite with autocorrelation


Noncompliance probability
non-compliance probability

The population fraction measurements over the industrial hygiene limit value


Occupational exposure assessment

Comparing exposure with the limit value (prEN 689)


Omnibus

Term used by d'Agostino (1971) to characterise tests on shape that combine aspects of both skewness and kurtosis


Performance

General requirements on the effectiveness of the exposure assessment (prEN 482)


Periodic measurements

The regular check if exposure conditions have changed (prEN 689)


Population

Collection of elements on which the conclusions of the statistical evaluation are related to


Power

The chance of rejecting a unvalued null hypothesis


Precision

•	Random error

•	The size of the deviation from the mean of the observations (Hawkins 1991 163)

•	The closeness of agreement between the results obtained by applying the method several times under prescribed conditions (prEN 482)


Random drawing

•	Taking an element from a population with a method that is independent of all properties of the element


Range of accuracy

The values of measurement resluts which are considered to be reliable.


Reliability

See confidence


Robust

The property of a test that it works well for a wide variety of population types (Snedecor 1980 p 135)


Rankit

The expectation of the standard normal ordering (Fisher 1938)


Reference period

The specified period of time stated for the limit value of a specific agent (prEN 689)


Sample

A series drawings from a population


Scale

Variation


SEG

See Similar exposure group


Selectivity

Degree of independence from interferents (prEN 482)


Similar exposure group

•	A group of workers performing the same tasks on the average and with a long term exposure variability that outshines any systematic between worker exposure variability (ad hoc).


Skewed distribution

An asymmetrical distribution (Kendall)


Sustainment

•	he capacity of individuals or groups to bear exposure


Truncated distribution

A distribution with an unknown proportion result outside the measurement reach (Hald 1949)


Upper tolerance limit

•	The upper boundary containing at least the desired fraction of the population


Unbiased estimator

An estimator with the characteristic that the expectation equals the parameter for every sample size.


Workplace

The defined area or areas in which the work activities are carried out.


J About the author

Theo Scheffers is awarded in Environmental Health and Hygiene in 1979 at the Agricultural University in Wageningen on a study on the concentrations of Tetrachloro Ethylene in the breathing air of neighbours of dry-cleaning shops.

In 1979 he joined the occupational health research institute TNO-MBL.

Performed a health hazard survey among painters working in the Dutch construction industry (industrial hygiene measurements, toxicological evaluation of substances, developing an algorithm to assess and evaluate effect specific risk of exposure to different substances, group analysis of health surveillance outcome, epidemiological evaluation of causes of painters early retirement . In 1981 he joined the DSM Chemical company to manage the industrial hygiene activities on an industrial site of 750 ha with 51 chemical plants and 7000 employees.

Followed in the eighties several post-doc courses on biostatistics and epidemiology and performed and cooperated in several epidemiology studies. The exposure assessment in health and hygiene surveillance became the main branch of interest and from both that and the passion for industrial hygiene, statistics, computers and communication, the computer program HYGINIST evolved.

In 1989 joined the Dutch Occupational Hygiene Society's Limits and Measurement Methods Group, chair between 1991 and 1997.

As a spin-off the computer program www.dohsbase.nl with the largest library of health based occupational limit values and measurement methods is developed.

Full member of the American Industrial Hygiene Association AIHA's Exposure Assessment Strategies Committee and the WEEL committee in the nineties. In 1994 I incorporated the industrial hygiene education, consultancy and publishing activities in Scheffers IHPC and later on in TSAC.

Developing and writing the approach, the program and the enplaning manual started in 1980, as a spin-off of the painters exposure assessment. The biostatistical training and courses of Max Weinants (TNO) and Henk de Jonge (Universty Leiden) were a real inspiration for this work. Within DSM many small and large series exposure measurement really demanded statistical analysis

The first public MS DOS version in Dutch appeared in September 1987.

The first English version of HYGINIST was first presented at the AIHCE 1990, May 13-18 in Orlando Florida.

Theo Scheffers is a self-employed consultant (www.tsac.nl), living in Maestricht (the Netherlands) one of Europe's finest cities and in the Auvergne one of most beautiful regions in France.


Example 1 Reanalysing exposure data by adapting the number of degrees of freedom

*.HYG file	Description

HAW117	To make a file of the 15 TWA8 hour total dust measurement results from

Hawkins (1991 page 117), enter the sample size M=15.

SCHNE224	To estimate the survival duration of items under stress, based on

only the 15 items (Schneider 1986) who failed before the end of

the observation duration (6 TU's), enter M=15 and the rankit estimators

 GMg=9.1 and GSDg=2.12 (see Figure 5)


Example 2 Entering raw data

*.HYG file	Description

HAW117	Enter the 15 TWA8 hour random collected total dust samples

(OEL 10 mg/m3) from a similar exposure group

(Hawkins 1991 page 117) in an arbitrary order

2.9, 1.3, 2.8, 1.8, 2.1, 2.5, 2.1, 2.2, 1.9, 2.0, 2.5, 1.8, 2.2, 2.4, 2,5


Example 3 Range of accuracy

*.HYG	Description

HAW104	An 'Acid Operator' in a (hypothetical) Sodiumchlorine plant

is measured for chlorine gas. 10 random TWA8 hour workplace

air exposure samples were collected (Hawkins 1991 p 104).

The results in ascending order are

<.1, <.1, <.1, .1, .2, .2, .3, .3, .4, .5 PPM.

The lower accuracy limit of the measurement technique is .1 PPM.

Because one result is exactly .1 and three results are <.1,

the lower detection limit is established at .05.

The following data are entered

.05, .05, .05, .1, .2, .2, .3, .3, .4, .5  in a file called HAW104.HYG.


Example 4 Enter GM and GSD

*.HYG file	Description

-	To demonstrate "minimise sample size" in routine

long-term compliance control,

GSD=EXP(1)=2.71828 and GM=1 are entered

using the file name MU0SIG1.HYG.

OWEN716	Reanalyse the airborne Chlorine TWA8 hour (Owen 1980 p716)

using only the 8 uncensored grab sample data  within the

accuracy range of .25 and 9 PPM. Enter (See Figure 4)

in Screen 3a M=8 and in Screen 7ab the estimators

GMg=.88 PPM and GSDg=6.81 (Continued in Example 10).


Example 5 Show raw data file

*.HYG file	Description

LEIDL103	To eliminate the fixed background concentration of .1 PPM HF in the file

LDL103_10	LEIDL103.HYG, subtract .1 PPM from all data and save the result as

LDL103_10.HYG

SCHNE224	Items of which life time under stress is the quality characteristic, are tested

(Schneider 1988 p224). The survival time of 15 items from a batch of 50

were 1.6, 2.0, 3.3, 3.3, 3.4, 3.5, 3.8, 4.4, 4.5, 4.5, 4.8, 5.0, 5.8, 5.9, 5.9.

(Schneider 1988 Table 7.2.). The remaining thrityfive exceeded the survival

time  6.0. Change the default value zero to 6.0


Example 6a Making a *.HYG file using Word

The datafile HAW104.HYG (<.05, <.05, <.05, 0.1, 0.2, 0.2, 0.2, 0.3, 0.3, 0.4,0.5) is made using Word. The following numbers are typed on an empty page:

.05,.05,.05,.1,.2,.2,.2,.3,.3,.4,.5

The file is saved by clicking the mouse on menu button <File>, <Save as>

Now choose option <text file> and type HAW104.HYG<Enter>

More convenient is entering the data in a column using the <Enter> key and save it as an text file.

.05

.05

.05

.1

.2

.2

.2

.3

.3

.4

.5


Example 6b Copying a *.HYG file from EXCEL

Quite often exposure databases are developped in Excel or have a download function to Excel.

The picture below shows an Excel sheet with the TWA measurement outcome of Benzene and Toluene workplace air samples taken on different days and different shifts among operators in a Similar Exposure Group (SEG).

In order to analyse the benzene exposure using HYGINIST just select the benzene measurements (the blue area) using the mouse and copy the outcome (Ctrl+C).

Now open Notepad or any other text editor and paste (Ctrl+v) the outcome.

Save the outcome as <Name>.hyg  ( type all files) in the map of choice

You can open the file <Name>.hyg in HYGINST using Loading a file


Example 7 Generating a Lognormal Monte Carlo *.HYG file using Basic

The file HALD151 with 500 rivet head diameters is easily made using dBase because outcome were allocated in only 9 grouping intervals (see Figure 24 [image]).

The dBase control centre was left using F10 and 'Exit to the dot prompt'. The following command lines were used:

•	Command CREATE <database name>

•	Field Name (W10 characters),

•	Field type <Numeric>,

•	Width 10 digits (including the decimal point and sign),

•	Dec     5 decimal places,

•	Index   N,

Press <Ctrl> + <End> to stop CREATE database.

Command a MODIFY COMMAND <program name> and program the following lines:

DO WHILE RECNO()<=500

APPEND BLANK

ENDDO

Press <Ctrl> + <End> to stop MODIFY COMMAND,

Command DO <program name>.

Now command the following lines from the dBase prompt

REPLACE <Field name> WITH 13.39 FOR RECNO()=>1   .AND. RECNO()<191

REPLACE <Field name> WITH 13.42 FOR RECNO()=>191 .AND. RECNO()<287

REPLACE <Field name> WITH 13.47 FOR RECNO()=>287 .AND. RECNO()<359

REPLACE <Field name> WITH 13.52 FOR RECNO()=>359 .AND. RECNO()<427

REPLACE <Field name> WITH 13.57 FOR RECNO()=>427 .AND. RECNO()<468

REPLACE <Field name> WITH 13.62 FOR RECNO()=>468 .AND. RECNO()<486

REPLACE <Field name> WITH 13.67 FOR RECNO()=>486 .AND. RECNO()<498

REPLACE <Field name> WITH 13.72 FOR RECNO()=>498 .AND. RECNO()<500

REPLACE <Field name> WITH 13.77 FOR RECNO()=500

for entering the measurement results in the *.DBF file. Finally command a

COPY TO HALD151.HYG FIELD <Field name> DELIMITED

for making the HALD151.HYG file.


Example 8 Making a *.HYG file using dBase

With the algorithm of Abramowitz (1971, p 953, direct method) the 2000 deviates of the standard Lognormal distribution were generated and stored in the one-field ASCII delimited file (RANDOM20.HYG) using the following BASIC subroutine:

DIM C(2000)

L% = 0

RANDOMIZE CDBL(TIMER)

FOR I% = 1 TO 2000

 IF L% = 1 THEN

  Z = EXP(Y2 * V): L% = 0

 ELSE

  DO

   DO

    Y1 = 2# * CDBL(RND) - 1#

    Y2 = 2# * CDBL(RND) - 1#

    W = Y1 ^ 2 + Y2 ^ 2

   LOOP WHILE W >= 1#

   V = SQR(-2 * LOG(W) / W)

   Z = EXP(Y1 * V): L% = 1

  LOOP WHILE Z <= 1D+300# AND Z >= 1D-300#

 ENDIF

 C(I%) = Z

NEXT I%


Example 9 Rankit plots

*.HYG file

LEIDEL67	This example (Leidel 1977 p67) is used in this manual to explain the

NIOSH method for the calculation of geometric mean of long-term

exposure and the use of the probability of non-compliance when

deciding whether to install engineering control (see 5.1.2). On 10

different days in a period of 6 months an employee's TWA8 hour Dioxane

(H=100 PPM) concentration was measured (see Figure 1)

SOLV198	In a Health Hazard Survey among maintenance painters a stratified

sampling programme was performed in order to estimate

the current range of total Hydrocarbon exposure (in mg/m3)

during solvent based paint rolling and spraying (Scheffers 1987).

45 TWA8 hours were measured.

Although there was no randomisation by purpose, the goodness-

of-fit with the Lognormal model is appropriate (see Figure 2).

The two-sided tolerance limits (1-2α) are compared with the one-sided

tolerance lower (1-α) and upper (α) limit (continued in Example 31).

POSTB11I	Among a group inlayers in a fibreglass reinforced polyester

product manufacturing plant (Post 1989, 1991)

14 TWA8 hour 's styrene vapour were measured.

Figure 3 shows the characteristics of a mixed population situation:

two curved lines linked at an angle.

The study report confirms that the five lowest measurements

were taken at a different press than the highest nine.

To compare both populations see Example 39.

OWEN716	At an industrial site in the US, 15 grab sample airborne Chlorine

concentrations were gathered over a working day (Owen 1980 p716)

in order to classify for the federal TWA8 hour standard of 1 PPM.

The results are 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.50, 1.00, 1.00,

2.00,2.00, 6.00, 6.00, 6.50, 9.00 PPM.

The goodness-of-fit is poor (see Figure 4).


Example 10 Upper limit

*.HYG files	Description

SCHNE224	The survival of items under stress is Lognormal distributed (Schneider 1986 page

224). When the (accelerated) lifetime is above 1 time units (TU) an item conforms

the quality limit. 35 items out of a sample of 50 survived 6 time units (TU).

The results with an upper limit at 6 TU are plotted in Figure 5.

SCHNE70	Schneider (1986 example 4.3 page 69) used a sample of 96 locomotives with 37

failures before the (type I) upper censor point of 135,000 miles, assuming a

Lognormal distribution. This seems to be justified by the rankit Figure 6.

OWEN716	In order to classify the TWA8 hour exposure using 15 grab sample, detection tube

Chlorine concentrations  both upper (9 PPM) and lower limit (.25 PPM) should be

used (Owen 1980 p716). See Example 19 for more files with upper limits.


Example 11 Lower limit

*.HYG file	Description

LEIDL103	Hydrogen Fluoride exposure near a control panel in a production unit was measured

using a stationary grab sampler with a one-hour sequence (Leidel 1977 page 103).

The results are  0.11, 0.11, 0.12, 0.14, 0.14, 0.21, 0.33, 0.8, 0.91,

1.3, 2.6 and 10.0 PPM. The cumulative frequency distribution lacks

Lognormality in the left tail (see Screen 17a). Continued in Example 20.

HALD151	The diameter of population rivet heads follows a Gaussian distribution with

μ=13.426 mm and σ=0.111 mm (Hald 1952 p148). A device with a lower detection

limit of 13.4 mm was used to measure a sample of 500 rivet heads (.HYG).

190 diameters were below the detection limit.

The shape of the untransformed results are displayed in

Figure 24 (grouping interval 0.05 mm). Because of the small scale,

the shape of the sample conforms to both the Normal and Lognormal distribution.


Example 12 Rankit versus direct estimators

To show the effectivity of the rankit estimators a lower limit of 30 PPM was introduced in the 10 TWA8 hour (LEIDEL67.HYG) PAS Dioxane sample (Figure 1). Because this limit is between the default .9*C1 and C1 the rankit estimators are calculated from the complete sample: GMg=78.4 and GSDg=1.67. GSDg is about 2% higher than the direct estimator GSD=1.63 (see Example 17).


Example 13 Normal distributions

Conformity with other than the Lognormal distributions is found in the following examples from Table 1:

*.HYG file	Description	A(W)log 	A(W)unt

in %	in %

BAR_SI25	Carbon monoxide grab samples	64.4	79.5

HAW117	15 TWA8 hour total dust (Figure 11, Example 57),	35.6	85.5

DEWELL42	10 Formaldehyde grab samples	6.6	39.9

LEIDEL56	8 TWA20 min Ethyl Alcohol (Figure 10) A(W)X²=99.2%	41.8	94.9

X07-10	30 concentrations of chemical X. Aunt is 	17.6	25.9

equivalent to Gustafson (1991 chapter 7)

who finds Aunt(0.9541)=25.2%,

CONOV195	50 two-digit numbers from telephone book. 	2.9	23.1

Wunt=.964 is exactly the same as calculated

by Conover (1980 p365)

LEIDEL63	5 Short period exposures Hydrogen sulphide 	94.8	95.5

(see Example 57).


Example 14  Comparing xcg and scg with estimators from literature

*.HYG file	Description

HALD151	The rankit estimators of the untransformed diameters of rivet heads (=13,4304 mm

and s=0,1098 mm Figure 24) are in close agreement with the ML estimators

(=13,429 mm and s=0,111 mm) of Hald (1952). Both estimations are

based on the M`=310 rivet heads above the lower detection limit of 13.40 mm.

The number of degrees of freedom is df=310+190/2-1=404.

The standard deviation scg=0.11 mm overshadows the grouping interval -C=0.05 mm.

Because of the small relative standard deviation scg/xcg=.00812, the Lognormal

model may be effective as well, with GMg=13.4 mm and GSDg=1.00815.

SARH212	Students measuring Strontium-90 concentrations in milk.

Introducing both a lower limit of LL=8 pCu/l and an upper limit of

10 pCu/l results in M`=5 uncensored data out of M=10 (see Figure 25).

The untransformed rankit estimators of μ and σ are xcg=9.33 pCu/l and scg=1.87 pCu/l

which are equal to the values calculated by Sarhan (1962 page 212).

HAW104	10 TWA's chlorine (.HYG). 3 Below LL=.05 PPM. The untransformed Normal probability

plot (Figure 8) shows an almost perfect regression through the uncensored data.

The Normal descriptive statistics are xcg=.1948 PPM and scg=.1992 PPM.


Example 15 Other transformations

Conformity with other distributions than the Lognormal is found in the following examples from Table 1:

*.HYG file	Description

BILAN304	Bilan (1989 p304) indoor sprayer with MDI exposure:

A(W)log=43.7%, A(W)lglg=83%,

DEWELL24	Dewell (1989 p24) dust in foundry: A(W)log=34.3%, A(W)lglg=82%,

LEIDEL56	Leidel (1977 p56) 8 TWA20 min Ethyl Alcohol (Figure 10):

A(W)log=41.8%, A(W)unt= 94.9%, A(W)X²=99.2%


Example 16 Conformity with the Lognormal model. 28 files with A(W)>=5%
Example 16	Conformity with the Lognormal model. 28 files with A(W)≥5%

*.HYG file 	Description of the exposure data	Shapi	A(W)	Lognormal

name	ro W	in %	Conformity

LEIDEL67	10 one worker TWA8 hour PAS Dioxane (Figure 1)	0.99	99.5	Good

LEIDL104	24 TWA8 hour PAS Methyl Methacrylate (Figure 21)	0.99	97.3	Perfect

LEIDEL63	5 one worker, one shift TWA10 min PAS CS2	0.99	94.8	Good

LEIDEL61	35 random, momentary workplace Ozone read off's	0.98	92.1	Good

POST10P5	4 one worker, one press TWA8 hour PAS Styrene	0.98	90.4	Good

RANDOM20	2000 Standard Lognormal deviates	0.99	87.5	Good

BAR_SI25	6 Carbon monoxide grab samples	0.94	64.4	Rejected

DEWELL44	11 SEG TWA8 hour PAS welding [MIG] fume	0.94	51.4	Acceptable

POST08P4	5 one worker, one press TWA8 hour PAS Styrene vapour	0.92	50.8	Acceptable

LD103_10	12 corrected grab sample HF correction (Figure 13)	0.94	50.7	good*

COHEN132	20 maximum flood levels (Figure 14)	0.96	49.4	good*

BILAN304	5 TWA8 hour Methylene bisphenyl isocyanate. (Figure 9)	0.91	43.7	Acceptable

LEIDEL56	8 TWA20 min PAS Ethyl alcohol vapour (Figure 10)	0.92	41.8	Acceptable

CHIP123	10 TWA8 hour PAS lead dust	0.93	40.0	Acceptable

MOF134S	16 TWA10-30 min Methoxyfluorane. Scavenged (Figure 20)	0.90	37.2	Acceptable*

HAW117	15 SEG, random TWA8 hour PAS total dust	0.94	35.7	Acceptable*

DEWELL24	8 one worker TWA8 hour PAS on foundry respirable dust	0.91	34.3	Rejected

SOLV198	45 housepainter TWA8 hour PAS Hydrocarbon (Figure 2)	0.97	33.9	Acceptable

BOLEY62	12 one worker TWA8 hour PAS total dust (Figure 12 page 38)	0.93	33.4	Acceptable*

ALBRE220	4 PAS TWA8 hour Aspartame total dust	0.87	29.2	Acceptable

POSTB11I	14 TWA8 hour PAS Styrene vapour (Figure 3)	0.93	29.0	Rejected

X07-10	35 concentrations of chemical X	0.94	17.6	Rejected

GUPTA271	10 mice, survival (Figure 26)	0.89	14.8	Acceptable*

HAW104	10 random TWA8 hour PAS Chlorine (Figure 8)	0.87	10.1	Rejected

POST1008	combination of POST08P4 and POST10P5	0.85	7.6	Rejected

MOF134NS	16 TWA<30 min Methoxyfluorane. Nonscavenged (Figure 19)	0.90	7.6	Acceptable*

DEWELL42	10 TWA10 min PAS on formaldehyde	0.86	6.6	Rejected

LEIDL103	12 stationary, grab sample HF, one hour sequence	0.87	6.6	Rejected

*conformity decision after censoring


Example 17	Conformity with the Lognormal model based on the graph. Complete files with A(W)log<5%

*.HYG file 	Description of the exposure data	Shapi	A(W)	Lognormal

name	ro's W	in %	Conformity

SCHNE70	failure distance of 96 locomotives (Figure 6)	0.62	1.27D-37	very good

SCHNE224	survival of 50 items under stress (Figure 5)	0.54	8.6D-16	Good

OWEN716	15 grab sample airborne Chlorine (Figure 4)	0.83	0.97	Acceptable


Example 18 Comparing samples with literature data

*.HYG file	Description

LEIDL104	24 TWA8 hour Methyl Methacrylate results in GM=34.5 PPM and GSD= 1.89

LEIDEL67	10 TWA8 hour Dioxane (see Figure 1) result in GM=78.4 PPM and GSD= 1.63.

CHIP123	10 TWA8 hour lead result in GM=2.19 and GSD=1.78.

The first two series provide estimators of the descriptive statistics which are equal to the literature values (Leidel 1977 pages 67 and 104). Booher (1988) calculated GM=2.36 and GSD=1.76 from the lead exposure data among chippers. The difference cannot be explained.


Example 19 df, GMg and GSDg of censored Lognormal samples

*.HYG file 	Description of the exposure data	Sample units	LL	UL	uncen-df	GMg	GSDg

Name	Size	sored

M	M`

BOLEY62	TWA8 hour PAS papermill total dust	12	mg/m3	2.0	-	9	9	4.71	3.35

COHEN132	maximum flood levels	20	106	0.27	-	18	18	0.40	1.34

ft3/sec

DEWELL24	TWA8 hour respirable dust in 	8	mg/m3	1.3	2	6	6	1.22	1.56

foundry

DEWELL44	TWA8 hour PAS welding [MIG] fume	11	mg/m3	-	18.0	9	9	11.12	1.74

GUPTA271	mice survival after inoculation	10	days	-	65.0	7	7	56.0	1.24

with tuberculosis

HAW117	TWA8 hour PAS total dust	15	mg/m3	1.7	-	14	13	2.19	1.19

LEIDL103	stationary, grab sample, 	12	PPM	0.14	-	7	8	0.29	8.27

one hour sequence HF

OWEN716	grab samples airborne Chlorine	15	PPM	0.25	9.0	8	10	0.88	6.81

SCHNE224	survival of items under stress	50	TU	-	6.0	15	30	9.1	2.12

SCHNE70	failure distance of locomotives	96	103 	-	135.0	37	65	174.2	2.12

miles

SCHNE224.HYG the number of degrees of freedom is established as df=2*15=30 [because (50+15)/2-1D2*M]. All others df=(M+M`)\2-1.


Example 20 Correcting exposure variability for a fixed background

*.HYG file	Description

LEIDL103	The Lognormal probability plot on M=12 successive Hydrogen fluoride

concentrations (Leidel 1977 p103-104) clearly shows the fixed background

exposure level of about 0.1 PPM additional to Lognormal variation.

LD103_10	If 0.1 PPM is subtracted from all results of LEIDL103.HYG,

then GM=.18 PPM and GSD=9.75: exactly the same as the values calculated

by Leidel (1977 p103). The probability plot, however suggest the need

to introduce a lower limit of .01 PPM and this results in rankit estimators

of M'=10, GMg=0.16 PPM and GSDg=13.9: somewhat more accurate

Than the estimators read by Leidel (1977, figure I-4 page 104) from the

Probability plot GM=.16 and GSD=(84% value)/(50%value)=12.8.


Example 21 Comparing GMg and GSDg with estimators from literature

*.HYG file	Description

SCHNE224	GMg=9.1 and GSDg=2.12 (see Figure 5) of items under stress are

in close agreement with the biased corrected, restricted ML estimators

GM=10.942=8.7 TU and GSD=10.3123=2.05 (Schneider 1988 p 224).

LEIDL104	Leidel (1977 p105) estimates GM=34 PPM and GSD= 1.9 from the

Lognormal probability plot on 24 TWA8 hour Methyl Methacrylate

concentrations in the job category "Mix man". Introducing a

virtual lower limit of LL=8 PPM in Screen 17d (see Figure 21), results in

GMg=34.5 PPM and GSDg=1.91 PPM based on the complete M`=24 data.


Example 22 How to establish sample size from GM and GSD

6 TWA8 hour total dust samples from a hypothetical homogeneous population (with known μ=-0.1, σ=1) results in the GM and GSD values which are displayed in Screen 7ab. The gravimetric total dust TWA8 hour method has a CVt=0.25 (Leidel 1977 table D-1) which is smaller than the displayed sample relative standard deviation w/AM=1. Thus, Lognormality is not overshadowed by measurement error. The minimal sample size for long-term compliance control with H=10 mg/m3 and U=95% is estimated in chapter 7.


Example 23 Exceeding the limit (censored non-parametric)

*.HYG file	Description

HALD151	If one wishes to know what percentage of diameters of rivet

heads (Hald 1952) are below 13.3 mm, then Screen 21a will respond

"Between 0 and 38%" because of the lower detection limit of 13.40 mm

SCHNE224	The upper accuracy limit at 6 Time Units (Schneider 1988 page 224)

for the items under stress, inhibits the Nonparametric estimation

of the number of items exceeding 10 TU (see Figure 5).


Example 24 Using 95% as default

Nearly every application of statistics uses 95% as default extrapolation value, or its complement 5% as significance level:

•	Leidel (1977 page 69) uses in the compliance control α>0.05 to indicate that control measures are necessary.

•	The European-based Dutch legislation on Vinylchloride requires 95% confidence that the average annual concentration in the workplace air, calculated from sequential measurements, is below the limit value TWA1 year.

•	According to Leidel (1977 page 118) an employer should try to attain 95% confidence that no more than 5% of the employee days are over the limit value.

•	The one-sided tolerance (OTL) approach of Tuggle (1981 page 497) questions "Are we 95% confident that less than 5% of all exposures received in the workplace are above the PEL?"

•	In the 8 hour labour service, α=0.05 corresponds with a 24 minutes period and with 1 out of 20 shifts.


Example 25 Two-sided interval

In order to calculate the two-sided 95%:

•	confidence interval of the arithmetic mean by using the method of Jahr while running the procedure "Classification for TWA limit/Cumulative dose." (Screen 24, par. B.2.),

•	tolerance interval running the procedures "effectiveness of control measures" from NIOSH or Wilks (Screen 25 and Screen 26),

the desired percentage should alternate between U=2.5% and U=97.5%


Example 26 NIOSH tolerance limits and compliance probability

*.HYG name	File description	Size	units	df	H	AC>H %	ÇUW5%	ÇUD95%

LEIDEL67	TWA8 hour Dioxane	10	PPM	9	100	31.0	35.1	175.4

LEIDL104	TWA8 hour Methyl methacrylate	24	PPM	23	100	4.7	12.1	98.0

RANDOM20	standard Lognormal deviates	2000	-	1999	-	-	0.19	5.11

SCHNE70	Locomotive controls	96	103 miles	37	-	-	50.7	598.4

See Example 28 for more details.


Example 27 	Calculating standard normal tolerance limits from literature sources

*.HYG file	description

LEIDL104	With 24 TWA8 hour Methyl methacrylate in the job category "Mix man",

the NIOSH non-compliance probability is AC>H=4.7 %

(see screen 25 and Example 26).

Engineering controls are not necessary (Leidel 1977 p104).

This conclusion contrasts with the unbiased method (see Example 29).

LEIDEL67	Leidel (1977  4.4 p65) utilised 10 TWA8 hour Dioxane (see Figure 1) to illustrate

the NIOSH method of using the probability of non-compliance to decide

if engineering controls should be installed. The non-compliance probability

AC>H=31% equals Pn=.0309 calculated by Leidel (1977 page 69).

Since non-compliance is so obvious, there is no reason to criticise the use of

the standard normal method because of its small sample size (see table 7).

RANDOM20	The 5th and 95th percentile values in the series 2000 Monte Carlo

standard Lognormal deviates are 0.1933 and 5.053,

and agree with the calculated values .1927 of 5.110 (see Example 26)

SCHNE70	The Lognormal fit (see Figure 6) and the number of failed locomotives are

such that standard Normal extrapolation is allowed (see table 4). Schneider

(1986 example 6.3) calculates the 10th percentile as 101.826+3=66,988 Miles

using the bias corrected estimators of μ and σ. The standard Normal

lower tolerance limit is almost equal: ÇUW10%=66,634 Miles.


Example 28 Wilks tolerance limits and compliance probability

*.HYG name	File description	Size	Units	df	H	AC>H%	ÇU≤5%	ÇU≥95%

BOLEY62	TWA8 hour PAS 	12	mg/m3	9	10	28.3	0.46	48.2

papermill total dust

COHEN132	maximum flood levels	20	106ft3/sec	18	-	-	0.23	0.68

DEWELL24	TWA8 hour respirable 	8	mg/m3	6	5	0.08	1.02	2.37

dust in foundry

DEWELL44	TWA8 hour PAS 	11	mg/m3	9	5	89.8	3.82	32.4

welding [MIG] fume

GUPTA271	mice survival after 	10	Days	7	-	-	36.2	86.6

inoculation with

tuberculosis

HAW117	TWA8 hour PAS 	15	mg/m3	13	10	7*10-5	1.59	3.02

total dust

SCHNE224	Survival of items 	50	TU	30	1	99.7	2.5	33.4

under stress

For SCHNE224 a lower quality limit is introduces of H=1 TU, which should be exceeded by 99% of the items.


Example 29	Unbiased estimate of the long-term TWA control effectiveness

*.HYG file	Description

LEIDEL67	The 10 TWA8 hour Dioxane, see Figure 1 and screen 25),

sampled on different days in a period of 6 months

on one employee are tested against the H8 hour=100 PPM.

Because GSD=1.63 and LOG(H/GM)=0.24 are both small,

the bias of the standard normal method is also small (see table 9).

The unbiased estimate AC>H=32.4% corresponds with

the Pn=.0309 calculated by Leidel (1977 page 69).

LEIDL104	With 24 TWA's in the job category "Mix man" in a facility using

Methyl methacrylate the unbiased estimate of the non-compliance

probability is AC>H= 5.7068 %, indicating (in deviation with the

NIOSH method see Example 27) that control measures are necessary.

VINCHL91	In a PVC production plant, the SEG polymerisation shift workers are monitored on

Vinylchloride using a routine plan using a stratified PAS TWA8 hour sampling plan

(every four weeks, one day, three consecutive measurements, around the clock).

The results since 1987 are displayed in the exposure control chart Figure 15.

A limit H8 hour=7 PPM is derived from the European Community exposure

limit HEC,1 year=3 PPM (EC 1978 L197/16). The Lognormal fit of the

37 TWA8 hour data in 1991 is complete (Figure 16 and AW=0.974=63 %).

With df=36, GM=0.37, GSD=2.73 unbiased estimate is AC>H=0.3 % and the upper

tolerance limit ÇU≥95%=2.1 PPM, indicating that the control measures are effective.

See Example 34 for the test against H1 year=3 PPM.

   -	In a sample with GSD=2.71828 the ratio upper tolerance limit/geometric mean is for:

df=1 -> C95%/EXP(μ)≥2182.

So compliance is reached if the geometric mean exposure EXP(μ) is below

0.05% of the limit value H. The lower accuracy limit of measurement methods

for contaminants in workplace air will in most cases not include H/2000.

Increasing df to infinite decreases C95%/EXP(μ)

asymptotically to the standard Normal ratio of 5.18 (see further chapter 7).


Example 30 Different number of degrees of freedom

*.HYG file	Description

SCHNE224	The survival of items under stress is Lognormal distributed (Schneider 1986 page

224; see Figure 5). If the (accelerated) lifetime is above 1 time units (TU), then an

item conforms the quality limit. 15 items out of a sample of 50 failed before 6 TU.

In a conservative approach, using df=M'-1=14, AC>1 TU=99.4% and Ç5%=2.3 TU,

indicates only a borderline difference from the values calculated in Example 29.


Example 31 Noncentral student tolerance limits

*.HYG file	Description

LEIDL104	The 24 TWA8 hours indicate that the confidence of being in compliance for

job category "Mix man" in a facility using Methyl methacrylate is δ=51%.

Thus consecutive sampling plans with M=24,

will have a chance of 51% of finding non-compliance probability αW5%.

SOLV198	From 45 TWA8 hours Hydrocarbons during solvent

based paint rolling and spraying the two-sided 95% tolerance limits

with δ=95% confidence (9.4 and 1076 mg/m3) were calculated

using the tolerance factor k7=2.408 from Ciba-Geigy (1980).

The one-sided tolerance factor for calculating the 2.5% and

97.5% limits with δ=95% is Tdf,α,δ=2.463 and provides 8.9-1141 mg/m3.

-	Tuggle (1981 p 491) evaluated 3 measurements

of 0.60, 0.58 and .63 with a PEL of 1.0.

The sample 10log=-0.22 (GM=0.6) and

s=0.02 (in real s=0.018 thus GSD=1.02).

With the use of the tolerance factor Tdf,α=5,δ=95=7.655 the

UTL=-0.22+7.655*.22=-0.08 is less than 10log(PEL)=0.

Only because of the unrealistic small sample GSD

this small sample size problem is in compliance.

SCHNE70	The 97.5% UCL of U=90% of the 96 locomotives,

With 37 failures before 135,000 Miles is estimated from the data presented

by Schneider (1986 example 6.3 page 202) as 547,016 Miles.

This mileage value corresponds, however, with

DC{α<10%}>547,016=90.5% for the Noncentral Student with df=65.

The tolerance limit calculated with table 1.4.1. of Odeh (1980) is

Çα<10%,δD97.5%,df=65=174,249*2.117181.657=603,883 Miles.

HAW117	From 14 random TWA8 hour PAS total dust

above LL=1.4 mg/m3 the one-sided upper tolerance limit including 90% of

the concentrations with 95% confidence and df=13 is H=3.1712 mg/m3.

This is comparable with the values calculated by Hawkins (1991)

page 140 table IV.2 bottom line (UTLc=3.06 and 3.29). See also Example 57.

-	In a sample with GSDD2.71828 the ratio upper tolerance limit/geometric mean is for:

-	df=1 º CδD95%,α<5%,df=1/EXP(μ)D2.5384*1011

-	df=2 º CδD95%,α<5%,df=2/EXP(μ)D2113.28

Due to the limitations in the industrial hygiene sampling/analytical methods, a

concentration of H/2000 is difficult to assess for most contaminants in workplace air.

Increasing df decreases CδD95%,α<5%/EXP(μ) asymptotically to 5.18.


Example 32	The UMP test for the arithmetic mean of a Lognormal distribution

*.HYG file	Description

HAW117	With 14 random TWA8 hour PAS total dust above LL=1.4 mg/m3

the chronic health hazard was tested. The plotting positions

y=10log(GM/H)=-0.66 and s=10log(GSD)=0.08 (see screen 24a)

falls inside compliance area of Nomogram 4.3 in Leidel

(1977 page 58). Since GSD is in part explained by CVt

(see Example 57), the situation is in real compliance.

LEIDEL56	With 8 TWA20 min  Ethyl alcohol PAS data the TWA8 hour

is classified against H=1000 PPM (Leidel 1977 page 56).

Entering y=0.002 and s=0.14 in the nomograms,

results that the situation is classified as possible

overexposure (like Leidel concluded 1977 p.57).

Because the location parameter GM is independent of CVt,

overexposure is real even without good knowledge of the

corrected GSD (see Example 57).

BAR_SI25	In an industrial plant 6 grab sample measurements of carbon

monoxide were performed for a particular employee at the hours

9, 10, 11, 12, 14, and 16. (Bar-Shalom 1975 page I-25).

If the resulting y= -0.02 and s=0.22 are entered

in the nomograms, then the situation is classified

as possible overexposure against a TWA8hour=50 PPM.

OWEN716	The 15 grab sample airborne Chlorine concentrations are

used to classify for a TWA8 hour standard of 1 PPM.

After introducing a two-sided accuracy range of 0.25-9 PPM the

rankit estimators are GMg=.88 PPM, GSDg=6.81 and df=10.

Extrapolation towards the plotting positions

y=-0.00 and s=0.67 for df+1=11 in Leidel (1977 figure 4.3.).

indicates possible over exposure (Owen 1980 p716)


Example 33	Comparing different estimators of the confidence interval of the arithmetic mean

Armstrong (1992 table II) calculated the two-sided 95% confidence limits for the 8 TWA20 min's Ethyl alcohol (LEIDEL56.HYG) using the exact (Land 1971) and four approximate methods. The maximum likelihood estimator of the aritmetic mean of this series is AMML=exp(+s²/2)=1058 PPM. The bottom line confidence limits are calculated with the approximate method using formula 5.13.

Method	two-sided 95%-tile in ppm

'Exact'	824	1437

simple Student	800	1294

Lognormal Student	808	1386

Cox	841	13322

modified Cox	802	1397

5.13	788	1402

Because the sample has a normal shape and GSD is small and completely explained by CVt (see Example 57 ), it is difficult to draw any solid conclusion. The approximate method 5.12 seems to have a high sensitivity of finding possible overexposure but a low specificity of rejecting compliance.

The exact procedure of Land (1988 6.1) used in HYGINIST provides a confidence range of 831.4 thru 1470 ppm, when entering  one-sided values of confidence D= 2.5% and D=97.5%


Example 34 Estimation of the average daily dose

*.HYG file	Description

ACN8_9	In a retrospective cohort mortality study (Swaen 1992) among Dutch

workers occupational exposed to Acrylonitrile (ACN), the average daily

dose was assessed using the exposure control chart (Figure 17) of the

similar exposure group (=SEG) ACN production workers. The M=116

PAS TWA8 hour ACN, sampled in 1977 and 1978, fit the Lognormal

model (see Figure 18) when a lower detection limit of LL=0.05 PPM is

introduced. The M`=56 uncensored data provides df=85 degrees of

freedom. Using the rankit estimators GMg=0.05 PPM and GSDg=7.3,

the average daily dose in 1977/1978 is, for this SEG, estimated as

AM1977-1978=0.37 PPM (90% confidence range of 0.25-0.53 PPM).

VINCHL91	The M=37 results of the Vinylchloride PAS sampling in a SEG PVC

polymerisation shift workers (see Example 29) sampled in 1991 fit the

Lognormal model (see Figure 16). With df=36, GM=0.36, GSD=2.90

the average daily dose is estimated as AM1991=0.60 PPM.

The compliance against the European Community exposure limit of

HEC=3 PPM (a one year average of all TWA8 hour's) is A(β>H)=10-9, indi

cating that the long term control measures are effective for this SEG.

HAW117	From 14 random TWA8 hour PAS total dust above LL=1.4 mg/m3

the chronic health hazard was assessed (see Example 57).

With AM=2.2 mg/m3 and H=10 mg/m3 the approximate probability

that β exceeds limit H is A(β>H)=7*10-12%. The two-sided 95%

confidence interval including β is 2.0-2.47 mg/m3.

Though the algorithms for the interval calculation by Hawkins (1991

page 130-133 approach 1 and 2) are quit different, the result (Hawkins

1991 page 134 table III.2 two last lines) are comparable (Normal

approach 1.97-2.43 mg/m3, Lognormal approach 1.93-3.42 mg/m3).

-	From formula 5.13, the Student table (Ciba-Geigy 1980) and GSD=2.71828

it follows that:

for df=1, Çβ,δ≥95%/β=552.1

for df=9, Çβ,δ≥95%/β=6.311.

If sample size increases, then Çβ,δ/β decreases towards unity.


Example 35  Estimation of grab sample based TWA

*.HYG file	Description

OWEN716	From GMg=.88 PPM, GSDg=6.81 and df=10 of the series grab sample

airborne Chlorine , the two-sided confidence interval is 1.3-11.7 PPM,

indicating real overexposure against H8 hour=1 PPM (Owen 1980 p716).

BAR_SI25	From GM=47.5 PPM and GSD=1.675 on carbon monoxide grab

samples a TWA8 hour=53.0 PPM is estimated. The probability that

β=TWA8 hour exceeds H8 hour=50 PPM is AßDH=59.4% (90%

confidence interval 33.3-84.3 PPM) indicating possible overexposure

(Bar-Shalom 1975 page I-25).

LEIDEL61	From 35 direct reading Ozone concentrations, the estimators of the

untransformed descriptive statistics μ and σ are =.0831 and s=.023 PPM.

The one-sided 95% upper confidence limit is calculated as UCL=.089

and the situation was concluded to be in compliance with the

H8 hour=.1 PPM (Leidel 1977 p61-62). Using formula 5.12 the 95% UCL

of β is Çβ,U%=95=0.090, which leads to the same conclusion.


Example 36 Compliance with a ceiling limit value (distribution free)

*.HYG file	description

-	After grab sampling M=480 (8 hours of 60 minutes) consecutive

periods on a shift with a non-Lognormal exposure distribution, the

confidence δ that Ceiling noncompliance probability is AC>H<1% is:

-	for k=0 -> D(480,0,0.01)≥99.2%

-	for k≤1 -> D(480,1,0.01)≥95.3%

using the cumulative binomial test in TRUE EPISTAT.

Using the Poisson distribution on these data (p is small, n is large),

with the number of cases expected 480*.01=4.8 and the number of

cases observed 1, results in DPoisson=99.23%. As could be expected

the Poisson value is similar to the cumulative binomial.


Example 37 Compiance with a ceiing limit value (distribution free)

*.HYG file	Description

LEIDEL63	5 short period exposures to Hydrogen sulphide were sampled and

tested against a ceiling of 20 PPM (Leidel 1977 page 65).

With A(W)=95%, GM=13.9 PPM and GSD=1.12 the NIOSH

noncompliance probability (screen 25) is AC>H=0.00073.

Because all 5 sampled periods were below the ceiling,

Leidel (1977 page 65) calculates the chance that the 16-5=11

nonsampled periods in the population are also in compliance as

Pc=(.9993)11=.992. In this example the following methodological

shortcomings can be stipulated:

- GSD is (almost) completely determined by CVt (see Example 57),

- The Normal shape is superior over the Lognormal,

- The standard normal method is biased for small sample size.

However, because the GSD is extreme small and overestimated,

the chance on exceeding the ceiling value in the 11 nonsampled

periods of this work situation, can be neglected.

-	A M=25 grab sample, exposure sampling plan from a complete

Lognormal distribution results in GM=1 and GSD=2.71818. With limit

H=10 the NIOSH noncompliance probability is calculated as

AC>H/100=0.01065 indicating that k=1 out of M=93 is in noncompliance.

The confidence that ceiling compliance is αC>HW5%, is estimated as

D(93,1,0.05)=95%.Using the Poisson distribution on these data with the

number of cases expected .05*93=4.65 and the number of cases

observed 1, results in D(4.65,1)=94.6%. As could be expected the

Poisson value is similar to the cumulative binomial. To get compliance

with the Poisson test the sampling plan should be increased to at least

95 grab samples.


Example 38 Compliance with a ceiling limit vaue (Noncentral Student)

*.HYG file	Description

LD103_10	The unbiased probability that a grab sample Hydrogen fluoride

concentration (Leidel 1977 pages 103-104) is above the ceiling limit of

3 PPM HF, based on M`=10, LL=.01 PPM, GMg=.258 PPM and

GSDg=13.87, is AC>H=19.9%. The confidence δ that Ceiling H is

exceeded α<1% of the times is estimated as D(Cα<1%>H)=7.89%

using the Noncentral Student (method 6 table 11). Since δ should

be more than 95%, control measures are necessary to get in

compliance with the ceiling.

LEIDEL63	5 TWAshort period Hydrogen sulphide were sampled and tested

against a ceiling of H=20 PPM (Leidel 1977 page 65). With M=5,

GM=13.9 PPM and GSD=1.12 the confidence δ that Ceiling H is

exceeded α<5% of the times is estimated as D(Cα<5%>H)=87.7%,

indicating noncompliance with the ceiling. Because the population is

confined (see Example 54) recalculating the confidence with df=5 is

permitted and results in D(Cα<5%>H)=91%. Since, however, the

sample variance is completely determined by CVt the compliance

conclusion can be drawn solely based on GM<H.

-	Using an imaginary, grab sample, exposure sampling plan with

GM=1, GSD=2.71828 and Ceiling H=100. If ceiling compliance is

defined as 100-δ=αW1%, then MD13 grab samples are sufficient:

D(Cα<1%>H)=99.2%


Example 39 Comparing two GSD's

*.HYG file	Description

POSTB11I, 	In a plant manufacturing fibreglass reinforced polyester materials,

POST08P4	14 Styrene PAS TWA8 hour concentrations were collected within a 15 days period

&POST10P5	 on 7 inlayers working at 5 different presses (Post 1989, 1991).

The Lognormal probability plot (see Figure 3) suggest a mixture of at least two

distributions and the raw data in the base report support this (Post 1989).

Four TWA8 hour concentrations from worker 8 at press 4 are compared with the

five TWA8 hour of worker 10 on press 5 (measured on nearly the same days).

The scale parameters GSD=1.21 and GSDref =1.14 (see screen 29b) are from the

same base: the two sided change AGSD=GSDref =57.4% (continued in Example 40).

VINCHL89 & VINCHL91	The exposure control chart Figure 15 of the TWA8 hour Vinylchloride in the SEG PVC

polymerisation shift workers since 1987 shows a loglinear decrease in exposure

over time. To quantify the decrease the 37 data of 1991 are compared with the 20

results of 1989. The scale parameters GSDdf=36=2.73 and GSDdf=20=4.97 differ

significantly with a two-sided probability AGSD=GSDref =1.5 % (continued in Example 41).

-	In the 1972-1974 randomized experiment in Colorado (Crow 1977 page 973),

the mean hail mass on Mn=16 nonseeded days was GMn=2.3632 with GSDn=7.9135

and on the Ms=17 seeded days GMs=3.3434 with GSDs=8.35.

Like Crow (1977), the calculated AGSDn=GSDs=92.53% supports the conclusion

that seeding does not influence the scale parameter of hail mass (continued in Example 40).

-	From the Variance ratio distribution table 26.9 of Abramowitz (1970), it can be derived that

two GSD's differ at a two-sided significant level of A=(2*QF¦df,df2)=5% for GSD=2.71828,

-	df=df2=1 and GSD2=1.11*10+11,

-	df=df2=8 and GSD2=8.21,

-	df=df2=30 and GSD2=4.22.

To establish differences in exposure variability with 1.4WGSDW3.5, large samples (M>30)

are needed.


Example 40 Comparing GM's while GSD's are equal

*.HYG file	Description

POST08P4 &	The Styrene PAS exposure level GM=38.6 PPM (see Example 9) from

POST10P5	worker 8 at press 4, is compared with GM=12 PPM of worker 10 on

press 5. Assuming equal GSD's (see Example 39) the two-sided

change AGM=GMref=0.002%  supports rejecting the null hypothesis:

The exposure level of inlayer 8 at press 4 is D3 times higher.

MOF134NS	The effectivity of scavenging on the Methoxyflurane exposure in the

MOF134S	breathing zone of veterinarian in small private practice, animal clinics

during surgeries was studied (Potts 1988 page 134). A comparison was

made between two series TWA10-30 min's measurements:

-	16 nonscavenged results (10 double censored data, Figure 19,

df=12) GM=0.48 PPM and GSD=5.7,

-	6 scavenged results (uncensored, Figure 20, df=5)

GMref=0.24 PPM and GSD2=2.9.The Wilcoxon rank sum test,

used by the authors, showed no statistical differences between

the two samples. Due to small sample size and large GSD the parametric

analogous with matching GSD's (AGSD=GSD2=29.4 %) also supports the

null hypothesis: scavenging does not influence exposure level (AGM=GMref=38.3 %).

-	The median hail mass GMn=2.36 on Mn=16 nonseeded days does not

differ from GMs=3.34 on the Ms=17 seeded days in the hail seeding

experiment in Colorado, (Crow 1977 page 973, example 5, exponential

transformation). The two sided probability A(GMn=GMs)=63.8%, based on

equal GSD's (see Example 39), supports the null hypothesis.

-	From the Student table 26.10 in Abramowitz (1970), it can be derived that

two GM's, from samples of equal size and scale, differ significantly at

two-sided A(t¦dft)=5% with GSD=2.71828,

-	dft=2 and GM/GMrefD 73.9

-	dft=16 and GM/GMrefD2.72

-	dft=60 and GM/GMrefD1.69.

With dfD10 and GSD≈2.7 significant differences in exposure level between

samples are easy to assess.	See also examples 41 and 42


Example 41 Comparing GMs while GSDs are unequal

*.HYG file	Description

VINCHL89&	Because the exposure variance between 1991 and 1989 differs

VINCHL91	(see Example 39) the location parameters for TWA8 hour

Vinylchloride in the SEG PVC polymerisation shift workers were

compared using the inference test of two GM`s with unequal GSD's.

Although the ratio of GM1989=0.83 PPM and GM1991=0.37 PPM is 2.2,

a significant difference is not confirmed: the two-sided probability for

dfpooled=27 is AGM=GMref=5.1%.

-	Illustrating the influence of unequal GSD's in comparing GM.

For M=M2=10, GSD=2.71828 and GSD2=7.43714 differ significantly.

AGM=GMrefW5% needs GMref/GMD4.6. This is 1.8 more than what is

necessary if the GSD's are equal (see paragraph 6.2.3.1 and

examples 40 and 41 ).


Example 42 Comparing two GSD's
Example 42 Comparing two GSDs

*.HYG file	Description

POST08P4&POST10P5	The GM and GSD's of Styrene PAS TWA8 hours of worker 8 at press 4

and worker 10 on press 5 (see Example 40, Example 39 and Post 1989),

are combined. The summed sample size is M+M2=9, the merged

GMt=23.5 PPM and the merged GSDt=1.8. These values are exactly

the same as when all raw date are combined (POST1008.HYG)

-	In a hypothetical fertilizer plant the plan is to perform a routine

program on total dust air sampling. In order to estimate an optimal

sample size two series of dust measurements from the past are

available, however, only the descriptive statistics were reported, the

raw data were lost. The sample estimators are:

-	M1=4, GM1=1.8 mg/m3  and GSD1=2.4

-	M2=4, GMref=2.24 mg/m3 and GSD2=2.4

Combining these descriptive statistics results in the following Mt=8,

GMt=2.00798 mg/m3 and GSDt=2.26803. Note that with equal GSD's

and GM's which are very close, the combined GSDt is smaller than in

the separate samples! See Example 46 for the assessment of the

optimal sample size.


Example 43 Censored sample confidence limits

*.HYG file	description

GUPTA271	In Example 53 (mice, inoculated with tuberculosis) different estimators

of EXP(μ) and EXP(σ) are compared. Using the rankit estimators, df=7

and the confidence factors the two-sided 95% CI is 46.7<EXP(μ)<66.1

and 1.15<EXP(σ)<1.56, which is comparable with Schneider`s

(1988 p196 example 6.1) two-sided 95% CI's: 48.1<EXP(μ)<66.7 and

1.13<EXP(σ)<1.59.

HAW110	Hawkins (1991 Appendix III p133) uses defective formulas for the

upper (GUCL) and lower (GLCL) "confidence limits on the true geometric

mean" (AMml in stead of GM based). For total dust (GM=2.6 mg/m3,

GSD=1.77) he calculates two-sided 95% confidence interval for EXP(μ),

of GLCL=2.28 and GUCL=4.1 mg/m3. A more appropriate interval, using

the inverse of formula 6.10, is 1.94-3.49 mg/m3.


Example 44 Regression analysis in exposure control chart

*.HYG file	Description

VINCHL##	The TWA8 hour Vinylchloride VCM in a SEG polymerisation shift

workers since 1987 (see Example 29) were presented

in an exposure control chart (Figure 15). In contrast with the comparison

of the 1989 and 1991 data, the regression line delineate a significant

decrease of exposure in time. The regression slope calculated using

TRUE EPISTAT indicates that the geometric mean exposure between

1987 and 1993 decreased every year with 100*[1-exp(-.1961)]≈18%.

(95% confidence bounds 12-24%).


Example 47 Extrapolation in time

The reference period of the following limit values obliges you to perform (1) a variable sampling plan and (2) extrapolation:

 -	the Dutch limit value for lead TWA40 hour,

 -	the EG asbestos cumulative action level for 3 months,

 -	the EG vinyl chloride limit for one year.

The Dutch MAC30 min for carbon monoxide is often measured by a series grab IR registrations. Using IR or indicator tubes makes it usually impossible to sample the total reference period (σti << T), so extrapolation in time is preferred. Statistical techniques are available to evaluate the TWA from partial-period or grab sampling (see 5.2).


Example 48 Lognormal

The Lognormal distribution in series industrial hygiene measurements was first recognised in the fifties at the coal face (Oldham, 1953). Lognormal goodness-of-fit has been demonstrated in the distribution of concentrations of gasses, vapours, dust, fibres and enzyme-activity in workplace air, in excretion products in urine, in exhaled air, in blood values and in (untransformed) noise intensities (kPa). Leidel (1975b page 7, 1977 page 122) indicates that Lognormal goodness-of-fit is observed in American, English and German industry. The Lognormal distribution is observed in series short-term (seconds) and long-term (days) sampling periods (Leidel 1975, 1977).


Example 49 Making rankits by Monte Carlo simulation

Rankits can be made with a Monte Carlo simulation:

•	generate a sample of M random standard Normal deviates Zi (Abramowitz 1971, page 953, direct method), and arrange them in ascending order,

•	repeat this procedure at least a thousand times,

•	the arithmetic mean of the 1000 deviates with rank i is an effective estimate of rankit Ri.


Example 50 The most effective measures to quantify exposure

Which descriptive statistics are used depends on the agent, the goal of the strategy, the desired extrapolation, the shape of the distribution and the limit value. Extremes are effective when dealing with Ceiling limits or when agents have an acute toxic response over a specific concentration (cyanide, ammonia and similar agents). The arithmetic mean is an effective measure for the mean mass for cumulating agents (asbestos, quartz and similar agents). Geometric mean and variance are essential for all extrapolation and inference statistics.  Log(GM) is being used in noise exposure (in dB(A))


Example 51 Arithmetic mean

In Figure 23 and Figure 24 the cumulative distributions of 2000 AMs are displayed on Log-probability scale. AMs are calculated from a series of M=50 or M=2 Monte Carlo Lognormal deviates (μ=0, σ=1). Lognormal fit of the AM distribution improves with increasing sample size. The Lognormal approximation of the AM distribution can be  described by the following descriptive statistics

•	EXP(μAM) is nearly EXP(μ+σ²/2)=1.6

•	EXP(σAM) is nearly EXP(σ)+SQR(1/df) =2.72 (df=1) & 1.15 (df=49).

The rankits estimators displayed in Figure 22 and Figure 23 are comparable:

•	GMgdf=1=1.7 and GSDgdf=1=2.73

•	GMgdf=49=1.7 and GSDgdf=49=1.19

The 50th and 1950th values of the sample data of Figure 22 are 1.19 and 2.29, respectively.

The 95% two-sided confidence interval of AM is:

•	e0.5-2.149/%(49)=1.21 and e0.5+2.827/%(49)=2.47, based on Land (1975 page 413; s=1, df=49), .

•	1.22 and 2.17, based on the approximate method of Jahr (1987) .

Figure 23 Rankit plot of 2000 AM values.	Figure 24	Rankit plot of 2000 AM values.

Monte Carlo Lognormal. Sample size 50	Monte Carlo Lognormal. Sample size 50


Example 52 Comparing untransformed linear estimators

Students measuring Strontium-90 concentrations in milk with μ=9.22 picoCuries per litre. The 2 lower and the 3 upper extremes (outliers) were excluded from the 10 observations (SARH212.HYG). From the untransformed, double censored sample the rankit regression estimators are mean =9.3251 and standard deviation s=1.8679. These values are equal to the alternative estimators =9.33 and s =1.87 and comparable with the exact estimators  x=9.29 and s=1.69 (Sarhan 1962).

Figure 26	10 measurements of Strontium-90 in milk (SARH212)


Example 53	Performance of estimators of censored sample descriptive statistics

Three out of ten mice inoculated with tuberculosis did not die within 60 days (GUPTA271). Schneider (1988 p69) used this Lognormal distributed data set to illustrate the performance of different estimators of μ and σ in small censored samples. The results of the rankit estimator was added.

Name of the method	page in	symbol	Estimators

Schneider (1986)	GM in days	GSD

Ignoring censored data	-	-	50.7	1.16

Censored data at 65 days	-	-	52.8	1.17

Best linear unbiased	85	BLU	55.2	1.23

Maximum likelihood	69	ML	55.2	1.20

Restricted ML	103	RML	55.4	1.21

Dixon's	88	-	55.5	1.23

Modified maximum likelihood	104	MML	55.2	1.20

Bias corrected ML	110	MLc	55.6	1.23

Rankit regression	80	LU	56.0	1.24

Using only the non-censored data (=1/7*σxj and s={σ(xj-)2/6}+1/2) or a fixed value for the censored data (Hornung 1990, Hawkins 1991 p104) underestimate both EXP(μ) and EXP(σ) rather extreme. The Rankit regression estimators result in the highest values for GMg and GSDg. This is suitable for industrial hygiene purposes because of the low chance of underestimating the location and variance of the exposure


Example 54 Degrees of freedom in confined populations

From Leidel (1977 page 63, 67):

•	During 5 out of MT=16 exposure periods to Hydrogen sulphide during one shift, a worker's exposure is sampled df=15*4/11≈5 (LEIDEL63.HYG).

•	10 PAS TWA8 hour Dioxane in a period of 6 months (Mτ=130 working days). Confined as it is, the influence on the degrees of freedom is too small: df=INT(9.67)=9 (LEIDEL67.HYG).

40 TWA8 hour's in a confined population of Mτ=200 shifts of one employee in one year results in df= 48.

5 TWA4 hour's in a population of Mτ=13 Friday morning shift in one season results in df=6.


Example 55 Degrees of freedom in censored samples

•	The 310 rivet heads with diameters (HALD151) above the lower limit of 13.4 mm (Hald 1952 page 151) in a sample of 500 (see Figure 24), provides a df=404.

•	The 15 items under stress (SCHNE224) with an accelerated lifetime below the 6 time units (TU) in a sample of 50 (see Figure 5), provides a df=31 (Schneider 1988 p224).

•	The 37 locomotives with failures before 135,000 Miles (SCHNE70.HYG) in a sample of 96 (see Figure 6), provides a df=65 (Schneider 1986 example 4.3 page 69).

•	The 7 grab sample airborne Chlorine concentrations (OWEN716) within the range of accuracy from a sample of 15 that were taken over a working day (Owen 1980 page 716) in order to classify for the federal 8-hour TWA standard of 1 PPM (See Figure 4), provides a df=10.


Example 56 Adjusting GSDs and w/AM for different values of M and CVt

Sample size 	Sample descriptive

Statistics	CVt=.05	CVt=.25

M	GSD	w/AM 	GSDadj	wadj/AMadj	GSDadj	wadj/AMadj

2	1.1	0.0952	1.0845	0.081	-	-

2	1.4	0.3303	1.3951	0.327	1.2562	0.223

2	2	0.6425	1.9970	0.641	1.9219	0.603

2	2.71828	0.8611	2.7157	0.860	2.6513	0.836

2	3.5	1.0024	3.4974	1.002	3.4334	0.984

5	1.1	0.0953	1.0846	0.081	-	-

5	1.4	0.3314	1.3952	0.331	1.2600	0.224

5	2	0.6822	1.9972	0.680	1.9287	0.636

5	2.71828	0.9679	2.7161	0.967	2.6633	0.936

5	3.5	1.1915	3.4980	1.191	3.4513	1.166

10	1.1	0.0954	1.0846	0.081	-	-

10	1.4	0.3395	1.3952	0.336	1.2623	0.228

10	2	0.6390	1.9974	0.717	1.9342	0.669

10	2.71828	1.0736	2.7164	1.072	2.6724	1.038

10	3.5	1.3907	3.4985	1.390	3.4637	1.363

50	1.1	0.0954	1.0846	0.081	-	-

50	1.4	0.3446	1.3953	0.341	1.2654	0.231

50	2	0.7680	1.9976	0.766	1.9407	0.714

50	2.71828	1.2387	2.7169	1.239	2.6831	1.202

50	3.5	1.7604	3.4991	1.759	3.4774	1.732

The adjustment of GSD and w/AM>CVt, increases if w/AM is about equal to CVt.


Example 57 CVt Influence on GSD in  example data

*.HYG	Description

file

LEIDEL63	5 short period exposures to hydrogen sulphide provides an uncorrected relative

standard deviation w/AM=0.11. Adjusting GSD=1.12 is not possible because

w/AM < CVt=0.12 (Leidel 1977 page 79 table D-1).

HAW117	After removing two results (because the local exhaust system had misfunctioned

during sampling) and entering a lower detection limit at LL=1.4 mg/m3 (outlier

correction), the remaining 14 TWA8 hour total dust (Hawkins 1991 p117) provides

GSDg=1.19 (Figure 11) and w/AM=0.18. Adjusting GSDg for random measurement

errors using df=13 and total dust CVt=0.15, provides a GSDadj=1.1

BOLEY62	Boleij (1987 page 63) corrected GSD for CVt, in a series TWA8 hour total dust from

a papermill. That is why the GSD=2.68, calculated on the complete sample, differs

from the GSD=2.5 presented by the author. Using the raw data, 9 out of 12 ex

ceed a lower detection limit of 1.8 mg/m3 (see Figure 12) providing GMg=4.7

mg/m3, GSDg=3.35 and w/AM=1.33, which overshadows any reasonable total

dust CVt. So adjusting GSD in this sample is not necessary.

For LEIDEL67.HYG and HAW117.HYG the untransformed Shapiro probability A(W) gives the highest conformity of shape (see Example 15), a second indication that random error determined the variance.


note 12

There is no single accepted way to handle undetectable levels (Leidel 1977 p 103). The procedure followed here is introduced to get a clear graphical presentation in the probability plot (screen 17).


note 13

Two measurements and descriptive statistics (entered through screen 7) cannot be examined by shape: certainty about conformity with the Lognormal shape should be obtained from the assessment strategy.


note 14

Low A(W) values of the omnibus W-test of Shapiro (1965) indicate low conformity with the Lognormal shape.


note 15

The Lognormal goodness-of-fit rank order, among the transformations (< less than, ≤ at most, => at least).


note 16

The number of exposure data M` within the accuracy range


note 17

This categorical classification increases from rejected (nonconformity), acceptable, good, very good, to perfect (complete conformity).


note 18

Statistical analysis can prove poor quality in a data series but cannot improve it (The "rubbish in, rubbish out" principle). The user should have basic knowledge on exposure assessment, including assessment strategy and compliance control and should act accordingly to perform extrapolation and compliance testing successfully.


note 19

If the measurement method random error (CVt*AM) or the grouping interval (@C) are larger than the arithmetic standard deviation w (see § 4.1.1 ), then GSD should be adjusted (see §B.6 ). If GSD>1.4, then random error is in most cases irrelevant.


note 20

See § 5.1.1 for the differences between the three statistical methods


note 21

The tables 1.#.# of Odeh (1980 page 18 through 69 using γ, 1-P and N for confidence γ, non-compliance probability α, and sample size M respectively) provide tolerance factors for:

δ= .995, .99, .975, .95, .9, .75, .5, .25, .1, .05, .01, .005

1-α= .75, .90, .95, .975, .99, .999

M= 2(1)100(2)180(5)300(10)400(25)650(50)1000, 1500, 2000, 3000,5000,10000, ∞


note 24

The nine process steps can also be applied in the effective control of environmental hygiene, process safety and quality.


note 25

 Combined exposure of several agents (WHO 1981, Scheffers 1985),

•	exposure through different routes of entry (lung, mucous membranes, skin and/or intestines) (Manz 1987, Thomas 1986),

•	specific sensitivity (ACGIH 1982, Stresemann 1988),

•	novel work schedules (Roach 1977, Hickey 1977, Brief 1986, Eide 1990),

•	physical exercise (WHO 1981),

•	extreme climate (Hertig 1975, WHO 1981 p29),

•	use of personal protection.

The WHO report (1981) contains a comprehensive reference list with inaccessible references from east European periodicals.


note 27

Statistics is a belief among experts. It is based on knowledge, logic and reproducible observations. Sampling is an art. Computing is a rigid, and in essence, simple skill. Fundamental sciences, and statistics in particular, are often misused. See e.g. the commonly found booklets "How to lie with ....".


note 28

formula B-1 shows that the W test statistic is the ratio of two different estimators of the variance in a sample. The F-ratio test is based on the ratio of the variances of two different samples.


Table 1 Example data from different sources

*.HYG file 	agent	Sample 	Limit 	dimension	Source

size M	value H

ALBRE220	TWA8 hr Aspartame	4	?	μG/M3	Albrecht (1989) p220

ACN8_9	TWA8 hr Acrylonitril	116	4	PPM	Swaen  (1992)

BAR_SI25	Grab Sample Carbon monoxide	6	50	PPM	Bar-Shalom (1975) pI-25

BILAN304	TWA8 hr Methylene bisphenyl 	5	0.005	PPM	Bilan (1989) p304 sprayer indoor

isocyanate (MDI)

BOLEY62	TWA8 hr Total dust	12	10	MG/M3	Boleij (1987) p62, paper plant

BOLEY85	TWA8 hr ZnCl2 total Dust	7	mg/m3	Boleij (1987) p85

CHIP123	Lead	10	50	μG/M3	Booher (1988) p123

COHEN132	max. Susquehanna River flood levels	20	-	106*ft3/sec	Cohen (1988) p132

CONOV195	two-digit telephone numbers	50	-	-	Conover (1980) p365

DEWELL24	TWA8 hr Respirable dust	8	5	MG/M3	Dewell (1989) p24

DEWELL42	TWA10 min Formaldehyde	10	2C	PPM	Dewell (1989) p42

DEWELL44	Welding fumes	11	5	MG/M3	Dewell (1989) p44

GUPTA271	Mice survival time	10	-	days	Gupta (1952) p271 &

Schneider (1986) p69 & 88

HALD151	Diameters of rivet heads	500	-	mm	Hald (1952) p151

HAW104	TWA8 hr Chlorine	10	0.5	PPM	Hawkins (1991) 104

HAW117	TWA8 hr Total dust	15	10	MG/M3	Hawkins (1991) 117

LEIDEL56	TWA20 min Ethyl alcohol	 8	1000	PPM	Leidel (1977) p56-60

LEIDEL61	Grab sampled Ozone	35	0.1	PPM	Leidel (1977) p61-62

LEIDEL63	TWA10 min Hydrogen Sulphide	5	20C	PPM	Leidel (1977) p63-64

LEIDEL67	TWA8 hr Dioxane	10	100	PPM	Leidel (1977) p67-69

LEIDL103	Grab sampled HF	12	3C	PPM	Leidel (1977) p103-4

LD103_10	HF minus background 0.1 ppm	12	3C	PPM	Leidel (1977) p103-4

LEIDL104	TWA8 hr Methylmethacrylate	24	100	PPM	Leidel (1977) p104

MOF134NS	TWA10-30 min Methoxyfluorane	16	-	PPM	Potts (1988) p134 Nonscavenged

MOF134S	TWA10-30 min Methoxyfluorane	6	-	PPM	Potts (1988) p134 Scavenged

OWEN716	Grab sampled Chlorine	15	1	PPM	Owen (1980) p 716

POSTB11I	TWA8 hr Styrene	14	100	PPM	Post (1989) A11 Inlayers 08 thru 14

POST1008	TWA8 hr Styrene	9	100	PPM	Inlayer/press 10/4 and 08/15

POST08P4	TWA8 hr Styrene	5	100	PPM	Inlayer 08 press 4

POST10P5	TWA8 hr Styrene	4	100	PPM	Inlayer 10 press 5

RANDOM20	Monte Carlo	2000	-	-	Lognormal distribution

EXP(μ)=1, EXP(σ)=2.71828

SARH212	90Sr in milk	10	-	nCu/M3	Sarhan (1962) p212

SCHNE224	Items under stress	50	1	time units	Schneider (1986) p224

SCHNE70	Failure distance of locomotives	96	?	103 miles	Schneider (1986) p70

SOLV198	TWA8 hr Hydrocarbons	45	575?	MG/M3	Scheffers (1985) p19

X07-10	Chemical X	30	-	PPB	Gustafson (1991) ch7


Table 2 Rankit estimators for Normal descriptive statistics

Estimator	Description

M'	the number of results between

Formula 3-2	the accuracy limit

xcg	arithmetic mean of the

Formula 3-3	untransformed data, estimated

using the data pairs between

the accuracy limits

scg	standard deviation of the

Formula 3-4	untransformed data, estimated

using the data pairs between

the accuracy limits


Table 3	Type of distribution according to the goodness-of-fit with a transformation

Best transformation fit	Distribution type

Ci	Normal, Gaussian

log(Ci)	If s/x ≈ constant for every Ci, then Lognormal

Sqrt(Ci)	If s² ≈ x for every Ci, then the Poisson distribution

1/Ci	If s ≈ x² for every Ci, then inverse normal


Table 4 Lognormal goodness-of-fit decision scheme

What's the shape of logarithmic 	Is the 	Goodness- 	Transfor- 	Uncen 	Lognormal

transformed scatterplot	sample	of-fit	mation	sored	conformity

within the accuracy range,	censored	A(W)%	fit	Sample

along the regression line ?	?	size

straight line	no	≥95	best	≥20	perfect

ditto	yes	-	best	≥20	very good

slightly curvilinear	no	≤95	best	≥20	good

linear tendency, slightly oscillating	no	≥95	best	≥3	good

ditto	no	5-95	≥2nd best	≥3	≥acceptable

ditto	yes	-	≥2nd best	≥3	≥acceptable

unknown (descriptive statistics only),

but reliable assessment strategy	-	-	-	≥2	Acceptable

Curvilinear	no	<95	<2nd best	≥3

Oscillating	no	<5	-	≥3	Lognormality

oscillating or curvilinear	yes	-	<2nd best	≥3	Rejected


Table 5	Characteristics of the complete sample estimators of the Lognormal descriptive statistics

Estimator	Description and properties

df	The number of degrees of freedom

Formula 4-1

GM	Estimator of the geometric mean EXP(μ).

Formula 4-2	Measure of source strength (Seixas 1988, Rock 1982)

0 < GM < ∞

Dimension ci

If GM > H, then at least one ci> H.

Biased estimator of EXP(μ): If M≤10 and GSD>2.7, then GM

overestimated at least 5% on average.

GMU	Like GM (see above) with the following exceptions:

Formula 4-3	Unbiased estimator of EXP(μ)

GMU<GM for all values of M and s

If GSD/M2>6, then "Cannot calculate

unbiased estimator GMu!" is displayed.

Relevant for the noise level pressure kPa.

GSD	Estimator of the geometric standard deviation EXP(σ)

Formula 4-4	Measure of scale in a Lognormal distribution

No dimension

>1

Unbiased estimator with minimum variance.

Normal values in the workplace atmosphere

ranges between 1.4 and 3.5.

AM	Estimator of the arithmetic mean β

Formula 4-5	Calculated using the following formula.

Unbiased minimum variance estimator

TWAreference period from series short period measurements

within a reference period (Bar-Shalom 1975)

The mean dose of a cumulating agent (Seixas 1988)

from series of more days TWA8 hour

Dimension ci> 0

w2	Unbiased minimum variance estimator

Formula 4-6	of the arithmetic variance w2 (the 2nd moment)

Dimension ci2

>0

Inverse proportional with ventilation rate

and the square of the volume (Roach 1977 p67).

w/AM	The sample coefficient of variation, to be compared with CVt,

rounding error and grouping interval ratio -C/AM.


Table 6 Characteristics of the complete sample estimators of the Lognormal descriptive statistics
Table 6	Characteristics of the censored sample estimators of the Lognormal descriptive statistics

Estimator	Description and properties additional to Table 5

M'	the number of results between

Formula 4-7	upper and lower limit

df	the number of degrees of freedom

Formula 4-8	of a censored sample: M'<M

GSDg	Geometric Standard Deviation estimated

Formula 4-9	using the data pairs between the accuracy limits.

GMg	Geometric mean estimated using the

Formula 4-10	data pairs between the accuracy limits.


Table 7	Choosing the most appropriate method to generalise and test series sample exposure data.


Table 8	Names, parameters and estimators for assessing long-term TWA control

Name	Population 	sample	chapter

    	parameter	estimate

Long-term non-compliance probability (NIOSH 1977 p65)	αC>H	AC>H	5.1.2 &

Percentage of the TWAs above the limit H	5.1.3

One-sided or right-sided fraction

Fraction TWAs in compliance with the limit value H

Chance αC>H that one TWAreference period exceeds H

Acute health hazard (Hawkins 1991 page 56)

Upper tolerance limit

One-sided or right-sided tolerance limit	CU>##%	ÇU>##%

Concentration above U% of the population	5.1.2 &

Lower tolerance limit	5.1.3

One-sided or left-sided tolerance limit	CU<##%	ÇU<##%

Concentration below 100-α% of the population

Confidence δ of desired α	δ(Cα<100-U>H)	D(Cα<100-U>H)	5.1.4

Confidence δ that <α% of the concentration are over H

non-compliance probability α with confidence δ	α(Cδ>U%>H)	A(CU>##%>H)	5.1.4

Fraction TWAs with confidence δ in compliance with H

Chance α with confidence δ that one TWAref per exceeds H

Upper tolerance limit with confidence δ	Cα<100-U,U>##%	Çα<100-U,U>##%	5.1.4

One-sided tolerance limit (OTL, Tuggle 1982)

Concentration above 100-α% of the population with confidence δ


Table 9	Statistical properties of 3 methods which assess the effectiveness of control

                        Method->	Standard Normal  	Unbiased 	Noncentral Student

___________________________________________________________________________________

Characteristic	Chapter 5.1.2	Chapter 5.1.3	Chapter  5.1.4

-------------------------------------------------------------------------------------------------------------------------------------

Expectation of A%:	E(A%)>α	E(A%)=α	E(A%)<α

- increase of the bias if:	GSD ↑,	Unbiased	GSD ↓,

H/GM ↑ or df ↓	H/GM ↓, or df ↑

Efficiency of Variance 	High	Moderate	Lowe

σ(A%) estimate

Shape of A%	Skewed, but asymptotic Normal if GSDº1 or H/GMº1

 - outlier incidence	Frequent and extreme	Moderate	lowest

 - kurtosis shape	Tapering	Moderate	flattest

Leptokurtosis	platykurtosis

Confidence δ of finding

non-compliance.

 If Ca=H, then	0<δA≥α<50%	50<δA≥α<100%	dA≥α=U%

 if df->0, then	δA≥α->0%	δA≥a->100%	δA≥α=U%


Table 10 Names, parameters and estimators of dose assessment

Name	Population 	Sample

Parameter	Estimate

_____________________________________________________________________________________

Probability α that mean β exceeds limit H	αβ>H	Aβ>H

non-compliance probability α of the arithmetic mean β.

Upper Confidence limit of β 	Cβ,U≥##%	Çβ,U≥##%

One-sided or right sided confidence limit of the mean

Upper concentration with confidence 100-α% over population mean β

Lower Confidence limit of β	Cβ,U≤##%	Çβ,U≤##%

One-sided or left sided confidence limit of the mean

Lower concentration with confidence α% over population mean β


Table 11 Methods to test Ceiling limits using TWAshort period

Lognormal conformity	kC>H	Sample size M	Statistical method	Chapter

Rejected	>0 and <p*M	>1/p	(cumulative) Binomial/Poisson	5.3.1

≥acceptable	n.r	≤1/p	adapted Binomial/Poisson	5.3.2

≥acceptable	n.r	>2	Lognormal Noncentral Student	5.3.3

kC>H: the number of TWAshort period grab samples exceeding the Ceiling limit;

p=1-U%/100: the fraction TWAshort period grab samples exceeding the Ceiling limit;

n.r. not relevant.


Table 12 Notations and terms used for inference test statistics.

Name	Population	sample 	chapter

 parameter	estimate

Two-sided probability, GSD = GSDref	αGSD=GSDref	AGSD=GSDref	6.2

Inference of two sample Geometric Standard Deviations

Two sample difference in scale

Two sample analysis of variance

Two-sided probability, GM = GMref	αGM=GMref	AGM=GMref	6.2.3

Inference of two sample Geometric Means

Two sample difference in location

Two-sided probability, GSD = EXP(σ)

)Inference with population Geometric Standard Deviation	αGSD=EXP(σ)	AGSD=EXP(σ)	6.3.1

Two-sided probability, GM = EXP(μ)	αGM=EXP(μ)	AGM=EXP(μ)	6.3.2

Inference with population Geometric Mean


Table 13 Effective control of occupational exposure risks

+----------+   +------------+

|         1|   | Limit     2|

| hygienic +-->| Value      +--+  +--------------+

| hazards  |   +------------+  +->|  Exposure   4|yes/unknown

+--|-------+   +------------+  |  |  compliance  +---+

   |   |       | Exposure  3+--+  +------|-------+   |

   |   |       +-----|------+            |           |   +-------------+     +------------+

   |   |             |         +---------+no         |   |            8| yes | Effective 9|

   |   |       +-----+------+  |  +--------------+   +-->| Sustainment +--->| Control     |

   |   |       |           5|<-+  |mental &     7+---|   |             |     |            |

   |   |       | Control    +---->|physical      |   |   +-------------+     +------------+

   |   +------>| measures   |     |resistance    |   |           |no               no |

   |           |            |     +--------------+   |           |                    |

   |           |            |     +--------------+   |           |                    |

   |           |            +---->|Co-exposure  6+---+           |                    |

   |           +-----|------+     +--------------+               |                    |

   |                 |                                           |                    |

   +-----------------+----------------------<--------------------+                    |

   +-----------------------------------------<----------------------------------------+


Table 14 Exposure assessment applications by domain

Sampling plan	One grab or TWA 	One series	D2 series exposure situa-	com-

meassurement.	exposure data.	tions. Comparing differen-	ment

ces in regimes of control

Domain

Process 	Incident, accident 	Continuous and 	Technical measures	A.2.1

safety/emission	and leakage	semi-permanent

Control	monitoring

Systems

Industrial hygiene 	Compliance with a 	Long term 	Technical and. 	A.2.2

(workplace oriented)	Standard	compliance control	Organisational

Control charts

Health surveillance 	Range finding	General 	Technical, organisational 	A.2.3

Similar exposure	assessment and	and behaviour measures.

Group	compliance control

Occupational 	Individual	long term 	Sustainment under 	A.2.4

Medicine	compliance	occupational load	Different circumstances

(single worker)

Occupational 	Range finding	dose estimate	Dose groups	A.2.5

epidemiology and

industrial toxicology


Table 15 Scheme for health based limit value setting in similar exposure groups

                   +--------------+

                   ¦Complaints or ¦

                   ¦Medical occu- +---+   +---------------+     +--------------+

                   ¦rences        ¦   ¦   ¦ Dose/Response ¦     ¦ Occupational ¦

                   +--------------+   +--?¦ relation      +----?¦   Limit      ¦

                   +--------------+   ¦   ¦               ¦     ¦  Value       ¦

                   ¦Exposure      +---+   +---------------+     +--------------+

                   ¦assessment    ¦

                   +--------------+


Table 16 Conventions in industrial hygiene statistics

Characteristic	Convention	Alternative	explanation

propo	Pragraph

sition

The shape of the	Lognormal	Normal, Nonparametric	1	A.4

distribution	Gamma, Weibull

Test for goodness	(Log)normal (median	describing population homo	2	B.1

normalorder) probability 	geneity, Rankit probability

-of-fit	paper. isher and Geary tests 	plot, W-test.Waters test

onkurtosis and skewness

Descriptivestatis	consistent, efficient	Unbiased	6	B.2

tics

Coping with 	C<dl = ½ Cdl	Maximum likelihood or	4	B.3

censored data	dl= accuracy limit	Rankit regression through

the uncensored data

Degrees of 	extrapolation to 	extrapolation to a 	3	B.4

freedom df	generalresults. 	confinedpopulation

df=M-1	Mô:df=(Mô-1)(M-1)/(Mô-M)

df in censored 	all data df=M-1 or the	the minimum value of 	5	B.4.3

samples	uncensored only: df=M`-1	df=(M+M`)\2-1 or df=2*M`

Extrapolation Extent	upper one sided 95%	two sided, different percentages	7	4.2

Extrapolation 	standard Normal	unbiased and 	8	4

Technique	Noncentral Student


Table 17 Notations used for  the Lognormal descriptive statistics

Name	Descriptive statistic	formula & page

Population parameter	Sample estimates	uncensored	censored

Measures for location

Mean of log(C)	μ	formula B-3 	-

Geometric Mean	EXP(μ)	GM, GMu, GMg	formula B-9 &	formula B-21 &

formula B-11  	formula B-11

Arithmetic Mean	β=EXP(μ+σ²/2)	AM	formula B-16 	formula B-16

Median	EXP(μ)	ME	-	-

Modus	EXP(μ-σ²)	-	-	-

Measures for scale

Variance of log(C)	σ²	s²	formula B-4  	-

Geom. Standard Dev.	EXP(σ)	GSD, GSDg	formula B-13 	formula B-20

Arithmetic Standard-	ω=EXP(μ+σ²/2)*	w	formula B-18 	formula B-18

Deviation (ASD)	sqr{EXP(σ²)-1}

Relative ASD	ω/β=sqr{EXP(σ²)-1}	w/AM	formula B-19 	formula B-19


Figure 1 Ten TWA8 hours Dioxane (LEIDEL.67)


Figure 2 45 TWA8 hours total hydrocarbons among maintenance painters (Solv198)


Figure 3 14 TWA8 hour Styrene on inlayers working on different presses (POSTB11I)


Figure 4 15 grab sample airborne chlorine concentrations (OWEN716)


Figure 5  50 Items under stress (SCHNE224)


Figure 6  The mileage of 96 locomotives (SCHNE70)


Figure 7  10 Chlorine TWA8 hour. Logarithmic transformed and uncensored (HAW104)


Figure 8  10 Chlorine TWA8 hour.  Untransformed and censored (HAW104)


Figure 9 	5 TWA8 hour MDI during indoor spraying. LogLog transformed (BILAN304)


Figure 10  8 TWA20 min Ethyl Alcohol. One worker, one shift (LEIDEL56)


Figure 11  15 Untransformed TWA8 hours dust (HAW117)


Figure 12  Total dust 12 TWA8 hours (BOLEY62)


Figure 13 	Susquechanna river maximum flood levels in ft3/sec (COHEN132)


Figure 14	12 CHF grab samples corrected for .1 PPM fixed background (LD103_10)


Figure 15	Vinylchloride Control chart in a SEG PVC operators TWA8 hours over 1987-1993


Figure 16  Lognormal probability distribution of 37 VCM TWA8hours


Figure 17  283 TWA8 hour ACN in a SEG production


Figure 18  116 TWA8 hour ACN in a SEG production 1977-78


Figure 19 	16 TWA10-30 min Methoxyfluane. Nonscavenged results (MOF134NS)


Figure 20 	6 TWA10-30 min Methoxyfluane. Scavenged results (MOF134S)


Figure 21  A family of Lognormal distributions with mean M and standard deviation s

GM=exp(M)

GSD=exp(s)

M=0; GM=1

s=0.25;  GSD=1.284

s=0.50;  GSD=1.649

s=0.75;  GSD=2.117

s=1.00;  GSD=2.718

s=1.25;  GSD=3.490

s=1.50;  GSD=4.482


Figure 22 Lognormal probability plot on 24 TWA8 hours methyl metacrylate (LEIDL104)


Figure 23 Rankit plot of 2000 AM values. Monte Carlo Lognormal. Sample size 50


Figure 24  Rankit plot of 2000 AM values. Monte Carlo Lognormal. Sample size 50


Figure 25  500 Rivet heads (HALD151)


Figure 26  10 measurements of Strontium-90 in milk (SARH212)


Figure 27  Mice survival time (GUPTA271, Schneider 1986 p 69 & 88)


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