Occupational Hazards

Industrial HygieneExposure

Assessments''Worst-case'' versus random sampling

By Jerome E. Spear

AN INDUSTRIAL HYGIENE exposure assessmentis the prtKess used to evaluate a person's exposureto a chemical or physical agent. To measure a work-er's actual exposure, a moriitor would need to beplaced in his/her breathing zone each day, some-thing that is cost-prohibitive and time-consuming.Since it is often not possible (or practical) to measureeach person's actual exposures to the chemical orphysical agent, judgments regarding the acceptabili-ty of exposure are made based on an estimate of theperson's dose via representative sampling.

The exposure assessment strategy employeddepends on the purpose and goal of the monitoringand what the sample{s) should represent. The twotypes of sampliiig strategies to consider when plan-ning an exposure assessment study are "worst-case"sampling atid randotn sampling. The broad differ-ence is that worst-case sampling involves more sub-jectivity than a random-sampling approach.

In worst-case sampling, workers who are subjec-tively believed to have the highest exposures arenonrandomly selected. It' no worst-case sampleexceeds the occupational exposure limit(s), one canbe subjecti\'ely satisfied (but not statistically confi-dent) that the exposure profile is acceptable. Forexample, operators who have similar job dutieswithin a plant's production unit may be identified asa similar exposure group (SEC). For such workers, aworst-case exposure might occur on a day that theirprocess unit generates ttie highest production out-put. Such a day would subjectively be consideredthe worst-case exposure period and would be tar-geted for evaluation.

A random-sampling strategy requires workerswithin an SEG atid the sample perictds to be ran-domly selected; exposure data is then subjected tostatistical analysis. Decisions on the acceptability ofthe exposure profile can then be determined with a

known level of confidence based on the central ten-dency and spread (or dispersion) of the sample dis-tribution. Applications of a random samplingstrategy include:

•Describe the eight-hour time-weighted average(TWA) concentrations over different days for a sin-gle worker or SEG.

•Describe the 15-minute TWA concentrationsover one workshift for a single worker or SEG.

•Estimate the full-shift fWA concentration overone workshift based on short-term (or grab) samplesfor a single worker or SEG.

Both types of sampling strategies have advan-tages and limitations. The primary advantage ofusing a worst-case strategy is that fewer samplesmust be collected, making it more cost-efficient andless time-consuming than a random-samplingapproach. A limitation of worst-case sampling is thatit requires the industrial hygienist to recognize theworst-case conditions, which may include profes-sional judgment about the specific task and/or a spe-cific work practices unique to anijidividual worker.

However, because a person's judg-ment may not be as good as perceived,worst-case (i.e., judgmental) samplestaken will likely be based on inherentpersonal biases. As a result, it is notpossible to measure the accuracy ofworst-case samples (Albright, et al 329).The conclusions about exposure willaiso include potential biases of judg-ments about job conditions, work prac-tices and/or other conditions believedto have an impact on exposure.

Random sampling eliminates suchbiases since samples of the populationare selected randomly. As a result, the

Abstract: Iridustrialhygiene exposure assess-ments are performedto evaluate a person'sexposure to a chemicalor physical agent. Twotypes of samplingstrategies should becor^sidered when plan-ning an exposure assess-ment study: worst-casesampling and randomsampling. This articlecompares the twostrategies and providesan eight-step processof profiling a simitarexposure group usinga random-samplingapproach.

Jerome E. Spear, CSP, CIH, ismanaging member of J.E. SpearConsulting LLC in Magnolia, TX. Hehas more than 15 years' experiencehelping organizations prevent andcontrol losses through theapplication of incident preventionand exposure control techniques.Spear has a B.S. in IndustrialEngineering with a specialization InSystem Safety Engineering fromTexas A&M University. He is aprofessional member of ASSE's GulfCoast Chapter, and is a member ofSystem Safety Society and AmericanIndustrial Hygiene Assn.

wwwasse.org AUGUST 20()5 PROFESSIONAL SAFETY 39

Table 1

Industrial Hygiene Assessment Strategies:Worst-Case Versus Random SamplingSamplingStrategy

Worst-CaseSampling

Advantages

•Fewer samples are typicallycollected to make a decision.•Statistical skills are notrequired.

Limitations

•Relies on subjective judgmentson worst-case exposureconditions.•Difficult to capture the actualworst-case exposure period(s).•Requires the industrial hygien-ist to recognize the environmen-tal conditions and employeework practices that have themost significant affect onemployees' exposures.•Decisions on exposure accept-ability are made without aknown level of confidence.

who have similar exposures.For example, the employeesassigned to operate propane-powered lift trucks in a ware-house may be grouped ashaving similar potential expo-sures to carbon monoxide. Ifmultiple SEGs are identified {asmost facilities have), one mustdevise a method for rankingdata collection needs. AlHA'sA Strategy for Assessing and Man-aging Occupational Exposuresprovides such a method forstudy based on the toxicity ofthe material, conditions of theworkplace environment andtheir likelihood to influenceexposures, and individual workpractices that are likely to influ-ence exposures (Mulhausen andDamiano 89-101).

Random Sampling •Exposure groups can be charac-terized with a known level ofcertainty.•Considered to be a more defen-sible strategy since the outcome isbased on an objective analysis.

•More samples are required inorder to profile the exposuregroup.•Takes more time to interpretand analyze the samplingresults.

40

variability in the data (due to work practice varia-tions between workers, day-to-day variations,process variations, etc.) is measured and used to esti-mate the exposure parameters. As a result, a randomsampling strategy is based on an objective analysisof the SFG. Table 1 provides a comparison of a thetwo types of sampling strategies.

Exposure Profiling: An Eight-Step ProcessStatistically speaking, it is always possible to

make the wrong decision no matter how confidentone is. However, quantifying the level of certaintythrough a random-sampling strategy maximizes thechances of making the right decision. With theavailability of computers and statistical softwareapplications, much of the statistical grunt work isautomated, making it easier to employ a random-sampling strategy. Several statistical terms and con-siderations must be understood when using thisapproach. These are described in the followingeight-step process to exposure profiling.

Step 1: Identify the SEG to ProfileThe key consideration in categorizing SFGs is to

select the exposure group in order to mirumize theamount of variation between the samples; other-wise, the resulting confidence intervals (calculatedfrom the mean and variance) will be too wide to beuseful. An SFG may be a single worker performinga single task; however, it is often impractical to per-form random sampling for each worker. A morepractical approach is to include multiple employees

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Step 2: Randomly SelectWorkers & Exposure Periodswithin the Selected SEG

A random sample is onewhere each worker and timeperiod has an equal probabilityof being selected for samplecollection. It is important tocollect samples as randomly as

possible; otherwise, the resulting statistics will bebiased. A random number table and/or the randomnumber function in a spreadsheet computer program (such as Microsoft Excel) are usehil tcxjls inthis process. Another consideration is the number ofsamples that should be collected in order for theexposure profile to be useful. The answer dependson several factors, including the variability of thesample. However, AIHA generally recommends thatsix to 10 samples (Mulhausen and Damiano 106) areneeded to perform a baseline exposure profile.

Step 3: Collect Breathing Zone Samples of theSelected Workers at Randomly Selected Intervals

Breathing zone samples should be collected nearthe employee's nose and mouth. The breathing zonecan be visualized as a hemisphere about six to nineinches around the employee's face. Those conduct-ing the monitoring should understand the nature ofthe job or process in which the agent(s) is used orgenerated as well as the basics of field samplingmetliods and techniques.

Although formal training and/or hands-on train-ing on exposure monitoring techniques and analyti-cal methods are useful, the mechanics of conductingpersonal air sampling can be self-taught. Severalsources of information are helpful in identifying theappropriate sampling and analytical methodologyand equipment. These include the OSHA TechnicalManual and the NIOSH Manual of Analytical Methods.An AIHA-accredited laboratory can provide guid-

ance and instructions on specific sam-pling methods as well.

Step 4: Calculate the DescriptiveStatistics for the Data Set

Descriptive statistics include themean, median, percent above occupa-tional exposure limit (OEL), range andstandard deviation that characterize thesample's distribution such as tbe centraltendency and the variability in the data.The mean and median are used to meas-ure the central tendency ol the data,whereas the range and standard devia-tion are measures of variability. By look-ing at the data from several perspectives,information and patterns in tbe data may be discov-ered. Many data sets can be interpreted simply bycomparing the OEL with descriptive statistics. Whenmost of tbe data are clustered well below or wellabove the OEL, a decision can generally be made onworkplace acceptability by using descriptive statistics(Mulhausen and Damiano 235).

The geometric mean (GM) and geometric stan-dard deviation (GSD) are descriptive statistics usedto estimate parameters of a lognormal distribution(see Step 5). The GM is the antSog of the arithmeticmean of tbe logtransformed values (sidebar, above).It is the value below and above which lie 50 percentof tbe elements in the population (i.e., the populationmedian). The GSD is the antilog of the standard devi-ation of the logtransformed values (sidebar, above). Itis unitless and reflects variability in the populationaround the GM; therefore, confidence intervals willhave a larger spread as the GSD increases.

Step S: Determine Whether the Data Fita Lognormal and/or Normal Distribution

Upper- and lower-confidence limits (UCL andLCL, respectively) and upper-tolerance limits (UTL)are calculated based on knowing (or assuming) a cer-tain underlying distribution of the data set. The typeof distribution (i.e., normal or lognormal) will gener-ate different confidence intervals and tolerance lim-its. A random variable is called normally distributedif the distribution (as plotted on a histogram) lookslike a bell-shaped curve (Figure 1).

However, industrial hygiene sampling data is often"skewed to the right" (Figure 2) since occupationalexposure values have a lower boundary (i.e., themeasured exposure value caruiot be less than zero).Taking tbe log of the variable often mitigates suchskewness. In such cases, the distribution is then con-sidered lognormally distributed—or lognormal—ifthe log of the variable is normally distributed. The log-normal distribution is often applied to occupationalexposures, yet tbe assumption of lognormality is sel-dom verified (Waters, et ai 493). If the data follow nei-ther a lognormal nor a normal distribution, the datamay not represent a single SHG. In sucb cases, the datamay need to be divided into two or more SEGs andanalyzed separately (Mulhausen and Damiano 242).

If the sample size is large with lots of values, the

Calculating the Geometric Mean& Geometric Standard Deviation

1) Transform the original data to the natural log (log ,).Yi = loge(Xi)

where Xj = original values and yj = logtransformed values

2) Calculate the mean (y) and standard deviation (s) of the logtransformed data.3) Take the antilog of the mean and the antilog of standard deviation of the log-

transformed data.

GM = antilog (y) = eyGSD = antilog (s) = e^

data can be visualized by creating a histogram of thedata (i.e., plotting the relative frequency of elementsfalling in specified intervals). However, industrialhygiene sampling data often consist of small datasets with fewer than 10 samples due to cost and/orother constraints. One way to qualitatively deter-mine whether the underlying distribution follows alognormal and/or normal distribution for smallsample sizes is to plot the data on probability paper.A lognormal distribution is suggested if the dataplotted on lognormal probability paper form astraight line. Likewise, a normal distribution is sug-gested if the data plotted on normal probabilitypaper form a straight line.

A major advantage of probability plotting is theamount of information that can be displayed in a com-pact form; however, it requires subjectivity in decidinghow well the model fits the data (Waters, et al 493)since probability plotting relies on whether the plotteddata forms a straight line. Identifying large deviationsfrom linearity is based on the subjective valuation ofviewing the probability plot. Probability paper isavailable for various types of sample distributions andplotting procedures are described in TechnicalAppendix I of NIOSH's Occupational Exposure Samp-ling Strategy Manual (Leidel, et al, 97-105). If a statisti-cal program is available, a more quantitative approachshould be used to evaluate the goodness-of-fit of thedistribution. If both a lognormal and normal distribu-tion are indicated, the confidence limits and upper-tol-erance limit should be calculated assuming alognormal distribution.

Step 6: Calculate the Estimated ArithmeticMean, One-Sided UCL & LCL of the ArithmeticMean, 9Sth Percentile & UTL for the Data Set

•Estimated arithmetic mean. For a normal distri-bution, tbe estimated arithmetic mean is the same asthe sample mean. However, if the data are lognor-mally distributed, several methods are available forestimating tbe arithmetic mean and for calculatingconfidence limits. The sample mean and t distributionconfidence limits ("Estimating" sidebar, pg. 43) havethe advantage of being easy to calculate, althoughthey can be more variable than other estimates(Mulhausen and Damiano 254). Other preferredmethods for estimating the arithmetic mean and com-

www.asse.org AUGUST 2005 PROFESSIONAL SAFETY 41

Figure 1

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Figure 2

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puting the corifidence limits are described in AIHA'sA Strategi/ for Assessing and Managing OccupatioimlExposures, (Mulhausen and Damiano 253-264).However, estimating the arithmetic mean and com-puting the confidence limits using such preferredmethods are difficult without the use of a computerand/or specialized software.

•UCLj 95% and LCL^ g^x of f^e arithmetic mean.When evaluating toxicants that produce chronic dis-eases, the mean exposure should be examined(Rappaport and Selvin 378). However, to evaluateacute (short-term) exposures, the UTL of the 95thpercentile should be examined. The UCLj 95% is theone-sided upper value at a 95-percent confidence

42 PROFESSIONAL SAFETY AUGUST 2005 wvvw.asse.org

level. Likewise, the LCL| 951/ isthe one-sided lower value at a95-percent confidence level. Ifthe UCLj 99 ,, is below the OEL,there is a 95-percent confidencelevel that the long-term aver-age exposure is below the OEL.

From a compliance perspec-tive, the burden of proof is onthe compliance officer to showthat the worker was overex-posed with at least 95-percentcertainty. Therefore, an OSHAcompliance officer must dem-onstrate that the LCL^ y5<>_exceeds OSHA's permissibleexposure limit (PEL). If the dataare lognormally distributed,different methods are availableto calculate the confidence lim-its foi" the arithmetic mean. Thesample mean and t distributionconfidence limits have theadvantage of being easy to cal-culate, but they can be morevariable than other estimates(Mulhausen and Damiano 254),

•95th percentile. The 95thpercentile is the value in which95 percent of the populationwill be included. For example,the median is the 50th per-centile.

• UTLggo/ 95nj_ This is theUTL of the 9^th percentile and istypically used to examine acute(short-term) exposures (e.g.,fast-acting contaminants). For alognormai distribution, theUTL95< , 95../ is calculated usingthis equation: VTL^^.',^,^^.,^^ = e(y+Ks) (Mulhausen and Damiano270-272) where, y and s are themean and standard deviation,respectively, of the logtrans-formed data. K is a factor for tol-erance limits that is obtainedfrom a table given the confi-dence level, percentile and

number of samples.

Step 7: Make a Decision on theAcceptability of the Exposure Profile

Generally, a UCLi93. ;, that results in a valuegreater than the long-term OEL suggests that theexposure profile is unacceptable, whereas aUCLj 95.1 , which results in a value below the long-term OEL suggests that the exposure profile isacceptable. For chemicals with acute (or short-term)effects, the UTL of the 95th percentile should beexamined.

However, calculating the VTUi^u.^^^^,,y^^ with fewdata points tends to produce a wide tolerance inter-

80 100

va!, which limits its usefulness.A UTLg n/,, 957,, which results ina value below the short-termexposure level and ceiling limitsuggests that the exposure pro-file is acceptable, but largenumbers of samples are need-ed to identify "acceptable"environments {Selvin, et al 89).

Step 8: Refine the SEGResults of the exposure pro-

file may indicate that the expt>sure group needs to be furtherrefined. For example, it mayappear that the sampling forcertain individuals results inhigher exposures. To statisticallytest the significance of this vari-ation, an analysis of variance(ANOVA) may be performed.An ANOVA is an inferential sta-tistical test that compares two ormore means to determine whether the means are sig-nificantly different. If the means are statistically differ-ent, the SEG may need to be further refined.

Case Studies:Applying Random Sampling Strategies

To illustrate the random-sampling approach, twocase studies are provided. One describes how toevaluate the exposure of a single worker using a ran-dom-sampling method. The other example involvesestimating a full-shift TWA based on random short-term samples.

Example 1: Estimating theLong-Term Exposure of a Single Employee

An employer requested an evaluation of a partic-ular employee's eight-hour TWA exposure (in rela-tion to OSHA's PEL) to formaldehyde during amanufacturing task. The first step in assessing expo-sures to environmental agents is to have a thoroughunderstanding of the processes, tasks and contami-nants to be studied. Information may be obtainedthrough observations and ptissibly the use of direct-reading devices. Interviews with workers, managers,maintenance personnel and other relevant personnel(such as technical experts) provide an additionalsource of information and knowledge. In addition, areview of records and documents (including pastexposure monitoring data), relevant industry stan-dards, and/or other literature can provide someinsights on the magnitude of exposures for givenprocesses and tasks performed at the worksite.

In this case, the employee operated equipmentthat forms fiberglass-matting material which is usedin building materials (such as backing for shingles).Potential exposure to formaldehyde was identifiedsince the MSDS for the resin used to bind the fiber-glass matting lists formaldehyde as a component. Toassess this employee's exposure using a worst-casesampling strategy, breathing zone air samples

Estimating the Aritiimetic Mean& Caiculating Confidence LimitsMultiple techniques can be used to estimate the arithmetic mean andcompute confidence limits. The sample mean and t distribution confi-dence limits has the advantage of being easy to calculate but can bemore variable than other estimates (Mulhausen and Damiano 254).The sample mean and t distribution confidence limits are calculatedas follows:

Step 1: Calculate the sample mean (y) and sample standarddeviation(s).

Step 2: Calculate the confidence limits (CL).

Where:•The value of t can be looked up in a "student-t" table available inmost statistics books.

Step 3: Compare the UCL^ 950/ and LCL] 95% to die long-term OEL.

would be collected on days believed to produce thehighest exposure to formaldehyde. Sampling resultswould then be used to derive conclusions based onprofessional judgment (and potential biases) ofworst-case conditions.

To eliminate potential biases or incorrect worst-case judgments, a random-sampling strategy wasdesigned. A total of five workdays were randomlyselected, which represented the eight-hour sampleperiods. A formaldehyde monitor was placed in theemployee's breathing zone for the duration of therandomly selected workdays to measure the TWAconcentration of formaldehyde. Descriptive statis-tics were calculated, which resulted in the following:

•Maximum: 0.85 ppm• Minimum: 0.43 ppm•Range: 0.42 ppm•Mean: 0.624 ppm• Median: 0.60 ppm•Standard deviation: 0.15 ppm•Geometric mean: 0.610 ppm•Geometric standard deviation: 1.274 ppmThese statistics indicate no substantial outliers in

the data since the mean and median are relativelyclose in value.

Next, to ensure that the data followed a normaland/or lognormal distribution, the data were plottedon probability paper and a statistical goodness-of-fittest was performed, which indicated both a lognormaland normal distribution. As a result, the arithmeticmean, UCL| 93<y and LCL^ 95,^ were estimated assum-ing a lognormal distribution (see below):

• Estimated arithmetic mean: 0.624 ppm0.823 ppmi 95 pp

•LCL] 957,,: 0.512 ppmIn this example, it can be concluded, with 95-per-

cent certainty, that this employee's exposure toformaldehyde will be less than 0.823 ppm on anygiven workday. Although the mean concentration offormaldehyde (0.624 ppm) for this employee is less

www.asse.org AUGUST 2lH)5 PROFESSIONAL SAFETY 43

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than OSHA's PEL of 0.75 ppm, the most conserva-tive approach would be to reduce exposures to alevel less than the UCL] 95.., . Therefore, for theemployer concerned with ensuring a safe work-place, additional interventions to reduce thisemployee's exposure to formaldehyde are warrant-ed since the employer cannot conclude with 95-per-cent certainty that his exposure is below the PEL.However, from a compliance perspective, it wouldnot be possible to demonstrate with 95-percent cer-tainty that the employee's exposure exceeds the PELsince the LCL^ 95% is less than the PEL.

Example 2: Estimating TWA ConcentrationBased on Random Short-Term Samples

An employer identified a potential exposure to1,6-hexamethylene diisocyanate (HDI) among em-ployees who were spray painting the exterior shellof an aboveground storage tank. Due to limitationswith the selected field sampling and analyticalmethod for HDi, the sample duration had to be lim-ited to approximately 15 minutes.

The spray-painting task was performed byemployees working from a boom-supported elevat-ed platform. At times, two painters worked from thesame platform; at other times, only one painter per-formed the task. As a result, a sampling strategy wasdeveloped that employed both worst-case and ran-dom-sampling techniques. Due to the samplingduration limitations, the strategy included collectingrandom, short-term samples from the breathingzone of each painter and estimating TWA concentra-tion for the task based on those samples. The worst-case exposure condition was also targeted. Randomshort-term samples were collected when bothpainters worked side-by-side from the same elevat-ed platform since this condihon was assumed to rep-resent the highest exposures to the painters.

Four random, short-term samples were collectedfrom the breathing zone of each painter (i.e., a totalof eight random samples), which resulted in the fol-lowing descriptive statistics;

•Maximum: 0.0042 mg/m-"*•Minimum: <0.00037mg/m-^•Range: 0.00394•Mean: 0.002•Median: 0.002•Standard deviation: 0.001•Geometric mean: 0.002 mg/m-'•Geometric standard deviation: 2.545 mg/m-^These statistics indicate no significant outliers in

the data since the mean and median are equivalent.To ensure that the data followed a normal and/or

lognormal distribution, the data were plotted onprobability paper and a statistical goodness-of-fittest was performed, which indicated both a lognor-mal and normal distribution. As a result, the arith-metic mean, LCL] 950, , and UCL] 950,;, were estimatedassuming a lognormal distribution:

•Estimated arithmetic mean: 0.002 mg/m^•UCL] 95%: 0.007 mg/m "*•LCL] 95%: 0.001 mg/m^In this example, one can conclude with 95-percent

certainty that the TWA concentration of HDI for the taskis less than 0.007 mg/m^. Since the UCL] 95-./, is belowthe PEL of 0.034 mg/m- , the exposure was determinedto be acceptable from both the employer's perspectiveand the OSHA compliance officer's perspective.

It is important to note that since the sampling waslimited to periods within a single workshift, this casestudy does not account for day-to-day variationwhich may exist. Therefore, the results represent theTWA concentration for the task that was performedon the date of the sampling. However, this concen-tration represents the worst-case condition for thistask since breathing zone samples were collectedduring worst-case conditions—when two painterswere spray painting from the same platform.

Beyond Airborne ExposuresHistorically, more attention has been given to air-

borne exposures than to exposures to physical agentsand dermal exposures. However, in many situations,ranciom-samplhig strategies may be applied to dataotht r than airborne samples. For some chemicals, skinabsorption may be the predominant route of exposureand airborne samples woutd not be the most appropri-ate variable to study such exposures. Biological moni-toring may be more appropriate in such circumstances.

Random-sampling approaches may also beapplied to physical agents. However, for noise dataand/or other variables measured in a logarithmicscale, analyzing the allowable dose (i.e., percent ofdosi.?), rather than decibels, should be considered sothat statistical tools can be applied to such exposuremeasurements.

Both worst-case sampling and random-samplingstrategies are useful in assessing exposures. It isimportant to understand the limitations of each and tocorrectly apply the selected sampling strategy. A pri-mary benefit of a random-sampling strategy is that itallows SEGs to be profiled with a known level of cer-tainty, which makes it a more defensible and objectivesampling strategy. The primary benefit of a worst-casesampling approach is that fewer samples are needed(making It a less costly and less time-consuming strat-egy) to make an exposure judgment. In some cases, acombination of both approaches may be beneficial. •

ReferencesAlbright, S., et al. Data Analysis and Decision Making with Micro-

soft E.xcel. Pacific Gnive, CA: Broiiks/Cok- Publishing Co., 1999.Leidel, N., et al. Occiipntiom! Exposure Sampling Strati'^/ Manual.

DHEW/NIOSH Pub. 77-173. Cincinnati, OH: NIOSH, 1977. "Mulhausen, J. and J. Damiano. A Stnite^ jvr A?^vsing and Mnn-

agiiiji Occiipntioml Exposures. 2nd t-d. Fairfax, VA: AIHA Press, 1998.NIOSH. NIOSH Manual of Amiylkai Methods. Washington,

DC: U.S, Dept. of Health and Human Services, CDC, NIOSH.<http://www.cdc.gov/niogh/nmam>.

OSHA. OSHA Tcrhiiicn! Maimnl. Washington, DC: U.S. Dept.oi Lahor, OSHA, <htlp://www.osha.go\7dts/osta/otm/otm_toc.html>.

Rappaport, S. and S. Selvin. "A Methixl for Evaluating theMean Exposure from a Lognormal Distribution." AltiA louriiai48(1987): 374-379,

Selvin, S., et al. "A Noto on the Assessment of ExposureUsing One-Sided Toler,ince Limib." AIHA louriiai. 48(1987): 89-93.

Waters, M., et al. "A Measure of Coodness-nf-Fit for thuLognormai Model Applied to Occupational Expt>sures." AIHA/ / 52(1991): 493-502.

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