PHLT 8702 Week 8 Variability Analysis Example

Same Sanders, Different Tuesdays: A Variability Analysis Splitting Sixteen Inhalable Wood Dust Results From a Composite Plant's Bench Sanders Into Day-to-Day and Worker-to-Worker Components

Student Name

Walden University

PHLT 8702: Environmental and Occupational Exposure Measurement and Assessment

Instructor Name

Month Day, Year

Same Sanders, Different Tuesdays: A Variability Analysis Splitting Sixteen Inhalable Wood Dust Results From a Composite Plant's Bench Sanders Into Day-to-Day and Worker-to-Worker Components

The Question

If the composite plant sampled its bench sanders again next week, the new results would not match the first round. Part of the difference would come from day-to-day changes in the work of each sander, and part from lasting differences between sanders. This paper separates those two components for the 16 inhalable dust results collected from eight randomly chosen bench sanders on two random days each, and argues which component should shape the next round of sampling.

The Data

Concentrations of airborne contaminants are usually right-skewed and close to lognormal, so the analysis works with natural logarithms of each result, as is standard in exposure assessment (Rappaport, 1991).

Table 1

Inhalable Wood Dust Results for Eight Bench Sanders, Two Days Each (Composite Figures, mg/m3)

Note. Composite figures; full-shift IOM samples analyzed gravimetrically.

The Model

A one-way random-effects model treats each log result as the sum of a group mean, a worker effect that persists across days and a day effect that varies around each worker's own mean. The model assumes that log exposures are roughly normal within each worker and that worker effects are independent of one another, assumptions that are standard but rarely checked with data this sparse. It yields two variance components: the between-worker component, describing how much workers' long-term means differ, and the within-worker component, describing how much one worker's exposure varies from day to day. With every worker sampled the same number of times, the components can be estimated directly from the analysis of variance (Lyles et al., 1997).

Results

The two components are of similar size. On any given day, a sander's exposure might be about one and a half times higher or lower than usual. At the same time, the long-term means of different sanders differ enough that 95% of them span roughly a sixfold range. The estimated probability that a randomly chosen sander's long-term mean exceeds the NIOSH recommended limit of 1 milligram per cubic meter is about 0.6.

Table 2

Variance Components for Bench Sanders (Composite Figures)

Note. Composite figures from a balanced one-way random-effects analysis of log-transformed results.

How These Results Compare

Across almost 60 published studies, Symanski et al. (2006) found that within-worker variability was usually larger than between-worker variability, with the between-worker component growing as groups mixed different jobs and locations. A between-worker component as large as the within-worker component, as here, suggests that the bench sander group is less uniform than it appears. Kromhout et al. (1993) also found greater day-to-day variability where local exhaust was absent, consistent with the variable condition of the plant's downdraft tables.

Where the Worker-to-Worker Difference Comes From

The two sanders with the highest means, S3 and S7, are the two who work at downdraft tables awaiting repair. Their geometric means, 2.73 and 1.84 milligrams per cubic meter, are about two to four times those of the other six. Two workers are too few to estimate a separate group, but the pattern is the kind of identifiable cause that Rappaport et al. (1993) found observational groupings often miss.

Which Component Should Shape the Next Round

The between-worker component should drive the design. It changes the decision the plant must make: whether exposures are acceptable for the group as a whole or only for some of its members. It also has a likely cause that can be checked, the tables. The next round should therefore split the bench sanders by table condition, sample every sander at a broken table, and sample enough workers at working tables to confirm whether they form one group.

The within-worker component still matters for how many days each worker is sampled. With a day-to-day geometric standard deviation near 1.6, two days give a rough estimate of each worker's mean; three or four days would narrow it. The next round should add a third day per worker, but adding workers is the higher priority. Any worker who moves between a broken and a repaired table during the round will be recorded, so that the comparison is not blurred by people who used both.

What the Plant Should Not Conclude

Three tempting conclusions do not follow from these data. The first is that the group "complies" because its geometric mean is close to 1 milligram per cubic meter and far below the general federal particulate limit; the relevant question for a carcinogen is the distribution of individual long-term means, and most of that distribution sits near or above the NIOSH recommendation. The second is that the two high sanders are simply careless; their tables, not their habits, are the more likely explanation, and the next round can test that. The third is that day-to-day variation is noise to be ignored. A within-worker geometric standard deviation near 1.6 means that a single result can mislead in either direction, which is why no worker's exposure should be judged from one day.

Limits

Eight workers and two days each give imprecise variance estimates; with this few data, the between-worker component could be considerably smaller or larger than estimated. The analysis assumes lognormal exposures and independence between days, which two days per worker cannot test. The results should be treated as a guide to the next round, not as a final characterization.

References

Kromhout, H., Symanski, E., & Rappaport, S. M. (1993). A comprehensive evaluation of within- and between-worker components of occupational exposure to chemical agents. Annals of Occupational Hygiene, 37(3), 253-270. https://doi.org/10.1093/annhyg/37.3.253

Lyles, R. H., Kupper, L. L., & Rappaport, S. M. (1997). Assessing regulatory compliance of occupational exposures via the balanced one-way random effects ANOVA model. Journal of Agricultural, Biological, and Environmental Statistics, 2(1), 64-86. https://doi.org/10.2307/1400641

Rappaport, S. M. (1991). Assessment of long-term exposures to toxic substances in air. Annals of Occupational Hygiene, 35(1), 61-121. https://doi.org/10.1093/annhyg/35.1.61

Rappaport, S. M., Kromhout, H., & Symanski, E. (1993). Variation of exposure between workers in homogeneous exposure groups. American Industrial Hygiene Association Journal, 54(11), 654-662. https://doi.org/10.1080/15298669391355198

Symanski, E., Maberti, S., & Chan, W. (2006). A meta-analytic approach for characterizing the within-worker and between-worker sources of variation in occupational exposure. Annals of Occupational Hygiene, 50(4), 343-357. https://doi.org/10.1093/annhyg/mel006