1

MEMORANDUM 

To: Timothy Leighton, EPA; Bob Ross, Summitec Inc.; Andrew Yin, Summitec Inc. 

From: Jonathan Cohen, ICF International, Inc. 

Date: October 3, 2012 

Re: Contract No.: EP-W-11-014 TAF 1-6-3: 

Liquid Pour AEATF Study Statistical Review for HSRB 

Introduction and Summary 

In August 2012, AEATF submitted the final report for their study “A Study for Measurement of Potential Dermal and 

Inhalation Exposure during Application of a Liquid Antimicrobial Pesticide Product During Manual Pouring of a 

Liquid Containing an AntiMicrobial.” ICF International, Inc. (ICF) was asked by EPA through Summitec Inc. to 

analyze the data from this study to investigate the relationship between dermal and inhalation exposures and the 

pesticide product usage. Note that much of the SAS code used for these analyses and some of the following description 

was adapted from Sarkar’s SAS code (which, in turn, was based on code provided by the AHETF) and his June 2010 

Statistical Review “Review of Statistical Analyses in Agricultural Handler Exposure Task Force (AHETF) 

Monographs.” 

The study report describes the experimental study methodology and the measurements in detail. Briefly, the study was 

carried out at an indoor test site in Concord, Ohio. Each of 18 volunteer subjects performed both the following scripted 

Conventional Pour study and the following scripted Reduced Splash, in a randomly selected order. 

For the Conventional Pour (CP) study, 18 volunteer subjects, referred to here as “workers,” were randomly assigned 

into three groups of six subjects, numbered 1, 2 and 3, and the workers in group 1 were randomly assigned into two 

groups of three subjects, referred to as groups 1a and 1b. The workers in group 1a were assigned a task of pouring a 

liquid containing the active ingredient DDAC from a set of 10 conventional small source containers of sizes 24, 32, and 

64 fl oz into 32 fl oz trigger spray bottles. The workers in group 1b were assigned a task of pouring a liquid containing 

the active ingredient DDAC from a set of 10 conventional small source containers of sizes 24, 32, and 64 fl oz into 2 

gallon buckets. The workers in group 2 were assigned a task of pouring a liquid containing the active ingredient 

DDAC from a set of 10 conventional medium source containers of sizes 128, 202, and 256 fl oz into either 2 gallon 

buckets, 4 gallon buckets, or 50 gallon low-walled troughs, where the three receiver container types were each 

randomly assigned to two of the group 1 workers. The workers in group 3 were assigned a task of pouring a liquid 

containing the active ingredient DDAC from a set of conventional large source containers of sizes 640 fl oz (5 gallon 

buckets) with standard flat lids into 50 gallon low-walled troughs. All subjects in group 1 and 4 randomly selected 

subjects in group 2 used a measuring cup. For each subject in groups 1 and 2, it was randomly determined whether the 

receiving containers would be placed on the floor or on a table (at waist to chest height). For all subjects in group 3, 

the receiving containers were on the floor. 
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For the Reduced Splash (RS) study, the same 18 volunteer subjects, referred to here as “workers,” were randomly 

assigned into three groups of six subjects, numbered 1, 2 and 3, and the workers in group 1 were randomly assigned 

into two groups of three subjects, referred to as groups 1a and 1b. All these assignments were independent of the 

Conventional Pour study assignments, so that a worker might not be in the same groups for the CP and RS studies. 

The workers in group 1a were assigned a task of pouring a liquid containing the active ingredient C14 ADBAC from a 

set of 10 reduced splash small source containers of size 64 fl oz into 32 fl oz trigger spray bottles. The workers in group 

1b were assigned a task of pouring a liquid containing the active ingredient C14 ADBAC from a set of 10 reduced 

splash small source containers of size 64 fl oz into 2 gallon buckets. The workers in group 2 were assigned a task of 

pouring a liquid containing the active ingredient C14 ADBAC from a set of 10 reduced splash medium source 

containers of sizes 96, 128 and 180 fl oz into either 2 gallon buckets, 4 gallon buckets, or 50 gallon low-walled troughs, 

where the three receiver container types were each randomly assigned to two of the group 1 workers. The workers in 

group 3 were assigned a task of pouring a liquid containing the active ingredient C14 ADBAC from a set of large 

source containers of sizes 640 fl oz (5 gallon buckets) that had lids with a pull-out pour spout into 50 gallon low-walled 

troughs. All subjects in group 1, and 4 randomly selected subjects in group 2, used a measuring cup. For each subject in 

groups 1 and 2, it was randomly determined whether the receiving containers would be placed on the floor or on a table 

(at waist to chest height). For all subjects in group 3, the receiving containers were on the floor. 

Each subject was given inner and outer dosimeters to wear and was also given a personal air-sampling pump attached 

to an OVS air sampling tube. The air sampling pump was switched on at the beginning of the first monitoring 

experiment (ME) and turned off once the pouring was completed. The subject sat on a chair covered with plastic 

sheeting until the preparation of the containers for the second ME was completed. Then the air sampling pump was 

switched on again for the second ME and turned off once the pouring was completed. The air sampling tubes, hand 

wash, face/neck wipes, outer dosimeters, and inner dosimeters, were collected by a researcher and were later analyzed 

by the laboratory to measure the mass of DDAC (attributable to the Conventional Pour active ingredient) and the mass 

of C14 ADBAC (attributable to the Reduced Splash active ingredient). 

The exposure measurements in the report were corrected for the average percentage recovery of field fortification 

samples and for the removal efficiency of hand wash (90%) and face and neck (89%) wipe samples. These analyses 

used the corrected measurements. An Excel spreadsheet containing the data in the report was supplied by the Study 

Director and used for these analyses. This included the units conversion of the amounts of active ingredient from mg 

into pounds and of the mass from μg to mg. The report data for inhalation exposure were unchanged other than the 

units conversions and some corrections to the tabulated air sampling durations in the original study report that were 

noted by the Study Director in September 2012. The dermal exposure data were used to develop exposure 

measurements for four dermal exposure routes, as follows: 

• Long Dermal. This case represents the dermal exposure for a subject wearing long pants and long-sleeved 

shirts, without gloves. The exposure is the sum of the mass from hand wash, face and neck, and the six inner 

dosimeters (lower arm, upper arm, lower leg, upper leg, front torso, rear torso). 

• Short Dermal. This case represents the dermal exposure for a subject wearing short pants and short-sleeved 

shirts, without gloves. The exposure is the sum of the mass from hand wash, face and neck, the outer dosimeters 

for the lower arm and lower leg, and the six inner dosimeters (lower arm, upper arm, lower leg, upper leg, front 

torso, rear torso). 

• Long Short Dermal. This case represents the dermal exposure for a subject wearing long pants and shortsleeved shirts, without gloves. The exposure is the sum of the mass from hand wash, face and neck, the outer 

dosimeter for the lower arm, and the six inner dosimeters (lower arm, upper arm, lower leg, upper leg, front 

torso, rear torso). 
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• Hands Only. This case represents the dermal exposure to the hands only and is the mass from hand wash. This 

case is used for comparison purposes. 

The report only considered the dermal exposure for the “Long Dermal” case, and used the same definition. However 

for our analyses we chose a more consistent, and more conservative (i.e., more health protective) approach to deal with 

values reported as being below the level of quantitation (LOQ): 

Several of the measured values were below the level of quantitation (LOQ). Such values are called “non-detects.” The 

experimental protocol also required that measurements of the inner dosimeters were not taken if the outer dosimeter 

was below the LOQ, although this did not in fact apply for any of the outer dosimeter measurements made in this study. 

As a slightly more conservative (i.e., more health protective) approach than the method used in the report, we replaced 

any value that was either a non-detect or was not measured by one half the LOQ. If any inner or outer dosimeter value 

was below the LOQ, 3 μg, each such value was replaced by 1.5 μg = 0.0015 mg. For example, if all the inner 

dosimeters were below the LOQ, then the total would be replaced by 0.009 mg. If the face and neck measurement was 

below the LOQ, 50 ng, it was replaced by 25 ng = 0.000025 mg. If the inhalation mass OVS measurement (mg) was 

below the LOQ, 10 ng, it was replaced by 5 ng = 0.000005 mg. All the hand wash measurements in the study were 

above the LOQ. For the Conventional Pour, 4 of the 18 face and neck measurements, 67 of the 108 outer dosimeter 

measurements, 107 of the 108 inner dosimeter measurements, and 6 of the 18 OVS measurements were below the 

LOQ. For the Reduced Splash, 0 of the 18 face and neck measurements, 41 of the 108 outer dosimeter measurements, 

105 of the 108 inner dosimeter measurements, and 9 of the 18 OVS measurements were below the LOQ. In Tables 10 

and 11 below, we present the results of alternative analyses of values below the LOQ that demonstrate that the impact 

of the method for analyzing non-detect samples is negligible. 

For three subjects and MEs (Reduced Splash ME 1 in group 1a, Reduced Splash ME 7 in group 2, and Conventional 

Pour ME 6 in group 1b), the hand exposure measurements were much higher than values for all other subjects in the 

same group. The liquid pour scenario is one in which unusually large hand exposures can occur through random 

dripping and spilling events that may be poorly associated with the total amount of active ingredient used. No 

adjustments were made in these analyses for these potential outliers. In Table 10 below, we analyze the impact of 

removing these outliers. 

Inhalation exposure was measured using the air sampling OVS tubes. The inhalation exposure concentration (mg/m3

) 

was calculated by dividing the corrected residue mass by the volume of air drawn. The following exposure 

concentrations are analyzed in this memorandum: 

• Inhalation Concentration (mg/m3

). Concentration measured by the OVS tube.

• Inhalation Dose (mg). Inhalation Concentration (mg/m3

) × Air Sampling Duration (hr) 

× Breathing Rate for Light Activity (m3

/hr). A breathing rate of 1 m3/hr is assumed.

• 8-Hour Time Weighted Average (TWA) Concentration (mg/m3

). Average concentration over eight hours 

that includes this period of liquid pouring activity. 

Inhalation Concentration (mg/m3

) × Air Sampling Duration (hr) / 8 (hr).

In this memorandum we present the analysis of the unit or normalized exposure defined as the dermal or inhalation 

exposure divided by the pounds of active ingredient handled. Estimates of the arithmetic and geometric means and 

standard deviation as well as the 95th percentile are computed using the empirical data for each group as well as two 

statistical models: the lognormal simple random sampling model for each group and the lognormal mixed model with 

groups. Because the study design used predetermined groups of containers, these analyses take into account the 

possibility that the mean exposure depends upon the group, which in statistical terminology represents a fixed effect 

rather than a random effect. Unlike the previously analyzed mop, wipe, and aerosol studies, this study does not have a 
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random cluster effect and so the statistical models used here are very different. The empirical model calculates statistics 

for all the unit exposure measurements on a group of subjects assuming the data are statistically independent with a 

possibly different distribution for each group. The lognormal simple random sampling model calculates statistics for all 

the unit exposure measurements on a group of subjects assuming the unit exposure measurements are statistically 

independent with a lognormal distribution that can be different for each group. The lognormal mixed model is fitted to 

the entire set of 36 exposure measurements, from both studies, and assumes that the logarithm of the exposure has a 

normal distribution with a mean that varies between groups, a random worker effect, and a residual error. The random 

worker effect is a random value associated with each of the 18 workers that represents the possibility of clustering or 

association between the two measurements made for that worker (one for conventional pour and one for reduced 

splash), expressing the possibility that some workers have a tendency for getting more highly exposed to antimicrobials 

than other workers. 

Although the experimental design randomized for the effects of whether a measuring cup was used and whether the 

receiving container was placed on the floor or on a table, we treated these effects as part of the random error and did 

not directly include those effects in the statistical models. However, in many cases we found a strong worker effect, and 

so this effect is specifically included in the mixed model so that correlations between consecutive measurements on the 

same worker (e.g., for the conventional pour and reduced splash MEs) can be adjusted for. 

As discussed below, we considered various groupings. Initially we separately considered the six groups of container 

sizes 1, 2 and 3 separately for CP and RS. Since groups 1a and 1b represent very different scenarios of pouring into 

trigger sprays versus pouring into a larger container, with much higher observed exposures for trigger sprays due to the 

more complex nature of that task, we also considered separating group 1 into groups 1a and 1b. We also considered 

combining the data for the CP and RS for each of these container size groups. For the final lognormal mixed model we 

used three groups: 1a with CP and RS combined; 1b, 2 and 3 for CP only, and 1b, 2 and 3 for RS only. Separation of 

the 1a group is justified due to the large difference between scenarios of pouring into larger containers and scenarios of 

pouring into small trigger spray bottles. For the pouring into trigger spray bottles, the CP and RS unit exposure values 

were not statistically significantly different and so could be combined. Although the remaining groups 1b, 2 and 3 have 

large differences in unit exposure, it is appropriate to combine these data into a single group of container sizes because 

of the difficulties in creating different regulations for pouring liquids from containers of different sizes. However for 

the pouring into non-trigger spray bottles, the unit exposure values were significantly different between CP and RS and 

so those scenarios were also separated. In summary we present results for the following groupings: 

Initial groupings: 

• 1aCP. Pouring from small conventional pour containers into trigger spray bottles 

• 1aRS. Pouring from small reduced splash containers into trigger spray bottles 

• 1a. Pouring from small containers into trigger spray bottles 

• 1bCP. Pouring from small conventional pour containers not into trigger spray bottles 

• 1bRS. Pouring from small reduced splash containers not into trigger spray bottles 

• 1b. Pouring from small containers not into trigger spray bottles 

• 2CP. Pouring from medium conventional pour containers 

• 2RS. Pouring from medium reduced splash containers 

• 2. Pouring from medium containers 
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• 3CP. Pouring from large conventional pour containers 

• 3RS. Pouring from large reduced splash containers 

• 3. Pouring from large containers 

Final groupings used in lognormal mixed model: 

• Bottle. Pouring from CP and RS containers into trigger spray bottles 

• Conventional. Pouring from conventional containers not into trigger spray bottles 

• Reduced Splash. Pouring from reduced splash containers not into trigger spray bottles 

For each summary statistic we present confidence intervals. We also compute the fold relative accuracy of the summary 

statistics and compare with the study design benchmark of 3-fold accuracy, which was met for the mixed model used 

for the main statistical analyses for all the dermal and inhalation exposures except for dermal exposures in the Bottle 

grouping. To evaluate the statistical models we present quantile-quantile plots to compare the fit of normal and 

lognormal distributions to the data. 

The statistical models for the normalized exposure assume that the mean value of the logarithm of the exposure is equal 

to an intercept plus the slope times the logarithm of the amount of active ingredient used, where the slope equals 1. To 

test this “log-log-linearity” assumption, the mixed model with a slope term was fitted to the data and a 95% confidence 

interval for the slope was calculated. A statistical test was used to determine if the slope was 1 or 0, corresponding 

either to a valid normalized exposure model or to a case where the exposure is independent of the amount of active 

ingredient used. We applied this test to the three dermal exposures and to the three inhalation exposures using the 

statistical mixed model. For dermal exposures it is reasonable to assume on physical grounds that the same patterns 

ought to apply to any type of dermal exposure, so that the slope should either be one for all types of dermal exposure or 

not one for all types of dermal exposure. To evaluate this issue we applied the same log-log-linearity test to a 

hypothetical all dermal exposure case representing a janitor with no clothing, using a dermal exposure estimated as the 

sum of the exposures measured on the face and neck, hands, and all the inner and outer dosimeters. We also developed 

a statistical repeated measures model to analyze the three main types of dermal exposure (excluding hands only) in a 

single statistical model, accounting for within-worker correlations and within-location clustering. We also evaluated 

quadratic regression models. 

The results for all the dermal concentration exposure routes show that the estimated intra-cluster correlation (ICC) 

coefficient for the worker effect is between 0.2 and 0.4, which implies that there are some worker effects, and therefore, 

in particular, differences between exposures for different workers, as might be expected. The results for the inhalation 

exposures show an ICC of zero, showing no worker effects. 

The mixed model results for the four dermal exposure routes show small positive or negative slopes of between -0.3 

and 0.2. These dermal exposure models consistently reject log-log-linearity (slope equals one) at the 5% significance 

level. These dermal exposure models also consistently do not reject independence (slope equals zero) at the 5% 

significance level. The finding that the dermal exposure could be independent of the amount of active ingredient may 

be due to the fact that the dermal exposure is primarily caused by accidental splashes and spills which may be related to 

the shape and volume of the source container but otherwise not very strongly to the volume poured. The experimental 

design did not allow the concentrations to be varied within the Conventional or Reduced Splash experiments since 

using much higher concentrations would require the need for protective gloves. For this scenario a stronger log-loglinearity between exposure and concentration can be expected than between exposure and volume poured. For the 

inhalation exposures, the estimated slopes are close to one, log-log-linearity is not rejected, and independence is 

rejected. 
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Summary statistics of exposure per pounds of active ingredient handled 

Tables 1 to 7 summarize the normalized exposure data (per lb active ingredient handled) with the summary statistics 

from the 18 measurements for each dermal and inhalation exposure route, for the various container groups described 

above. These analyses assume that the exposure measurements within each group come from some unspecified 

distribution for that group. 

Table 1. Summary statistics for normalized long dermal exposure (mg/lb AI) using empirical sampling model. 

Statistic 1a 1aCP 1aRS 1b 1bCP 1bRS 2 2CP 2RS 3 3CP 3RS Bottle Convent 

ional 

Reduced 

Splash 

Arithmetic 

Mean 

155 111 200 11 20 3 7 7 7 2 4 0 155 8 4

Arithmetic 

Standard 

Deviation 

152 14 227 13 14 3 9 6 12 4 5 0 152 9 8

Geometric 

Mean 

116 110 123 6 17 2 4 4 4 1 2 0 116 4 1

Geometric 

Standard 

Deviation 

2 1 3 4 2 3 4 5 3 4 3 2 2 4 4

Min 40 95 40 1 10 1 0 0 1 0 1 0 40 0 0

 5% 40 95 40 1 10 1 0 0 1 0 1 0 40 0 0

10% 40 95 40 1 10 1 1 0 1 0 1 0 40 1 0

25% 95 95 40 1 10 1 2 2 2 0 1 0 95 1 0

50% 107 115 99 8 14 1 4 7 3 1 1 0 107 6 1

75% 122 122 459 14 35 7 10 14 4 1 4 1 122 14 3

90% 459 122 459 35 35 7 15 15 31 4 14 1 459 15 7

95% 459 122 459 35 35 7 31 15 31 14 14 1 459 35 31

Max 459 122 459 35 35 7 31 15 31 14 14 1 459 35 31

Table 2. Summary statistics for normalized short dermal exposure (mg/lb AI) using empirical sampling model. 

Statistic 1a 1aCP 1aRS 1b 1bCP 1bRS 2 2CP 2RS 3 3CP 3RS Bottle Convent 

ional 

Reduced 

Splash 

Arithmetic 

Mean 

158 114 202 13 22 3 8 8 8 3 4 1 158 9 4

Arithmetic 

Standard 

Deviation 

153 11 229 14 16 3 9 6 12 4 6 1 153 10 8

Geometric 

Mean 

119 113 124 7 18 3 4 5 4 1 2 1 119 5 2

Geometric 

Standard 

Deviation 

2 1 3 3 2 2 3 4 3 3 3 2 2 4 3
7

Statistic 1a 1aCP 1aRS 1b 1bCP 1bRS 2 2CP 2RS 3 3CP 3RS Bottle Convent 

ional 

Reduced 

Splash 

Min 41 102 41 2 11 2 1 1 1 0 1 0 41 1 0

 5% 41 102 41 2 11 2 1 1 1 0 1 0 41 1 0

10% 41 102 41 2 11 2 1 1 1 1 1 0 41 1 1

25% 100 102 41 2 11 2 2 2 2 1 1 1 100 1 1

50% 109 116 100 9 14 2 4 7 4 1 2 1 109 6 2

75% 123 123 465 14 40 7 11 14 4 2 4 1 123 14 4

90% 465 123 465 40 40 7 15 15 32 4 16 2 465 16 7

95% 465 123 465 40 40 7 32 15 32 16 16 2 465 40 32

Max 465 123 465 40 40 7 32 15 32 16 16 2 465 40 32

Table 3. Summary statistics for normalized long short dermal exposure (mg/lb AI) using empirical sampling model. 

Statistic 1a 1aCP 1aRS 1b 1bCP 1bRS 2 2CP 2RS 3 3CP 3RS Bottle Convent 

ional 

Reduced 

Splash 

Arithmetic 

Mean 

156 111 201 11 20 3 8 8 7 2 4 0 156 8 4

Arithmetic 

Standard 

Deviation 

152 14 228 13 13 3 9 6 12 4 5 0 152 9 8

Geometric 

Mean 

117 110 123 6 17 2 4 5 4 1 2 0 117 4 1

Geometric 

Standard 

Deviation 

2 1 3 4 2 2 3 4 3 4 3 2 2 4 4

Min 41 95 41 1 10 1 1 1 1 0 1 0 41 1 0

 5% 41 95 41 1 10 1 1 1 1 0 1 0 41 1 0

10% 41 95 41 1 10 1 1 1 1 0 1 0 41 1 0

25% 95 95 41 2 10 1 2 2 2 0 1 0 95 1 0

50% 108 116 100 8 14 2 4 7 3 1 1 0 108 6 1

75% 123 123 461 14 35 7 11 14 4 1 4 1 123 14 3

90% 461 123 461 35 35 7 15 15 31 4 14 1 461 15 7

95% 461 123 461 35 35 7 31 15 31 14 14 1 461 35 31

Max 461 123 461 35 35 7 31 15 31 14 14 1 461 35 31

Table 4. Summary statistics for normalized hands only dermal exposure (mg/lb AI) using empirical sampling model. 
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Statistic 1a 1aCP 1aRS 1b 1bCP 1bRS 2 2CP 2RS 3 3CP 3RS Bottle Convent 

ional 

Reduced 

Splash 

Arithmetic 

Mean 

153 109 197 11 20 3 7 7 7 2 4 0 153 8 4

Arithmetic 

Standard 

Deviation 

152 14 227 13 14 3 9 6 12 4 5 0 152 9 8

Geometric 

Mean 

114 108 119 6 17 2 4 4 3 1 2 0 114 4 1

Geometric 

Standard 

Deviation 

2 1 3 4 2 3 4 5 3 4 3 2 2 4 5

Min 38 93 38 1 10 1 0 0 1 0 1 0 38 0 0

 5% 38 93 38 1 10 1 0 0 1 0 1 0 38 0 0

10% 38 93 38 1 10 1 1 0 1 0 1 0 38 1 0

25% 93 93 38 1 10 1 2 2 2 0 1 0 93 1 0

50% 105 113 97 8 14 1 4 7 3 1 1 0 105 6 1

75% 120 120 457 14 35 6 10 14 4 1 4 1 120 14 3

90% 457 120 457 35 35 6 15 15 31 4 13 1 457 15 6

95% 457 120 457 35 35 6 31 15 31 13 13 1 457 35 31

Max 457 120 457 35 35 6 31 15 31 13 13 1 457 35 31

Table 5. Summary statistics for normalized inhalation concentration ((mg/m3)/lb AI) using empirical sampling model. 

Statistic 1a 1aCP 1aRS 1b 1bCP 1bRS 2 2CP 2RS 3 3CP 3RS Bottle Convent 

ional 

Reduced 

Splash 

Arithmetic 

Mean 

0.0347 0.0388 0.0305 0.0076 0.0121 0.0030 0.0106 0.0175 0.0037 0.0124 0.0189 0.0058 0.0347 0.0170 0.0044

Arithmetic 

Standard 

Deviation 

0.0058 0.0041 0.0038 0.0090 0.0119 0.0005 0.0117 0.0132 0.0034 0.0151 0.0197 0.0033 0.0058 0.0151 0.0031

Geometric 

Mean 

0.0343 0.0387 0.0303 0.0052 0.0089 0.0030 0.0057 0.0121 0.0027 0.0078 0.0120 0.0051 0.0343 0.0113 0.0035

Geometric 

Standard 

Deviation 

1.1858 1.1138 1.1376 2.3129 2.5264 1.1635 3.4127 3.0232 2.3450 2.6313 3.0588 1.8229 1.1858 2.7484 2.0072

Min 0.0262 0.0343 0.0262 0.0027 0.0051 0.0027 0.0010 0.0017 0.0010 0.0019 0.0019 0.0022 0.0262 0.0017 0.0010

 5% 0.0262 0.0343 0.0262 0.0027 0.0051 0.0027 0.0010 0.0017 0.0010 0.0019 0.0019 0.0022 0.0262 0.0017 0.0010

10% 0.0262 0.0343 0.0262 0.0027 0.0051 0.0027 0.0013 0.0017 0.0010 0.0022 0.0019 0.0022 0.0262 0.0019 0.0013

25% 0.0322 0.0343 0.0262 0.0028 0.0051 0.0027 0.0018 0.0076 0.0013 0.0035 0.0081 0.0035 0.0322 0.0053 0.0022

50% 0.0337 0.0399 0.0322 0.0043 0.0053 0.0028 0.0059 0.0146 0.0027 0.0080 0.0130 0.0053 0.0337 0.0131 0.0035

75% 0.0399 0.0423 0.0331 0.0053 0.0259 0.0036 0.0146 0.0331 0.0042 0.0130 0.0202 0.0079 0.0399 0.0259 0.0071
9

Statistic 1a 1aCP 1aRS 1b 1bCP 1bRS 2 2CP 2RS 3 3CP 3RS Bottle Convent 

ional 

Reduced 

Splash 

90% 0.0423 0.0423 0.0331 0.0259 0.0259 0.0036 0.0331 0.0337 0.0101 0.0202 0.0571 0.0107 0.0423 0.0337 0.0101

95% 0.0423 0.0423 0.0331 0.0259 0.0259 0.0036 0.0337 0.0337 0.0101 0.0571 0.0571 0.0107 0.0423 0.0571 0.0107

Max 0.0423 0.0423 0.0331 0.0259 0.0259 0.0036 0.0337 0.0337 0.0101 0.0571 0.0571 0.0107 0.0423 0.0571 0.0107

Table 6. Summary statistics for normalized inhalation dose (mg/lb AI) using empirical sampling model. 

Statistic 1a 1aCP 1aRS 1b 1bCP 1bRS 2 2CP 2RS 3 3CP 3RS Bottle Convent 

ional 

Reduced 

Splash 

Arithmetic 

Mean 

0.0093 0.0086 0.0099 0.0011 0.0016 0.0006 0.0017 0.0027 0.0008 0.0011 0.0013 0.0009 0.0093 0.0019 0.0008

Arithmetic 

Standard 

Deviation 

0.0009 0.0006 0.0007 0.0009 0.0012 0.0000 0.0018 0.0022 0.0007 0.0010 0.0013 0.0006 0.0009 0.0017 0.0005

Geometric 

Mean 

0.0092 0.0086 0.0099 0.0009 0.0013 0.0006 0.0011 0.0019 0.0006 0.0008 0.0008 0.0008 0.0092 0.0013 0.0007

Geometric 

Standard 

Deviation 

1.1045 1.0700 1.0757 1.8321 2.0497 1.0161 2.9094 2.6705 2.3240 2.3476 2.9358 1.9434 1.1045 2.6982 1.9286

Min 0.0080 0.0080 0.0094 0.0006 0.0008 0.0006 0.0003 0.0003 0.0003 0.0002 0.0002 0.0004 0.0080 0.0002 0.0003

 5% 0.0080 0.0080 0.0094 0.0006 0.0008 0.0006 0.0003 0.0003 0.0003 0.0002 0.0002 0.0004 0.0080 0.0002 0.0003

10% 0.0080 0.0080 0.0094 0.0006 0.0008 0.0006 0.0003 0.0003 0.0003 0.0004 0.0002 0.0004 0.0080 0.0003 0.0003

25% 0.0086 0.0080 0.0094 0.0007 0.0008 0.0006 0.0003 0.0015 0.0003 0.0005 0.0005 0.0005 0.0086 0.0006 0.0004

50% 0.0093 0.0086 0.0096 0.0007 0.0011 0.0007 0.0014 0.0023 0.0005 0.0008 0.0008 0.0009 0.0093 0.0015 0.0007

75% 0.0096 0.0092 0.0107 0.0011 0.0030 0.0007 0.0024 0.0028 0.0012 0.0015 0.0017 0.0014 0.0096 0.0028 0.0013

90% 0.0107 0.0092 0.0107 0.0030 0.0030 0.0007 0.0028 0.0067 0.0020 0.0017 0.0038 0.0016 0.0107 0.0038 0.0016

95% 0.0107 0.0092 0.0107 0.0030 0.0030 0.0007 0.0067 0.0067 0.0020 0.0038 0.0038 0.0016 0.0107 0.0067 0.0020

Max 0.0107 0.0092 0.0107 0.0030 0.0030 0.0007 0.0067 0.0067 0.0020 0.0038 0.0038 0.0016 0.0107 0.0067 0.0020

Table 7. Summary statistics for normalized inhalation 8-hour time weighted average concentration ((mg/m3

)/lb AI) 

using empirical sampling model. 

Statistic 1a 1aCP 1aRS 1b 1bCP 1bRS 2 2CP 2RS 3 3CP 3RS Bottle Convent 

ional 

Reduced 

Splash 

Arithmetic 

Mean 

0.0012 0.0011 0.0012 0.0001 0.0002 0.0001 0.0002 0.0003 0.0001 0.0001 0.0002 0.0001 0.0012 0.0002 0.0001

Arithmetic 

Standard 

Deviation 

0.0001 0.0001 0.0001 0.0001 0.0002 0.0000 0.0002 0.0003 0.0001 0.0001 0.0002 0.0001 0.0001 0.0002 0.0001
10

Statistic 1a 1aCP 1aRS 1b 1bCP 1bRS 2 2CP 2RS 3 3CP 3RS Bottle Convent 

ional 

Reduced 

Splash 

Geometric 

Mean 

0.0012 0.0011 0.0012 0.0001 0.0002 0.0001 0.0001 0.0002 0.0001 0.0001 0.0001 0.0001 0.0012 0.0002 0.0001

Geometric 

Standard 

Deviation 

1.1045 1.0700 1.0757 1.8321 2.0497 1.0161 2.9094 2.6705 2.3240 2.3476 2.9358 1.9434 1.1045 2.6982 1.9286

Min 0.0010 0.0010 0.0012 0.0001 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0010 0.0000 0.0000

 5% 0.0010 0.0010 0.0012 0.0001 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0010 0.0000 0.0000

10% 0.0010 0.0010 0.0012 0.0001 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0010 0.0000 0.0000

25% 0.0011 0.0010 0.0012 0.0001 0.0001 0.0001 0.0000 0.0002 0.0000 0.0001 0.0001 0.0001 0.0011 0.0001 0.0000

50% 0.0012 0.0011 0.0012 0.0001 0.0001 0.0001 0.0002 0.0003 0.0001 0.0001 0.0001 0.0001 0.0012 0.0002 0.0001

75% 0.0012 0.0011 0.0013 0.0001 0.0004 0.0001 0.0003 0.0003 0.0001 0.0002 0.0002 0.0002 0.0012 0.0003 0.0002

90% 0.0013 0.0011 0.0013 0.0004 0.0004 0.0001 0.0003 0.0008 0.0003 0.0002 0.0005 0.0002 0.0013 0.0005 0.0002

95% 0.0013 0.0011 0.0013 0.0004 0.0004 0.0001 0.0008 0.0008 0.0003 0.0005 0.0005 0.0002 0.0013 0.0008 0.0003

Max 0.0013 0.0011 0.0013 0.0004 0.0004 0.0001 0.0008 0.0008 0.0003 0.0005 0.0005 0.0002 0.0013 0.0008 0.0003

The summary statistics shown in Tables 1 to 4 show that the results for the four dermal scenarios (long dermal, short 

dermal, long short dermal, and hands only) are very similar. This is reflected by the fact that the dermal exposures are 

dominated by the large measured values on the hands. The results for Tables 1 to 7 also show that the statistics for 

groups 1aCP and 1aRS are quite similar, especially in view of the fact that they are only based on 3 workers per group, 

and that there are big differences between 1bCP and 1bRS. The differences between the conventional pour and reduced 

splash exposures are relatively small within groups 2 and 3. The results show some large differences between groups 

1b, 2 and 3, especially between dermal exposures in groups 1b and 2. 

To evaluate the differences between the groups, an analysis of variance was used to test for statistically significant 

differences. The following statistical mixed model fitted to all the exposure data (separately for each exposure route) 

was used for this test: 

Log(normalized exposure) = group + worker + error 

For this model, the (fixed effect) group variable is the group category that allocates each exposure measurement to one 

of the eight groups 1aCP, 1aRS, 1bCP, 1bRS, 2CP, 2RS, 3CP, 3RS. Thus the geometric mean depends upon the 

container size category (1a, 1b, 2 or 3) and the type of container (conventional or reduced splash). The worker term is a 

random effect that represents the correlation between multiple measurements on the same worker; each worker has 

their own random exposure effect that is added to the overall group mean (after taking logarithms). The worker effects 

are drawn from a normal distribution with mean zero. Each of the 36 measurements also has a random error term drawn 

from another normal distribution with mean zero. This model was fitted to the data and then used to test for the 

following differences between the eight groups using a statistical contrast: 

• RS=CP for bottles. This tests if the means for groups 1aCP and 1aRS are equal. A non-significant difference 

supports combining the 1a data from conventional and reduced splash containers. 
11

• RS=CP for other. This tests if the means for groups 1bCP and 1bRS are equal, and the means for groups 2CP 

and 2RS are equal, and the means for groups 3CP and 3RS are equal. A non-significant difference supports 

combining the data from conventional and reduced splash containers of the same size, when the receiving 

container is not a trigger spray bottle. It does not evaluate whether the size groups 1b, 2, and 3 can be combined. 

• 1b=2=3 for CP. This tests if the means for groups 1bCP, 2CP, and 3CP are equal. A non-significant difference 

supports combining the conventional pour data from containers of difference sizes, when the receiving 

container is not a trigger spray bottle. 

• 1b=2=3 for RS. This tests if the means for groups 1bRS, 2RS, and 3RS are equal. A non-significant difference 

supports combining the reduced splash data from containers of difference sizes, when the receiving container is 

not a trigger spray bottle. 

• bottles=other for CP. This tests if the means for groups 1aCP, 1bCP, 2CP, and 3CP are equal. A non-significant 

difference supports combining the conventional pour data from containers of difference sizes, and whether or 

not the receiving container is a trigger spray bottle. 

• bottles=other for RS. This tests if the means for groups 1aRS, 1bRS, 2RS, and 3RS are equal. A non-significant 

difference supports combining the reduced splash data from containers of difference sizes, and whether or not 

the receiving container is a trigger spray bottle. 

The results are shown in Table 8. P-values at or below 0.05 indicate statistically significant differences at the 5 percent 

significance level. The “RS=CP for bottles” test is not significant for all the exposure routes, which supports combining 

the group 1a data for CP and RS into a single group. The “1b=2=3 for CP” test is significant for the dermal exposures 

but not for the inhalation exposures, which fails to support combining the CP data for the different container sizes. The 

“1b=2=3 for RS” test is significant for the dermal exposures but not for the inhalation exposures, which fails to support 

combining the RS data for the different container sizes. The “bottles=other for CP” test is significant for all the 

exposure routes except for the inhalation concentration, which fails to support combining the CP data for the different 

container sizes and for pouring into trigger spray bottles. The “bottles=other for RS” test is significant for all the 

exposure routes, which fails to support combining the RS data for the different container sizes and for pouring into 

trigger spray bottles. Despite these findings, it is not feasible to apply separate unit exposure estimates (and, ultimately, 

regulatory decisions) for pouring liquids from containers of different sizes, so it was decided that the three groups 1b, 2, 

and 3 would be combined for the statistical mixed modeling. Under the mixed models, the geometric mean exposure is 

assumed to be the same for groups 1b, 2 and 3 (although different between conventional pour and reduced splash 

containers) and any differences between container size groups are treated as being part of the random variability in 

exposure. Therefore the final mixed models used three groups only:- Bottle: 1a-Pouring into trigger spray bottles; 

Conventional: 1bCP, 2CP, and 3CP-Pouring from conventional pour containers not into trigger spray bottles; and 

Reduced Splash: 1bRS, 2RS, and 3RS-Pouring from reduced splash containers not into trigger spray bottles. 

Table 8. Statistical tests comparing different groups of source and receiving containers. 

Normalized Exposure Test P-Value 

Long Dermal mg per pound AI RS=CP for bottles 0.88 

Long Dermal mg per pound AI RS=CP for other 0.01 

Long Dermal mg per pound AI bottles=other for CP 0.00 

Long Dermal mg per pound AI bottles=other for RS 0.00 
12

Normalized Exposure Test P-Value 

Long Dermal mg per pound AI 1b=2=3 for CP 0.02 

Long Dermal mg per pound AI 1b=2=3 for RS 0.00 

Short Dermal mg per pound AI RS=CP for bottles 0.84 

Short Dermal mg per pound AI RS=CP for other 0.03 

Short Dermal mg per pound AI bottles=other for CP 0.00 

Short Dermal mg per pound AI bottles=other for RS 0.00 

Short Dermal mg per pound AI 1b=2=3 for CP 0.01 

Short Dermal mg per pound AI 1b=2=3 for RS 0.03 

Long Short Dermal mg per pound AI RS=CP for bottles 0.87 

Long Short Dermal mg per pound AI RS=CP for other 0.01 

Long Short Dermal mg per pound AI bottles=other for CP 0.00 

Long Short Dermal mg per pound AI bottles=other for RS 0.00 

Long Short Dermal mg per pound AI 1b=2=3 for CP 0.01 

Long Short Dermal mg per pound AI 1b=2=3 for RS 0.00 

Hands Only Dermal mg per pound AI RS=CP for bottles 0.86 

Hands Only Dermal mg per pound AI RS=CP for other 0.01 

Hands Only Dermal mg per pound AI bottles=other for CP 0.00 

Hands Only Dermal mg per pound AI bottles=other for RS 0.00 

Hands Only Dermal mg per pound AI 1b=2=3 for CP 0.03 

Hands Only Dermal mg per pound AI 1b=2=3 for RS 0.00 

Inhalation Concentration mg/m3 per pound AI RS=CP for bottles 0.74 

Inhalation Concentration mg/m3 per pound AI RS=CP for other 0.03 

Inhalation Concentration mg/m3 per pound AI bottles=other for CP 0.22 

Inhalation Concentration mg/m3 per pound AI bottles=other for RS 0.02 

Inhalation Concentration mg/m3 per pound AI 1b=2=3 for CP 0.89 

Inhalation Concentration mg/m3 per pound AI 1b=2=3 for RS 0.45 

Inhalation Dose mg per pound AI RS=CP for bottles 0.83 

Inhalation Dose mg per pound AI RS=CP for other 0.10 

Inhalation Dose mg per pound AI bottles=other for CP 0.01 
13

Normalized Exposure Test P-Value 

Inhalation Dose mg per pound AI bottles=other for RS 0.00 

Inhalation Dose mg per pound AI 1b=2=3 for CP 0.22 

Inhalation Dose mg per pound AI 1b=2=3 for RS 0.80 

Inhalation 8hr TWA mg/m3 per pound AI RS=CP for bottles 0.83 

Inhalation 8hr TWA mg/m3 per pound AI RS=CP for other 0.10 

Inhalation 8hr TWA mg/m3 per pound AI bottles=other for CP 0.01 

Inhalation 8hr TWA mg/m3 per pound AI bottles=other for RS 0.00 

Inhalation 8hr TWA mg/m3 per pound AI 1b=2=3 for CP 0.22 

Inhalation 8hr TWA mg/m3 per pound AI 1b=2=3 for RS 0.80 

The statistical analyses use the following three alternative statistical models. Let X be the normalized exposure and X = 

exp(Y) so that Y = log (X), where log denotes the natural logarithm. LnGM is the log of the geometric mean for a 

given group. Let Z95 be the 95th percentile of a standard normal distribution, approximately 1.645. 

• Empirical simple random sampling model. Code “s.” Assumes that all the values of X from a given group g 

were randomly drawn from an unspecified distribution. Ignores within-worker correlations. Gives empirical 

estimates such as in Tables 1 to 7 above. 

o Each of the following statistics depends upon the group g and only uses the X and Y values from that 

group 

o Y = LnGM + Error. Error is independent and identically distributed with mean 0 and a variance that 

depelognormal nds upon the group g. 

o AMs = Arithmetic mean of X values 

o GMs = Geometric mean of X values = exp(LnGM) (= GMu) 

o GSDs = Geometric standard deviation of X values (= GSDu) 

o P95s = 95th percentile of X values 

• Lognormal simple random sampling model. Code “u.” Assumes that all the values of X from a given group g 

were randomly drawn from a log-normal distribution. Ignores within-worker correlations. 

o Each of the following statistics depends upon the group g and only uses the X and Y values from that 

group 

o Y = LnGM + Error. Error is normally distributed with mean 0, variance Vu, and standard deviation Su = 

√Vu. 

o AMu = Modeled arithmetic mean of X values = exp(LnGM) exp(1⁄2 Vu) 

o GMu = Modeled geometric mean of X values = exp(LnGM) 

o GSDu = Modeled geometric standard deviation of X values = exp(Su) 
14

o P95u = Modeled 95th percentile of X values = exp(LnGM) exp(Z95×Su) 

• Lognormal mixed model. Code “m.” There are three groups, Bottle, Conventional Pour, and Reduced Splash, as 

defined above. Each group has a different geometric mean. Assumes that the 18 worker random effects were 

independently randomly drawn from a normal distribution and that the 36 random error terms were 

independently drawn from another normal distribution. The error term for each worker and exposure 

measurement is the sum of the worker effect for that worker and the within-worker random error term. 

o Y = LnGM + Worker + Error. Worker is normally distributed with mean 0, variance Vw, and standard 

deviation Sw = √Vw. Error is normally distributed with mean 0, variance Vr, and standard deviation Sr 

= √Vr. Define V = Vw + Vr and S = √V. V is the variance of Y, and S is the standard deviation of Y. 

LnGM depends upon the group. 

o ICC = Intra-worker correlation coefficient = Vw/V. 

o AMm = Modeled arithmetic mean of X values = exp(LnGM) exp(1⁄2 V). Depends upon the group. 

o GMm = Modeled geometric mean of X values = exp(LnGM). Depends upon the group. 

o GSDm = Modeled geometric standard deviation of X values = exp(S) 

o P95m = Modeled 95th percentile of X values = exp(LnGM) exp(Z95×S). Depends upon the group. 

For the lognormal mixed model, the ICC value estimates the clustering effect of multiple measurements on the same 

worker and lies between 0 (no clustering) and 1 (complete clustering and negligible within-cluster variation). An ICC 

of 0 is when repeated measurements on the same worker are uncorrelated. An ICC of 1 is when all the exposure 

measurements on the same worker are identical. 

Table 9 presents the arithmetic mean and 95th percentile estimates from the lognormal mixed model, together with 95% 

confidence intervals, for all the exposure routes. These are the values of AMm and P95m. The other summary statistics 

are presented in more detail below. 

Table 9. Arithmetic mean and 95th percentile estimates from lognormal mixed model for normalized exposure. 

Exposure Route Clothing Group 

Arithmetic Mean 

(95% confidence 

interval) 

95th percentile 

(95% confidence 

interval) 

Dermal 

(mg/lb AI) 

Long pants and long 

sleeves 

Bottle 298.5 (89.9, 1005.7) 1105.5 (309.4, 

3817.5) 

 Conventional 10.0 (4,5. 22.8) 36.9 (15.4, 86.7) 

 Reduced Splash 3.1 (1.4, 7.4) 11.6 (4.9, 28.1) 

Short pants and short 

sleeves

Bottle 207.4 (77.3, 568.3) 706.5 (241.3, 2009.2) 

 Conventional 9.0 (4,7. 17.6) 30.7 (14.6, 63.2) 

 Reduced Splash 4.0 (2.1, 7.9) 13.6 (6.4, 28.7) 

Long pants and short 

sleeves 

Bottle 280.7 (89.5, 892.7) 1020.9 (300.8, 

3350.0) 

 Conventional 9.9 (4.7, 21.7) 36.0 (15.6, 81.8) 
15

Exposure Route Clothing Group 

Arithmetic Mean 

(95% confidence 

interval) 

95th percentile 

(95% confidence 

interval) 

 Reduced Splash 3.0 (1.4, 6.8) 11.0 (4.8, 25.7) 

Hands only Bottle 314.0 (89.8, 1115.2) 1178.7 (315.1, 

4245.5) 

 Conventional 10.3 (4.5, 24.6) 38.8 (15.7, 93.7) 

 Reduced Splash 3.1 (1.3, 7.5) 11.4 (4.6, 28.6) 

Inhalation 

Concentration 

(mg/m3

/lb AI) 

Bottle 0.047 (0.024, 0.093) 0.128 (0.061, 0.264) 

 Conventional 0.016 (0.010, 0.024) 0.042 (0.025, 0.071) 

 

Reduced Splash 0.0049 (0.0032, 

0.0076) 

0.0132 (0.0079, 

0.0223) 

Inhalation Dose 

(mg/lb AI)

Bottle 0.012 (0.006, 0.024) 0.033 (0.016, 0.066) 

 

Conventional 0.0017 (0.0011, 

0.0026) 

0.0046 (0.0028, 

0.0075) 

 

Reduced Splash 0.00091 (0.00061, 

0.00140) 

0.00242 (0.00148, 

0.00401) 

Inhalation 8-hr 

TWA (mg/m3/lb 

AI) 

 Bottle 0.0016 (0.0008, 

0.0030) 

0.0041 (0.0020, 

0.0083) 

 Conventional 0.00021 (0.00014, 

0.00033) 

0.00057 (0.00035, 

0.00093) 

 Reduced Splash 0.00011 (0.00008, 

0.00018) 

0.00030 (0.00019, 

0.00050) 

For each exposure route, the above three statistical models were fitted to the observed data and the summary statistics 

listed above were calculated together with 95% confidence intervals. The 95% confidence intervals in Table 9 were 

computed using a parametric bootstrap. For these calculations, the parametric bootstrap simulations were all generated 

from the fitted lognormal mixed model, even for the empirical and simple random sample summary statistics, on the 

basis that the mixed model is the best choice for modeling the data, even if the summary statistics are developed from a 

simpler statistical model. For example, in Tables 1 to 7, the empirical arithmetic means are presented, which are the 

arithmetic means of the group measurements (between 3 and 15 measurements per group). To estimate the uncertainty 

of those empirical arithmetic means, data are simulated from the lognormal mixed model to calculate the parametric 

bootstrap confidence intervals. The arithmetic means in Table 9 are estimated using the lognormal mixed model, which 

is also used to estimate the confidence intervals in Table 9. The unit exposure estimates (from the lognormal mixed 

model) displayed in Table 9 are recommended over the empirical arithmetic means and 95th percentiles displayed in 

Tables 1 to 7. (For the original groupings the detailed results in Tables 1 to 7 may be preferable). 

The algorithm used was as follows: 

Step 1: 
16

Simulate 36 random variables Y, X from the estimated lognormal distribution superimposed upon the observed sampling structure ---; 

W = RanNor (Seed) ×Sw (18 values, one for each worker) 

Y = W + LnGM + RanNor(Seed)×Sr 

X = exp(Y) 

where: 

LnGM = group intercept of mixed effect log-log regression model 

Sw = square root of between worker variance 

Sr = square root of within worker variance under mixed-effect model 

The allocation of each worker to two groups (one for each measurement) is exactly the same as the observed random design 

configuration. 

Step 2: 

For Y: 

Calculate GMs = exp(EAM) 

Calculate GSDs = exp(Su) 

Calculate AMu = GMs×exp(0.5×Su×Su) 

Calculate P95u = GMs× exp(Z95×Su) 

Fit mixed lognormal model to simulated Y values 

Under mixed-effects model: 

Calculate GMm= exp(group intercept of mixed-effects model) 

Calculate GSDm = exp(square root (total variance V under mixed-effects model)) 

Calculate ICC = Vw /V 

Calculate AMm = exp(group intercept + 0.5×V) 

Calculate P95m = exp(group intercept + Z95×S) 

where: 

EAM = sample arithmetic mean of Y over group = AMu 

Su = standard deviation of Y over group 

V = total variance under mixed-effects model 

S = square root of V 

Vw = between worker variance. 

For X: 

Calculate arithmetic mean for group AMs

Calculate 95th percentile for group P95s

Step 3: Repeat Steps 1 and 2 10,000 times. 

Steps 1 to 3 result in 10,000 values each for each of GSDs, GMs, GMm, AMs, AMm, AMu, P95s, P95m, and P95u for each group and 10,000 

values each for GSDm and ICC. 95% confidence intervals can be defined for each parameter by the 2.5th and 97.5th percentiles (lower and 

upper, respectively) of the bootstrap distribution of that corresponding parameter. Note that by definition, GSDs = GSDu and GMs = GMu. 
17

The dermal exposure results in Table 9 based on the lognormal mixed model show that for all three groups the 

arithmetic mean for long pants and long sleeves is higher than the arithmetic mean for long pants and short sleeves, and 

that for the Bottle and Conventional groups the arithmetic mean for long pants and short sleeves is higher than the 

arithmetic mean for short pants and short sleeves. These results would appear to be contrary to the fact that the 

calculated exposures for short sleeves versus long sleeves are higher due to the outer dosimeter for the lower arm and 

the calculated exposures for short pants versus long pants are higher due to the outer dosimeter for the lower leg. These 

results occurred because the estimated arithmetic mean based on the lognormal mixed model is given by the formula 

GMm×exp(1⁄2 V) where GMm is the estimated geometric mean and V is the estimated variance. Even if the estimated 

geometric mean increases, the estimated variance can decrease producing a net decrease in the estimated arithmetic 

mean even though the true arithmetic mean must increase. Since all three dermal exposure measures for this liquid pour 

scenario are dominated by the hands only exposure, the differences in the estimated arithmetic means and between the 

estimated 95th percentiles for the three dermal exposure measures are small compared to the very wide confidence 

intervals. For this reason we regard this issue as a statistical “quirk” attributable to large uncertainty in the fitted models

for dermal exposure. In the section “Alternative models for dermal exposure” we investigate alternative models and 

outlier treatments to further understand these statistical “quirks.” 

Outliers and non-detects 

For all the analyses presented in this memorandum, except for Tables 10, 11 and 20 (see below for discussion on Table 

20), all the data values were used and values below the LOQ were replaced by one half of the LOQ. For three subjects 

and MEs (Reduced Splash ME 1 in group 1a, Reduced Splash ME 7 in group 2, and Conventional Pour ME 6 in group 

1b), the hand exposure measurements were much higher when normalized by the amount of active ingredient than 

values for all other subjects in the same group. The liquid pour scenario is one in which unusually large hand exposures 

can occur through random dripping and spilling events that may be poorly associated with the total amount of active 

ingredient used. To investigate the impact of this potential outlier, we recomputed the arithmetic mean and 95th

percentile estimates (and parametric bootstrap confidence intervals) for Long Dermal exposure after excluding the 

dermal data for these measurements. As shown in Table 10, the mean is reduced by between 29% and 42% (for Bottle 

using zero substitution) and the 95th percentile is reduced by between 33% and 45% (for Bottle using zero substitution) 

for Long Dermal exposure. The outliers have a substantial effect. 

Also investigated in Table 10 (for Long Dermal) and in Table 11 (for inhalation concentration) is the impact of the 

values below the LOQ. All the hand wash in the study were above the LOQ. For the Conventional Pour, 4 of the 18 

face and neck measurements, 67 of the 108 outer dosimeter measurements, 107 of the 108 inner dosimeter 

measurements, and 6 of the 18 OVS measurements were below the LOQ. For the Reduced Splash, 0 of the 18 face and 

neck measurements, 41 of the 108 outer dosimeter measurements, 105 of the 108 inner dosimeter measurements, and 9 

of the 18 OVS measurements were below the LOQ. For the Long Dermal exposure we computed the arithmetic mean 

and 95th percentiles using the recommended substitution of one half the LOQ for values below the LOQ and compared 

the estimates using alternative substitutions of the LOQ (the maximum possible exposure estimate) and of zero (the 

minimum possible exposure estimate. For the inhalation concentration and dose we computed the arithmetic mean and 

95th percentiles using the recommended substitution of one half the LOQ for values below the LOQ and compared the 

estimates using the alternative substitutions of the LOQ (the maximum possible exposure estimate); substitution of zero 

for inhalation exposure is not useful because the statistical models use the logarithms of the exposure which cannot be 

calculated when the minimum exposure is zero. We also investigated a statistical imputation scheme described in the 

following paragraphs. 

Note that in some cases replacing non-detect values by zero increased the estimated arithmetic mean and 95th percentile 

compared to using the default half LOQ method, and replacing non-detect values by the LOQ decreased the estimated 

arithmetic mean and 95th percentile compared to using the default half LOQ method. This paradoxical finding occurred 

because using zero instead of half the LOQ increased the estimated variance and using the LOQ instead of half the 
18

LOQ decreased the estimated variance; the arithmetic mean and 95th percentile estimates from the mixed model adjust 

the geometric mean using the estimated variance of the logarithms. 

As a more exact approach for analyzing values below the LOQ, a multiple imputation approach using maximum 

likelihood methods for censored data was applied, as follows. Each dermal exposure value is known to be between L 

and U, where L is the value obtained by replacing all values below the LOQ by zero and summing the values for hand 

wash, face and neck, and the dosimeters, and U is the value obtained by replacing all values below the LOQ by the 

LOQ and summing the values for hand wash, face and neck, and the dosimeters. The dermal exposure totals data are 

thus censored and lie between L and U. For inhalation exposure, the values of L and U are equal to the measured value 

if it is above the LOQ and are given by L equals zero and U equals the LOQ if the value is below the LOQ. 

To estimate the unknown values for the dermal exposure, the following mixed model was fitted to the combined 

censored and uncensored data: 

 Log (Exposure) = Group + Slope × Log (Pounds of Active Ingredient) + Worker + Error 

In this model, the value of Slope is not necessarily 1, Group is a fixed effect value for each of the three groups Bottle, 

Conventional, and Reduced Splash giving the intercept for each group, Worker is a normally distributed random effect 

variable with independent, identically distributed values for each worker, and Error is a normally distributed error 

variable with independent, identically distributed values for each total exposure measurement. Note that this model 

ignores any information in the data about which of the values were non-detects. This model was fitted using the SAS 

procedure NLMIXED, using code adapted from the article “Analysis of Lognormally Distributed Exposure Data with 

Repeated Measures and Values below the Limit of Detection Using SAS” (YAN JIN, MISTY J. HEIN, JAMES A. 

DEDDENS and CYNTHIA J. HINES, Ann Occup Hyg (2011) 55(1): 97-112, doi:10.1093/annhyg/meq061). For these 

calculations, the marginal likelihood averaged over the random effects is maximized. The fitted model has values for 

the following parameters: three Group intercepts, Slope, Variance of Worker, Variance of Error. Separate models were 

fitted for each clothing and inhalation scenario. 

Exposure values were randomly generated from the fitted model by first simulating the eighteen Worker random 

effects, and then simulating values for the random error using the conditional distribution given that the total exposure 

for each censored value is between L and U. Uncensored values (where all components were above the LOQ) were not 

changed. In this manner, all 36 exposure values for a given scenario were simulated. To account for the uncertainty in 

the simulations, the entire simulation was repeated 5 times for each scenario, producing 5 independent imputation data 

sets. 

For the multiple imputation data, each statistic and confidence bound was averaged over the five imputations to give an 

overall average statistic and confidence interval. Note that this approach does not fully account for the uncertainty due 

to the imputation. Instead, the Bayesian methods of Rubin might have been used to account for the variance from the 

imputation, but those methods use the standard errors of the statistics rather than the confidence intervals, and so would 

ignore the skewness in the estimated parametric bootstrap confidence intervals. 

Table 10. Long Dermal summary statistics calculated with and without the potential outlier data for Reduced Splash 

ME 1 in group 1a, Reduced Splash ME 7 in group 2, and Conventional Pour ME 6 in group 1b, and using alternative 

estimated exposures for values below the LOQ. 
19

Group Data Method for 

substituting 

values 

below the 

LOQ 

Arithmetic mean (mg / lb 

AI) 

95th percentile (mg / 

lb AI) 

Bottle All 36 

Values 

Substitute 1⁄2 

LOQ 

298.5 (89.9, 1005.7) 1105.5 (309.4, 

3817.5) 

Bottle All 36 

Values

Substitute 

LOQ 

288.3 (90.1, 932.9) 1055.0 (305.7, 

3515.3) 

Bottle All 36 

Values

Substitute 

zero 

313.9 (89.8, 1114.2) 1177.9 (314.9, 

4241.3) 

Bottle All 36 

Values

Multiple 

imputation 

298.6 (89.7, 1008.3) 1106.2 (309.3, 

3818.5) 

Bottle Exclude 

outlier data 

Substitute 1⁄2 

LOQ 

177.5 (59.9, 550.7) 616.4 (193.9, 1961.3) 

Bottle Exclude 

outlier data 

Substitute 

LOQ 

171.1 (60.8, 520.0) 592.9 (193.7, 1820.6) 

Bottle Exclude 

outlier data 

Substitute 

zero 

183.5 (59.8, 597.7) 651.2 (196.5, 2173.3) 

Bottle Exclude 

outlier data 

Multiple 

imputation 

177.6 (59.4, 553.8) 618.2 (194.0, 1981.6) 

Conventional All 36 

Values 

Substitute 1⁄2 

LOQ 

10.0 (4.5, 22.8) 36.9 (15.4, 86.7) 

Conventional All 36 

Values

Substitute 

LOQ 

9.7 (4.5, 21.5) 35.5 (15.2, 81.5) 

Conventional All 36 

Values

Substitute 

zero 

10.4 (4.5, 24.6) 38.8 (15.7, 93.8) 

Conventional All 36 

Values

Multiple 

imputation 

10.0 (4.5, 22.9) 37.0 (15.4, 86.9) 

Conventional Exclude 

outlier data 

Substitute 1⁄2 

LOQ 

7.1 (3.5, 14.8) 24.6 (11.1, 54.1) 

Conventional Exclude 

outlier data 

Substitute 

LOQ 

6.9 (3.5, 14.2) 23.6 (10.9, 50.9) 
20

Group Data Method for 

substituting 

values 

below the 

LOQ 

Arithmetic mean (mg / lb 

AI) 

95th percentile (mg / 

lb AI) 

Conventional Exclude 

outlier data 

Substitute 

zero 

7.3 (3.5, 16.0) 25.9 (11.4, 59.6) 

Conventional Exclude 

outlier data 

Multiple 

imputation 

71. (3.5, 14.8) 24.8 (11.2, 55.1) 

Reduced Splash All 36 

Values 

Substitute 1⁄2 

LOQ 

3.1 (1.4, 7.4) 11.6 (4.9, 28.1) 

Reduced Splash All 36 

Values

Substitute 

LOQ 

3.2 (1.5, 7.3) 11.8 (5.0, 27.7) 

Reduced Splash All 36 

Values

Substitute 

zero 

3.1 (1.3, 7.5) 11.5 (4.7, 28.8) 

Reduced Splash All 36 

Values

Multiple 

imputation 

3.1 (1.4, 7.3) 11.6 (4.8, 28.0) 

Reduced Splash Exclude 

outlier data 

Substitute 1⁄2 

LOQ 

2.0 (1.0, 4.1) 6.9 (3.1, 15.0) 

Reduced Splash Exclude 

outlier data 

Substitute 

LOQ 

2.1 (1.1, 4.1) 7.0 (3.2, 14.8) 

Reduced Splash Exclude 

outlier data 

Substitute 

zero 

1.9 (0.9, 4.1) 6.8 (3.0, 15.3) 

Reduced Splash Exclude 

outlier data 

Multiple 

imputation 

2.0 (1.0, 4.1) 6.9 (3.1, 15.1) 

Table 11. Inhalation concentration summary statistics calculated using alternative estimated exposures for values below 

the LOQ. 

Group Data Method for 

substituting 

values 

below the 

LOQ 

Arithmetic mean (mg / 

m3

/lb AI) 

95th percentile (mg / 

m3/ lb AI) 

Bottle All 36 Substitute 1⁄2 0.047 (0.024, 0.093) 0.128 (0.061, 0.264) 
21

Group Data Method for 

substituting 

values 

below the 

LOQ 

Arithmetic mean (mg / 

m3/lb AI) 

95th percentile (mg / 

m3/ lb AI) 

Values LOQ 

Bottle All 36 

Values

Substitute 

LOQ 

0.086 (0.049, 0.150) 0.206 (0.111, 0.377) 

Bottle All 36 

Values

Multiple 

imputation 

0.001 (0.001, 0.002) 0.003 (0.001, 0.007) 

Conventional All 36 

Values 

Substitute 1⁄2 

LOQ 

0.016 (0.010, 0.024) 0.042 (0.025, 0.071) 

Conventional All 36 

Values

Substitute 

LOQ 

0.016 (0.011. 0.023) 0.039 (0.025, 0.060) 

Conventional All 36 

Values

Multiple 

imputation 

0.017 (0.011, 0.029) 0.051 (0.028, 0.090) 

Reduced Splash All 36 

Values 

Substitute 1⁄2 

LOQ 

0.0049 (0.0032, 0.0076) 0.0132 (0.0079, 

0.0223) 

Reduced Splash All 36 

Values

Substitute 

LOQ 

0.0058 (0.0041, 0.0084) 0.0141 (0.0092, 

0.0217) 

Reduced Splash All 36 

Values

Multiple 

imputation 

0.0049 (0.0030, 0.0081) 0.0143 (0.0081, 

0.0257) 

The results in Tables 10 demonstrate that all the alternative approaches for treating values below the LOQ have a very 

small effect on Long Dermal exposure (the change in the estimates is less than 7%). The results were similar for Short 

Dermal and Long Short Dermal exposure. 

The results in Table 11 demonstrate very large impacts of the alternative approaches for treating values below the LOQ 

on the inhalation concentration, because of the large percentage of OVS values below the LOQ: For the Bottle group, 

using the LOQ substitution instead of the half LOQ substitution increases the arithmetic mean and 95th percentile by up 

to 81%, and using the multiple imputation instead of the half LOQ substitution decreases the arithmetic mean and 95th

percentile by up to 98%. For the Conventional and Reduced Splash groups, using the LOQ substitution instead of the 

half LOQ substitution changes the arithmetic mean and 95th percentile by up to 8%, and using the multiple imputation 

instead of the half LOQ substitution increases the arithmetic mean and 95th percentile by up to 20%. The inhalation 

exposure results were similar for the inhalation dose and the inhalation 8-hour time weighted average concentration; 

results not shown. 
22

Fold relative accuracy 

Fold relative accuracy (fRA) is a measure that can be used to determine how well a statistic can describe its population 

parameter. Let us assume θ is a parameter and T is the sample statistic of θ (i.e., an estimate of θ). If the 2.5th and 

97.5th percentiles of the sampling distribution of T can be denoted by T2.5 and T97.5, respectively, then the 95th percentile 

of sample fold relative accuracy can be theoretically calculated using the following formula provided in the AHETF 

Governing Document (AHETF, 2007, pg. 136 and AHETF, 2011, pg. 120): 

 fRA95 = Max (T97.5 / θ, θ / T2.5) 

The actual value of θ is unknown. Thus, fRA95 was calculated by substituting θ with T. If the fRA95 of a statistic were 

equal to 3, then it would be correct to say: “At least 95% of the time the sample statistic will be accurate to within 3-

fold of the population value”. According to the AHETF Governing Document, the statistical design of the exposure 

monitoring study should be adequate to produce a fRA95 less than or equal to 3. Thus the confidence intervals calculated 

in the above algorithm can be used to estimate the fold relative accuracy and compare the observed fRA with the study 

design benchmark of 3. If the observed fold relative accuracy is greater than 3, this means that the experiment did not 

meet the benchmark, which would be due to differences between the distributions of the CMA data used to design the 

study and the experimental data collected in the study. If the fold relative accuracy benchmark is not met, then it might 

be desirable to collect more data for this scenario in order to meet the benchmark. Fold relative accuracy was not 

computed for the ICC since the estimated ICC is 0 in many cases. 

In previously reported statistical analyses, following HSRB recommendations, confidence intervals were estimated 

using both a parametric bootstrap approach and a non-parametric bootstrap approach. For this scenario, non-parametric 

confidence intervals were not developed because of the difficulty in accounting for both the worker and group effects in 

a fully non-parametric framework. 

Detailed summary statistics with parametric confidence intervals and fold relative accuracy 

Tables 12 to 18 present the estimates, parametric confidence intervals and fold relative accuracy values for all the 

summary statistics for the four dermal and twelve inhalation exposure routes, respectively. 

Table 12. Arithmetic mean, geometric mean, geometric standard deviation, and 95th percentiles (with 95% confidence 

intervals and fold relative accuracy), for different statistical models of the normalized long dermal exposure (mg/lb AI). 

 Bottle Conventional Reduced Splash 

Parameter Estimate Lower 

Bound 

Upper 

Bound 

Fold 

Relative 

Accuracy 

Estimate Lower 

Bound 

Upper 

Bound 

Fold 

Relative 

Accuracy 

Estimate Lower 

Bound 

Upper 

Bound 

Fold 

Relative 

Accuracy 

GSDs 

2.2 1.7 8.7 4.0 4.0 2.3 6.4 1.7 4.3 2.4 6.4 1.8 

GSDm 3.9 2.8 5.4 1.4 3.9 2.8 5.4 1.4 3.9 2.8 5.4 1.4 

ICC 0.3 0.0 0.7 0.3 0.0 0.7 0.3 0.0 0.7 

GMs 116.2 39.5 376.4 3.2 4.1 2.0 8.0 2.0 1.2 0.6 2.5 2.0 

GMm 120.0 39.1 370.3 3.1 4.0 2.0 7.9 2.0 1.3 0.6 2.5 2.0 

AMs 155.3 63.4 1007.6 6.5 8.4 3.8 24.3 2.9 3.7 1.2 7.6 3.2 

AMu 158.1 70.1 1755.5 11.1 10.9 4.1 28.1 2.6 3.6 1.3 8.9 2.8 
23

 Bottle Conventional Reduced Splash 

Parameter Estimate Lower 

Bound 

Upper 

Bound 

Fold 

Relative 

Accuracy 

Estimate Lower 

Bound 

Upper 

Bound 

Fold 

Relative 

Accuracy 

Estimate Lower 

Bound 

Upper 

Bound 

Fold 

Relative 

Accuracy 

AMm 298.5 89.9 1005.7 3.4 10.0 4.5 22.8 2.3 3.1 1.4 7.4 2.3 

P95s 459.5 132.4 4287.3 9.3 35.2 11.5 210.6 6.0 31.4 3.6 65.5 8.7 

P95u 422.3 183.6 6158.5 14.6 40.9 12.8 106.7 3.2 13.7 4.0 33.8 3.5 

P95m 1105.5 309.4 3817.5 3.6 36.9 15.4 86.7 2.4 11.6 4.9 28.1 2.4 

Table 13. Arithmetic mean, geometric mean, geometric standard deviation, and 95th percentiles (with 95% confidence 

intervals and fold relative accuracy), for different statistical models of the normalized short dermal exposure (mg/lb 

AI). 

 Bottle Conventional Reduced Splash 

Parameter Estimate Lower 

Bound 

Upper 

Bound 

Fold 

Relative 

Accuracy 

Estimate Lower 

Bound 

Upper 

Bound 

Fold 

Relative 

Accuracy 

Estimate Lower 

Bound 

Upper 

Bound 

Fold 

Relative 

Accuracy 

GSDs 

2.2 1.6 6.2 2.8 3.7 2.1 4.8 1.8 3.0 2.1 4.7 1.6 

GSDm 3.1 2.3 4.2 1.3 3.1 2.3 4.2 1.3 3.1 2.3 4.2 1.3 

ICC 0.4 0.0 0.7 0.4 0.0 0.7 0.4 0.0 0.7 

GMs 118.6 41.7 288.4 2.8 4.6 2.7 8.4 1.8 2.0 1.2 3.7 1.8 

GMm 108.1 42.2 279.0 2.6 4.7 2.7 8.3 1.8 2.1 1.2 3.7 1.8 

AMs 157.8 60.0 583.7 3.7 9.1 4.2 18.4 2.2 4.2 1.9 8.1 2.3 

AMu 160.7 64.3 828.4 5.2 10.7 4.5 20.0 2.4 3.7 1.9 8.8 2.4 

AMm 207.4 77.3 568.3 2.7 9.0 4.7 17.6 2.0 4.0 2.1 7.9 2.0 

P95s 464.6 114.9 2175.6 4.7 40.0 11.5 130.2 3.5 32.2 5.1 59.7 6.3 

P95u 427.9 151.8 3060.5 7.2 39.0 12.5 75.6 3.1 12.1 5.5 33.2 2.7 

P95m 706.5 241.3 2009.2 2.9 30.7 14.6 63.2 2.1 13.6 6.4 28.7 2.1 

Table 14. Arithmetic mean, geometric mean, geometric standard deviation, and 95th percentiles (with 95% confidence 

intervals and fold relative accuracy), for different statistical models of the normalized long short dermal exposure 

(mg/lb AI). 

 Bottle Conventional Reduced Splash 

Parameter Estimate Lower 

Bound 

Upper 

Bound 

Fold 

Relative 

Accuracy 

Estimate Lower 

Bound 

Upper 

Bound 

Fold 

Relative 

Accuracy 

Estimate Lower 

Bound 

Upper 

Bound 

Fold 

Relative 

Accuracy 
24

 Bottle Conventional Reduced Splash 

Parameter Estimate Lower 

Bound 

Upper 

Bound 

Fold 

Relative 

Accuracy 

Estimate Lower 

Bound 

Upper 

Bound 

Fold 

Relative 

Accuracy 

Estimate Lower 

Bound 

Upper 

Bound 

Fold 

Relative 

Accuracy 

GSDs 

2.2 1.7 7.9 3.6 3.6 2.3 5.9 1.6 4.2 2.3 5.9 1.8 

GSDm 3.6 2.6 5.0 1.4 3.6 2.6 5.0 1.4 3.6 2.6 5.0 1.4 

ICC 0.3 0.0 0.7 0.3 0.0 0.7 0.3 0.0 0.7 

GMs 116.7 42.0 364.5 3.1 4.4 2.2 8.3 2.0 1.3 0.7 2.5 1.9 

GMm 121.6 41.3 357.2 2.9 4.3 2.2 8.3 1.9 1.3 0.7 2.5 1.9 

AMs 155.8 65.1 896.8 5.8 8.5 4.0 23.1 2.7 3.8 1.2 7.0 3.1 

AMu 158.5 71.4 1477.6 9.3 10.1 4.3 26.1 2.6 3.7 1.3 8.0 2.8 

AMm 280.7 89.5 892.7 3.2 9.9 4.7 21.7 2.2 3.0 1.4 6.8 2.2 

P95s 461.2 133.5 3704.9 8.0 35.2 11.8 190.7 5.4 31.5 3.6 57.8 8.8 

P95u 423.1 181.4 5285.8 12.5 36.6 13.0 99.5 2.8 13.8 3.9 30.6 3.5 

P95m 1020.9 300.8 3350.0 3.4 36.0 15.6 81.8 2.3 11.0 4.8 25.7 2.3 

Table 15. Arithmetic mean, geometric mean, geometric standard deviation, and 95th percentiles (with 95% confidence 

intervals and fold relative accuracy), for different statistical models of the normalized hands only exposure (mg/lb AI). 

 Bottle Conventional Reduced Splash 

Parameter Estimate Lower 

Bound 

Upper 

Bound 

Fold 

Relative 

Accuracy 

Estimate Lower 

Bound 

Upper 

Bound 

Fold 

Relative 

Accuracy 

Estimate Lower 

Bound 

Upper 

Bound 

Fold 

Relative 

Accuracy 

GSDs 

2.2 1.8 9.4 4.2 4.2 2.4 6.8 1.7 4.6 2.4 6.8 1.9 

GSDm 4.1 2.9 5.7 1.4 4.1 2.9 5.7 1.4 4.1 2.9 5.7 1.4 

ICC 0.2 0.0 0.6 0.2 0.0 0.6 0.2 0.0 0.6 

GMs 113.6 37.3 385.3 3.4 4.0 1.9 8.0 2.1 1.1 0.6 2.3 2.0 

GMm 118.0 37.0 379.2 3.2 3.9 1.9 7.9 2.0 1.1 0.6 2.3 2.0 

AMs 153.1 61.4 1111.4 7.3 8.3 3.8 26.1 3.2 3.6 1.1 7.7 3.4 

AMu 156.3 68.8 2027.0 13.0 11.1 4.1 31.0 2.8 3.6 1.2 9.2 3.1 

AMm 314.0 89.8 1115.2 3.6 10.3 4.5 24.6 2.4 3.1 1.3 7.5 2.4 

P95s 456.9 131.8 4862.3 10.6 35.0 11.6 235.2 6.7 31.3 3.4 68.1 9.2 

P95u 422.5 182.1 7036.8 16.7 42.1 12.9 116.7 3.3 14.0 3.8 34.7 3.7 
25

 Bottle Conventional Reduced Splash 

Parameter Estimate Lower 

Bound 

Upper 

Bound 

Fold 

Relative 

Accuracy 

Estimate Lower 

Bound 

Upper 

Bound 

Fold 

Relative 

Accuracy 

Estimate Lower 

Bound 

Upper 

Bound 

Fold 

Relative 

Accuracy 

P95m 1178.7 315.2 4245.5 3.7 38.8 15.7 93.7 2.5 11.4 4.6 28.6 2.5 

Table 16. Arithmetic mean, geometric mean, geometric standard deviation, and 95th percentiles (with 95% confidence 

intervals and fold relative accuracy), for different statistical models of the normalized inhalation concentration 

(mg/m3/lb AI). 

 Bottle Conventional Reduced Splash 

Parameter Estimate Lower 

Bound 

Upper 

Bound 

Fold 

Relative 

Accuracy 

Estimate Lower 

Bound 

Upper 

Bound 

Fold 

Relative 

Accuracy 

Estimate Lower 

Bound 

Upper 

Bound 

Fold 

Relative 

Accuracy 

GSDs 

1.1858 1.3981 3.6254 3.1 2.7484 1.6565 2.9691 1.7 2.0072 1.6592 2.9904 1.5 

GSDm 2.2311 1.8484 2.7008 1.2 2.2311 1.8484 2.7008 1.2 2.2311 1.8484 2.7008 1.2 

ICC 0.0000 0.0000 0.4762 0.0000 0.0000 0.4762 0.0000 0.0000 0.4762 

GMs 0.0343 0.0180 0.0651 1.9 0.0113 0.0076 0.0171 1.5 0.0035 0.0024 0.0053 1.5 

GMm 0.0343 0.0178 0.0655 1.9 0.0113 0.0076 0.0171 1.5 0.0035 0.0024 0.0053 1.5 

AMs 0.0347 0.0220 0.0929 2.7 0.0170 0.0097 0.0245 1.8 0.0044 0.0030 0.0076 1.7 

AMu 0.0348 0.0229 0.1045 3.0 0.0189 0.0099 0.0253 1.9 0.0045 0.0031 0.0079 1.8 

AMm 0.0473 0.0240 0.0930 2.0 0.0156 0.0102 0.0243 1.6 0.0049 0.0032 0.0076 1.6 

P95s 0.0423 0.0377 0.2912 6.9 0.0571 0.0211 0.1184 2.7 0.0107 0.0065 0.0373 3.5 

P95u 0.0453 0.0453 0.3503 7.7 0.0598 0.0225 0.0785 2.7 0.0111 0.0070 0.0249 2.2 

P95m 0.1283 0.0613 0.2640 2.1 0.0424 0.0253 0.0705 1.7 0.0132 0.0079 0.0223 1.7 

Table 17. Arithmetic mean, geometric mean, geometric standard deviation, and 95th percentiles (with 95% confidence 

intervals and fold relative accuracy), for different statistical models of the normalized inhalation dose (mg/lb AI). 

 Bottle Conventional Reduced Splash 

Parameter Estimate Lower 

Bound 

Upper 

Bound 

Fold 

Relative 

Accuracy 

Estimate Lower 

Bound 

Upper 

Bound 

Fold 

Relative 

Accuracy 

Estimate Lower 

Bound 

Upper 

Bound 

Fold 

Relative 

Accuracy 

GSDs 

1.1045 1.3829 3.4757 3.1 2.6982 1.6294 2.8651 1.7 1.9286 1.6319 2.8850 1.5 

GSDm 2.1732 1.8116 2.6143 1.2 2.1732 1.8116 2.6143 1.2 2.1732 1.8116 2.6143 1.2 

ICC 0.0000 0.0000 0.4762 0.0000 0.0000 0.4762 0.0000 0.0000 0.4762 
26

 Bottle Conventional Reduced Splash 

Parameter Estimate Lower 

Bound 

Upper 

Bound 

Fold 

Relative 

Accuracy 

Estimate Lower 

Bound 

Upper 

Bound 

Fold 

Relative 

Accuracy 

Estimate Lower 

Bound 

Upper 

Bound 

Fold 

Relative 

Accuracy 

GMs 

0.0092 0.0049 0.0172 1.9 0.0013 0.0009 0.0019 1.5 0.0007 0.0005 0.0010 1.5 

GMm 0.0092 0.0049 0.0173 1.9 0.0013 0.0009 0.0019 1.5 0.0007 0.0005 0.0010 1.5 

AMs 0.0093 0.0060 0.0238 2.6 0.0019 0.0011 0.0026 1.8 0.0008 0.0006 0.0014 1.7 

AMu 0.0093 0.0062 0.0266 2.9 0.0021 0.0011 0.0027 1.9 0.0008 0.0006 0.0014 1.7 

AMm 0.0125 0.0065 0.0239 1.9 0.0017 0.0011 0.0026 1.5 0.0009 0.0006 0.0014 1.5 

P95s 0.0107 0.0101 0.0730 6.8 0.0067 0.0023 0.0123 2.9 0.0020 0.0012 0.0066 3.3 

P95u 0.0109 0.0121 0.0873 8.0 0.0065 0.0025 0.0083 2.6 0.0020 0.0013 0.0045 2.2 

P95m 0.0330 0.0162 0.0664 2.0 0.0046 0.0028 0.0075 1.7 0.0024 0.0015 0.0040 1.7 

Table 18. Arithmetic mean, geometric mean, geometric standard deviation, and 95th percentiles (with 95% confidence 

intervals and fold relative accuracy), for different statistical models of the normalized inhalation 8-hour time-weighted 

average (mg/m3/lb AI). 

 Bottle Conventional Reduced Splash 

Parameter Estimate Lower 

Bound 

Upper 

Bound 

Fold 

Relative 

Accuracy 

Estimate Lower 

Bound 

Upper 

Bound 

Fold 

Relative 

Accuracy 

Estimate Lower 

Bound 

Upper 

Bound 

Fold 

Relative 

Accuracy 

GSDs 

1.10454 1.38288 3.47565 3.1 2.69819 1.62939 2.86515 1.7 1.92864 1.63191 2.88502 1.5 

GSDm 2.17321 1.81159 2.61432 1.2 2.17321 1.81159 2.61432 1.2 2.17321 1.81159 2.61432 1.2 

ICC 0.00000 0.00000 0.47616 0.00000 0.00000 0.47616 0.00000 0.00000 0.47616 

GMs 0.00115 0.00062 0.00214 1.9 0.00016 0.00011 0.00024 1.5 0.00008 0.00006 0.00013 1.5 

GMm 0.00115 0.00061 0.00216 1.9 0.00016 0.00011 0.00024 1.5 0.00008 0.00006 0.00013 1.5 

AMs 0.00116 0.00075 0.00298 2.6 0.00024 0.00014 0.00033 1.8 0.00010 0.00007 0.00018 1.7 

AMu 0.00116 0.00078 0.00333 2.9 0.00026 0.00014 0.00034 1.9 0.00010 0.00007 0.00018 1.7 

AMm 0.00156 0.00081 0.00299 1.9 0.00021 0.00014 0.00033 1.5 0.00011 0.00008 0.00017 1.5 

P95s 0.00134 0.00126 0.00913 6.8 0.00084 0.00029 0.00154 2.9 0.00025 0.00015 0.00083 3.3 

P95u 0.00136 0.00151 0.01092 8.0 0.00081 0.00031 0.00103 2.6 0.00025 0.00016 0.00056 2.2 

P95m 0.00413 0.00202 0.00830 2.0 0.00057 0.00035 0.00093 1.7 0.00030 0.00018 0.00050 1.7 
27

Tables 12 to 18 show that the ICC estimated value is between 0.2 and 0.4 for the dermal exposure routes showing that 

there is some variation between workers and some correlation between measurements on the same worker. The ICC 

values were zero for all the inhalation exposure measures showing no variation between workers. For the Bottle group, 

most of the dermal exposure measures did not meet the study benchmark design value of 3 for the fold relative 

accuracy. For the empirical and lognormal simple random sampling model, this is partially explained by the fact that 

the bootstrap confidence intervals were based on a very different statistical model that assumed equal covariance 

parameters for all three groups, but several of the mixed model parameters also did not meet the study benchmark 

design value of 3. A plausible explanation is that the Bottle data was only based on 6 exposure measurements (although 

the mixed model was fitted to all 36 measurements). For the inhalation exposures in the Bottle group, the study 

benchmark design of 3 for the fold relative accuracy was met for the summary statistics that used the mixed model. For 

dermal exposures in the Conventional and Reduced Splash groups, the study benchmark design of 3 for the fold 

relative accuracy was met for the summary statistics that used the mixed model but was not met for several of the AMs, 

P95s, and P95u statistics. For inhalation exposures in the Conventional and Reduced Splash groups, the study 

benchmark design of 3 for the fold relative accuracy was met for all cases except for the empirical 95th percentile for 

the Reduced Splash group.

Quantile plots 

Quantile-quantile plots of the normalized exposure values were used to evaluate whether the data were lognormally 

distributed, as implied by the assumed statistical mixed models. In each case the quantile-quantile plot compared the 

observed quantiles of the 36 measured values with the corresponding quantiles of a normal or lognormal distribution. 

Since the mixed model assumes that the mean exposure can depend upon the group, the corresponding group mean 

normalized exposure was subtracted from the normalized exposure when creating the normal distribution plots, and the 

corresponding group mean logarithm of the normalized exposure was subtracted from the logarithm of the normalized 

exposure when creating the lognormal distribution plots. In this manner the quantile-quantile plots combined all 36 

measurements. A perfect fit would imply that the plotted values lie in a straight line. The quantile-quantile plots are 

presented in Figures 1 to 14. They clearly show that the lognormal distribution is a better fit than a normal distribution, 

and that the lognormal distribution fits reasonably well for all of the exposure routes.  
28

Figure 1

Quantile plot normalized long dermal exposure data with a normal distribution

Normalized by Pounds Active Ingredient Handled

-3 -2 -1 0 1 2 3

-200

-100

0

100

200

300

400

Normalized Long Dermal Exposure

Normal Quantiles
29

Figure 2 

Quantile plot normalized long dermal exposure data with a lognormal distribution

Normalized by Pounds Active Ingredient Handled

-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

4

log (Normalized Long Dermal Exposure)

Normal Quantiles

Figure 3 

Quantile plot normalized short dermal exposure data with a normal distribution

Normalized by Pounds Active Ingredient Handled

-3 -2 -1 0 1 2 3

-200

-100

0

100

200

300

400

Normalized Short Dermal Exposure

Normal Quantiles
30

Figure 4 

Quantile plot normalized short dermal exposure data with a lognormal distribution

Normalized by Pounds Active Ingredient Handled

-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

log (Normalized Short Dermal Exposure)

Normal Quantiles

Figure 5

Quantile plot normalized long short dermal exposure data with a normal distribution

Normalized by Pounds Active Ingredient Handled

-3 -2 -1 0 1 2 3

-200

-100

0

100

200

300

400

Normalized Long Short Dermal Exposure

Normal Quantiles
31

Figure 6 

Quantile plot normalized long short dermal exposure data with a lognormal distribution

Normalized by Pounds Active Ingredient Handled

-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

4

lnnrmdermls

Normal Quantiles

Figure 7 

Quantile plot normalized hands only exposure data with a normal distribution

Normalized by Pounds Active Ingredient Handled

-3 -2 -1 0 1 2 3

-200

-100

0

100

200

300

400

Normalized Hands Only Exposure

Normal Quantiles
32

Figure 8 

Quantile plot normalized hands only exposure data with a lognormal distribution

Normalized by Pounds Active Ingredient Handled

-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

4

log (Normalized Hands Only Exposure)

Normal Quantiles

Figure 9 

 

Quantile plot normalized inhalation conc exposure data with a normal distribution

Normalized by Pounds Active Ingredient Handled

-3 -2 -1 0 1 2 3

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

Normalized Inhalation Conc Exposure

Normal Quantiles
33

Figure 10 

Quantile plot normalized inhalation conc exposure data with a lognormal distribution

Normalized by Pounds Active Ingredient Handled

-3 -2 -1 0 1 2 3

-2.0

-1.5

-1.0

-0.5

0

0.5

1.0

1.5

2.0

log (Normalized Inhalation Conc Exposure)

Normal Quantiles
34

Figure 11 

Quantile plot normalized inhalation dose exposure data with a normal distribution

Normalized by Pounds Active Ingredient Handled

-3 -2 -1 0 1 2 3

-0.002

-0.001

0

0.001

0.002

0.003

0.004

0.005

Normalized Inhalation Dose

Normal Quantiles

Figure 12 

Quantile plot normalized inhalation dose exposure data with a lognormal distribution

Normalized by Pounds Active Ingredient Handled

-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

log (Normalized Inhalation Dose)

Normal Quantiles
35

Figure 13

Quantile plot normalized inhalation 8-hour TWA conc exposure data with a normal distribution

Normalized by Pounds Active Ingredient Handled

-3 -2 -1 0 1 2 3

-0.0004

-0.0002

0

0.0002

0.0004

0.0006

0.0008

Normalized Inhalation 8-hour TWA

Normal Quantiles

Figure 14 

Quantile plot normalized inhalation 8-hour TWA conc exposure data with a lognormal distribution

Normalized by Pounds Active Ingredient Handled

-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

log (Normalized Inhalation 8-hour TWA)

Normal Quantiles
36

Log-log-linearity analyses and estimated log-log slopes 

The following analyses evaluate whether the logarithm of exposure is linear in the logarithm of the amount of active 

ingredient handled (AI) with a slope of 1. We now refer to these analyses as the log-log-linearity analyses. In the 

Governing Documents and in our statistical memoranda analyzing previous AEATF studies we have referred to these 

analyses as a “proportionality” analysis, but this has caused some confusion because the statistical models do not 

assume that the exposure is directly proportional to the AI but instead assume that the logarithm of the exposure is 

linear in the logarithm of AI with a slope of 1, which is a related finding but a very different model, as explained here. 

We have therefore changed the terminology from “proportionality” to “log-log-linearity.” 

The use of the normalized or unit exposure is based on the assumption that the exposure is proportional to the 

normalizing variable pounds of active ingredient handled. Exact proportionality is defined as 

 Exposure = K × Pounds of Active Ingredient, 

where K is the proportionality constant. Exact proportionality implies that 

 Normalized Exposure = Exposure / Pounds of Active Ingredient = K, 

so that if the pounds of active ingredient is doubled, then the exposure is exactly doubled, which is not a reasonable 

assumption due to the variability of exposure for any given amount of active ingredient. Instead we allow for random 

multiplicative error terms, which do not depend on the amount of active ingredient, so that 

 Exposure = K × Pounds of Active Ingredient × Multiplicative Errors, or 

 Normalized Exposure = K × Multiplicative Errors. 

Since the above quantile plots support the assumption that the normalized exposure is log-normally distributed, rather 

than being normally distributed, we can take natural logarithms of both sides to get a log-log-linear model of the form 

 Log (Exposure) = Intercept + 1 × Log (Pounds of Active Ingredient) + Error Terms. 

The additive Error Terms are assumed to be normally distributed with a mean of zero. Thus proportionality of exposure 

to the pounds of active ingredient is statistically modeled by assuming a Slope equal to 1 in the more general log-log 

linear model: 

 Log (Exposure) = Intercept + Slope × Log (Pounds of Active Ingredient) + Error Terms. 

Using this general model, taking exponentials of both sides gives 

 Exposure = eIntercept × (Pounds of Active Ingredient)Slope × eError Terms, so that 

 Arithmetic Mean Exposure = C × (Pounds of Active Ingredient)Slope, where 

C = Arithmetic Mean {eIntercept × eError Terms}. 

Therefore, the arithmetic mean exposure will be proportional to the pounds of active ingredient if and only if the Slope 

in the log-log linear model equals 1. Note that the proportionality constant is C, which is very different to the estimated 

value of Slope. Also note that for this scenario in the mixed model we assume that the intercept, but not the slope, 

depends upon which group the source and receiving container belongs to. 
37

Possible alternative models include the same formulation with a Slope of zero, implying that the exposure does not 

depend upon the amount of active ingredient handled, even though the amount of active ingredient handled varied 

between the subjects as part of the study design. Other possible models include the same model with a slope not equal 

to zero or one, the quadratic models discussed below, or models with more complicated relationships between the 

exposure and the experimental conditions. To evaluate whether the slope is zero, one, or other possible values, we fitted 

the above statistical model and computed confidence intervals for the slope. 

To analyze the log-log-linearity, we also considered an additional hypothetical clothing scenario with no clothing at all. 

The dermal exposure for the No clothing scenario was calculated by summing all the inner and outer dermal exposure 

measurements: 

All Dermal. This case represents the dermal exposure for a subject wearing no clothes. The exposure is the sum of the 

mass from hand wash, face and neck, and the six inner and six outer dosimeters (lower arm, upper arm, lower leg, 

upper leg, front torso, rear torso). 

We can use these statistical models to calculate confidence intervals for the slope. The calculation of the confidence 

intervals depends upon the value of the denominator degrees of freedom for the mixed models used. A review of the 

alternative methods for calculating the denominator degrees of freedom for fixed effects in a mixed model using the 

SAS MIXED procedure is given in an article by Schaalje et al1

. Based on that article, the following Table 19 

summarizes the five available methods: 

Table 19. SAS Methods for Computing the Fixed Effects Denominator Degrees of Freedom in PROC MIXED. 

DDF Method SAS Abbreviation Comments 

Residual residual Uses residual degrees of freedom. 

Ignores covariance structure as 

defined by the RANDOM and 

REPEATED statements. This method 

is not recommended. 

Containment contain Default method when RANDOM 

statements are present. Accounts for 

the minimum contribution of the 

random effects that syntactically 

contain the fixed effects of interest. 

Between-Within bw Default method when REPEATED 

statements are present and RANDOM 

statements are not present. Only exact 

when the data are balanced and the 

design is a repeated measures design 

with compound symmetry, and where 

the levels of the within-subjects 

effects are not replicated within any 

of the subjects. Otherwise the method 

                                                           

1 Schaalje, G. B., J. B. McBride, G. W. Fellingham. “Approximations to Distributions of Test Statistics in Complex Mixed Linear Models 

Using SAS® Proc MIXED” Proceedings of the Twenty Sixth Annual SAS Users Group International Conference. April 2001. Long Beach, 

CA. ISBN 1-58025-864-6. SAS Institute, Cary, NC 27513. 
38

DDF Method SAS Abbreviation Comments 

is at best approximate and can be 

unpredictable. 

Satterthwaite / Fai-Cornelius satterth Designed to approximate the 

denominator degrees of freedom for 

split-plot designs with complicated 

covariance structures and/or 

unbalanced data sets. 

Kenwood-Rogers kr Designed to approximate the 

denominator degrees of freedom for 

designs with complicated covariance 

structures and/or unbalanced data 

sets. Results from simulations suggest 

better performance than the 

Satterthwaite method. If a covariance 

parameter has zero variance then this 

method ignores that covariance. 

To interpret this table for this study, note that the RANDOM statement was used to define the worker effect. If the ICC 

equals zero, then there is no worker clustering and the worker variance equals zero. The REPEATED statement was 

used to define the repeated measures model. A balanced data set is one where each treatment combination is applied to 

the same number of subjects. For this study, this implies that there are the same number of workers in every group, and 

each worker has the same number of measured exposure values. 

The study data were not balanced using the mixed model groups Bottle, Conventional, and Reduced Splash, since those 

groups had 6, 15, and 15 measurements, respectively. Based on this summary, the recommended method is the 

Kenwood-Rogers method for the mixed models and for the repeated measures model (detailed below). The confidence 

intervals for the regression coefficients presented in this memorandum follow these recommendations. Note that this 

issue does not impact the calculated confidence intervals for the summary statistics in Tables 12 to 18, since they were 

based on a bootstrap method. 

Table 20 shows the 95% confidence intervals for the slope calculated from the above lognormal mixed model. Also 

shown is the width of the confidence interval for the slope. A confidence interval that includes one but not zero 

supports the assumptions of the normalized exposure models. A confidence interval that includes zero but not one 

suggests that the exposure does not depend on the amount of active ingredient handled. A confidence interval that 

includes both zero and one suggests that either the basic statistical model is incorrect or there are not enough data to 

statistically infer whether the slope is zero or one. The Repeated Measures statistical model (bottom two rows) is 

described and discussed below. Note that, because the inhalation dose measured on the OVS tube is mathematically an 

exact multiple of the corresponding inhalation TWA measured on the OVS tube, the estimated slopes and confidence 

intervals are exactly the same. As discussed above, there were three MEs where the measured hands only exposure was 

unusually high compared to other measurements in the same subgroup (1a, 1b, 2, 3 with CP or with RS) and so the 

slope estimates for dermal exposures were computed with and without these potential outliers. 
39

Table 20. 95 percent confidence intervals for the slope of log exposure versus log pounds active ingredient handled. 

with and without the potential outlier dermal exposure data for Reduced Splash ME 1 in group 1a, Reduced Splash ME 

7 in group 2, and Conventional Pour ME 6 in group 1b. 

Exposure Route Clothing Data Estimate Lower Upper 

Confidence Interval 

Width 

Dermal (mg) Long pants and long 

sleeves 

All 36 

Values -0.28 -1.06 0.49 1.5 

 Exclude 

outlier data -0.14 -0.84 0.56 1.4 

 Short pants and short 

sleeves 

All 36 

Values -0.04 -0.68 0.60 1.3 

 Exclude 

outlier data 0.14 -0.50 0.78 1.3 

 Long pants and short 

sleeves 

All 36 

Values -0.26 -0.99 0.48 1.5 

 Exclude 

outlier data -0.13 -0.78 0.52 1.3 

 Hands Only All 36 

Values -0.31 -1.12 0.50 1.6 

 Exclude 

outlier data -0.17 -0.91 0.56 1.5 

 None All 36 

Values -0.05 -0.69 0.59 1.3 

 Exclude 

outlier data 0.16 -0.50 0.82 1.3 

Inhalation 

Concentration 

(mg/m3

) 

All 36 

Values 1.21 0.71 1.72 1.0 

Inhalation Dose 

(mg) 

 All 36 

Values 0.92 0.43 1.42 1.0 

Inhalation 

8-hour TWA 

(mg/m3) 

All 36 

Values 0.92 0.43 1.42 1.0 

Dermal (mg) 

Repeated 

Measures Model 

Any All 36 

Values 0.04 -0.61 0.68 1.3 

 Exclude 

outlier data 0.14 -0.42 0.71 0.7 

For all of the dermal exposure cases, the confidence interval for the slope includes 0 but not 1. Thus, for these cases, 

the assumption of independence was not rejected and the assumption of log-log-linearity with slope 1 was rejected. The 
40

estimate slopes are small but sometimes negative, ranging from -0.31 to 0.16. The slopes are higher when the potential 

outliers are excluded. The negative slope estimates are not expected since one would usually assume that the exposure 

will tend to increase if the amount of active ingredient increases. This may indicate some issues with the assumed 

statistical model, particularly the assumption that the geometric mean is the same for the three subgroups 1bCP, 2CP 

and 3CP that are combined into the Conventional group and is the same for the three subgroups 1bRS, 2RS, 3RS that 

are combined into the Reduced Splash group. As discussed above, this assumption was needed so that the same unit 

exposure estimates could be applied for source containers of all sizes not pouring into trigger spray bottles. 

In the section “Alternative models for dermal exposure” we investigate alternative models and outlier treatments to 

further understand these negative slopes and in particular to investigate models where the slope is different for the three 

groups Bottle, Conventional, and Reduced Splash. 

For all the inhalation exposure cases, the confidence interval for the slope includes 1 but not 0. Thus, for these cases, 

the assumption of independence was rejected and the assumption of log-log-linearity with a slope of 1 was not rejected 

and is therefore supported. The slope value for the inhalation concentration is above 1. As discussed below, when the 

slope is greater than one, the predicted means from the normalized exposure model will underestimate the predicted 

means from the mixed model with an estimated slope (of the log exposure against the log amount of active ingredient) 

when the amount of active ingredient is high. However, this underestimation will be small since the slope is only 

slightly above 1 for the inhalation concentrations, except if the amount of active ingredient handled is extremely high. 

The results in Table 20 show that the actual confidence interval widths were mostly less than 1.4 and were at most 1.6 

(for hands only). In previous statistical analyses of the AEATF studies, an expected confidence interval width of at 

most 1.4 was needed so that the statistical power of detecting log-log-linearity would be at least 80%. For this study the 

statistical design was very different and that power calculation does not apply. Nevertheless, the observed confidence 

intervals widths in this study are comparable to those found for the mop, wipe, and aerosol studies. 

The lognormal mixed model regression results are shown in Figures 15 to 22. The scatter plots show the data points in 

each of the three groups, Bottle, Conventional, and Reduced Splash. The fitted regression lines are shown for each 

group. The slopes of the regression lines are the same for all three groups (an assumption of the statistical model), but 

the intercepts are different. 
41

Figure 15 
42

Figure 16 
43

Figure 17
44

Figure 18 
45

Figure 19 
46

Figure 20 
47

Figure 21 
48

Figure 22 
49

Repeated measures model 

The above analyses of the log-log-linearity for dermal exposure show similar small slopes. To investigate this issue 

further, the following more complicated statistical model was fitted to the data of all three dermal exposures (excluding 

the unrealistic hands only and no clothing case) for all 18 subjects and both Conventional and Reduced Splash 

containers. The model was of the form: 

Log (dermal exposure) = LnGM (clothing type and group) + Slope × Log (Pounds of Active Ingredient) + 

Worker + Error 

In this model, the intercept depends upon the clothing type and group, so there are six intercepts. The slope is the same 

for all three clothing types and both groups. The Worker term accounts for possible within-worker correlations between 

their two MEs (i.e. the Conventional Pour and Reduced Splash experiments). Finally, to account for the expected 

correlations between different dermal exposure measurements on the same worker during the same ME, the three error 

terms (one per clothing type) for each worker are assumed to be correlated (with an unspecified covariance matrix), but 

errors for different workers are assumed to be independent. Thus in SAS terminology, the Worker effect is a 

RANDOM effect and the Error is a REPEATED effect where the subject is the combination of the worker and the ME. 

Thus each worker is treated as two subjects, for their two MEs. We will call this model the “Repeated Measures” 

model. The confidence interval for the slope using this statistical model are shown in the bottom two rows of Table 20. 

Since the confidence interval includes zero and does not include one, the log-log-linearity for dermal exposure has not 

been shown using this statistical model, but the positive slope estimate suggests that the exposure tends to increase as 

the AI increases. 

Quadratic models 

The log-log-linearity test was based on a linear model for log exposure versus log pounds active ingredient handled. 

The HSRB suggested that a quadratic model should also be considered. 

There are two quadratic models that could be considered. Since the original linear model is of the form 

 Log (Exposure) = Intercept + Slope × Log (Pounds of Active Ingredient) + Error Terms, 

where the intercept depends upon the group but the slope is the same for all three groups, the main quadratic model is 

of the form 

Log (Exposure) = 

Intercept + Slope × Log (Pounds of Active Ingredient) + 

Quad × {Log (Pounds of Active Ingredient)}2

 + Error Terms. 

The intercept depends upon the group, but the Slope and Quad parameters are the same for all three groups. Note that 

the quadratic term is the square of the logarithm of the pounds of active ingredient rather than the logarithm of the 

square; the latter approach produces an ill-defined model with two multiples of the logarithm of the pounds of active 

ingredient. 

Another approach might be to consider a quadratic model for exposure: 

Exposure = 

Intercept + Slope × (Pounds of Active Ingredient) + 

Quad × (Pounds of Active Ingredient)2

 + Error Terms. 
50

We do not recommend this second approach for these data since the exposures are known to be non-negative and the 

quantile plots indicate that the exposure data are better modeled using a log-normal distribution than using a normal 

distribution. Furthermore, unless the intercept is zero, this model predicts a nonzero exposure when the pounds of 

active ingredient is zero, and so a more realistic (though possibly poorer-fitting) model of this form would have a zero 

intercept for every group. For other exposure data a log-log-linearity test could be carried out by fitting the zero 

intercept model 

Exposure = Slope × (Pounds of Active Ingredient) + Quad × (Pounds of Active Ingredient)2 + Error Terms 

and testing if Quad equals zero. 

The parsimony principle suggests that the appropriate statistical procedure for this study is to first fit the quadratic 

regression model for the logarithm of the exposure 

Log (Exposure) = 

Intercept + Slope × Log (Pounds of Active Ingredient) + 

Quad × {Log (Pounds of Active Ingredient)}2

 + Error Terms. 

If the coefficient Quad is statistically significant at the 5% level, which is equivalent to requiring that the 95% 

confidence interval does not include zero, than the quadratic model is supported. Otherwise the linear model should be 

used. 

Table 21 presents the fitted quadratic models from the study for the mixed models of seven exposure measurements 

(Long Dermal, Short Dermal, Long Short Dermal, Hands Only, and for Inhalation Concentration, Dose and 8-Hour 

TWA) and for the Repeated Measures model for Dermal exposures. For the Repeated Measures model, the model has 

different intercepts (but the same Slope and Quad coefficients) for the six combinations of group and clothing type. In 

view of the earlier discussion about denominator degrees of freedom, the confidence intervals are calculated using the 

Kenwood-Rogers method. The group-specific intercepts are not shown. 

Table 21. Quadratic mixed models with 95% confidence intervals for the log exposure versus log pounds active 

ingredient handled. 

Exposure Parameter Estimate Degrees 

of 

Freedom 

Lower 

Bound 

Upper 

Bound 

GSD ICC Width of 

Confidence 

Interval 

Long 

Dermal

Slope -3.78 25.64 -9.10 1.54 3.19 0.35 10.64

Long 

Dermal

Quad -0.81 26.37 -2.03 0.41 3.19 0.35 2.44

Short 

Dermal

Slope -1.07 24.69 -5.52 3.37 2.74 0.42 8.89

Short 

Dermal

Quad -0.24 25.42 -1.26 0.78 2.74 0.42 2.05

Long Slope -3.75 25.57 -8.76 1.26 2.99 0.35 10.02
51

Exposure Parameter Estimate Degrees 

of 

Freedom 

Lower 

Bound 

Upper 

Bound 

GSD ICC Width of 

Confidence 

Interval 

Short 

Dermal

Long 

Short 

Dermal

Quad -0.81 26.29 -1.96 0.34 2.99 0.35 2.30

Hands 

Only 

Slope -4.08 25.80 -9.66 1.49 3.35 0.34 11.15

Hands 

Only 

Quad -0.88 26.53 -2.15 0.40 3.35 0.34 2.56

Inhalation 

Conc

Slope 0.96 31.00 -2.91 4.82 2.27 0.00 7.74

Inhalation 

Conc

Quad -0.06 31.00 -0.94 0.82 2.27 0.00 1.77

Inhalation 

Dose 

Slope 0.25 31.00 -3.52 4.02 2.22 0.00 7.54

Inhalation 

Dose 

Quad -0.15 31.00 -1.02 0.71 2.22 0.00 1.72

Inhalation 

TWA 

Slope 0.25 31.00 -3.52 4.02 2.22 0.00 7.54

Inhalation 

TWA 

Quad -0.15 31.00 -1.02 0.71 2.22 0.00 1.72

Dermal 

Repeated 

Measures 

Slope -0.96 25.10 -5.53 3.61 NA NA -1.91

Dermal 

Repeated 

Measures 

Quad -0.23 25.84 -1.28 0.82 NA NA -0.45

Since the 95% confidence intervals for Quad include zero in every case, the quadratic coefficient is not statistically 

significant and the quadratic models are not supported. 

Threshold Analyses 
52

As described above, the following two mixed models were fitted to the dermal and inhalation exposure data. 

Linear mixed model: 

 Log (Exposure) = Intercept1 + Slope × Log (Pounds of Active Ingredient) + Worker + Error 

Normalized exposure mixed model: 

 Log (Exposure) = Intercept2 + Log (Pounds of Active Ingredient) + Worker + Error, 

which is mathematically the same as 

 Log (Exposure/Pounds of Active Ingredient) = Intercept2 + Worker + Error 

The intercepts for these two models are denoted as Intercept1 and Intercept2 since their estimated values will in general 

be different. Intercept1 and Intercept2 both depend upon the group and so each has different values for Bottle, 

Conventional, and Reduced Splash exposures. 

Worker is a normally distributed random effect variable with independent, identically distributed values for each 

worker, and Error is a normally distributed error variable with independent, identically distributed values for each total 

exposure measurement. If the linear mixed model has a slope of 1, then the model is mathematically the same as the 

normalized exposure mixed model. 

These two statistical models can be compared by calculating the threshold value of the pounds of active ingredient at 

which both models predict the same mean exposure. The threshold values are computed as follows. 

Suppose first that the linear mixed model for log Exposure is correct. Then, as shown above, the predicted arithmetic 

mean exposure for a given amount of active ingredient is given by the equation 

Predicted arithmetic mean exposure from linear mixed model = 

C1 × (Pounds of Active Ingredient)Slope, (1) 

where C1 is given by 

C1 = Arithmetic Mean {eIntercept1 × eError Terms} for the linear mixed model, so that 

C1 = exp(Intercept1) × exp( 1⁄2 V1), 

where V1 is the total variance for the linear mixed model, calculated as the sum of the worker variance and the error 

variance. C1 and Intercept1 depends upon the group but V1 is the same for every group. The predicted arithmetic mean 

exposure is the expected value of the exposure for a given amount of active ingredient and thus estimates the average 

(arithmetic mean) exposure for a large number of scenarios that are all using the same amount of active ingredient. 

Suppose instead that the normalized exposure mixed model for log Exposure is correct. Then the predicted arithmetic 

mean exposure is given by the equation 

Predicted arithmetic mean exposure from normalized exposure mixed model = 
53

C2 × (Pounds of Active Ingredient)1, (2) 

where C2 is given by 

C2 = Arithmetic Mean {eIntercept2 × eError Terms} for the normalized exposure mixed model, so that 

C2 = exp(Intercept2) × exp( 1⁄2 V2), 

where V2 is the total variance for the normalized exposure mixed model, calculated as the sum of the worker variance 

and the error variance. C2 and Intercept2 depends upon the group but V2 is the same for every group. 

We now have two estimates of the predicted arithmetic mean exposure for a given amount of active ingredient, 

equations (1) and (2). The graphs in Figures 22 to 43 below compare the predicted arithmetic means for each clothing 

configuration (Long Dermal, Short Dermal, Long Short Dermal, Hands Only) and for the three inhalation exposure 

metrics. There are three plots for each exposure measure corresponding to the three groups, because the threshold value 

depends upon the group. Exposure is plotted against the pounds of active ingredient. To make it easier to see the effects 

of source container sizes, the data points in groups 1, 2, and 3 are labeled by their group number. The green curve gives 

the predictions for the linear mixed model in equation (1). The purple line gives the predictions for the normalized 

exposure mixed model in equation (2). The two estimates (1) and (2) are equal if the pounds of active ingredient equals 

the Threshold value: 

 Threshold = {C2/C1}1/(Slope – 1)

The Threshold values are tabulated in Table 22 below. 

Suppose that the estimated slope is less than 1. This is true for all the exposure measures studied here except for the 

inhalation concentration. The predicted arithmetic mean exposure from the normalized exposure mixed model will be 

greater than the predicted arithmetic mean exposure from the linear mixed model for amounts of active ingredient 

above the threshold (right hand side of the graph). The predicted arithmetic mean exposure from the normalized 

exposure mixed model will be less than the predicted mean exposure from the linear mixed model for amounts of 

active ingredient below the threshold (left hand side of the graph). What this means is that if we assume log-loglinearity and use the normalized exposure mixed model, then we will tend to over-predict the exposure unless the 

amount of active ingredient is below the threshold. (If the amount of active ingredient is below the threshold, then it 

will be low enough that the exposure will not usually be of concern). 

For the inhalation concentration, the estimated slope was greater than one. In these cases the inequalities are reversed: 

The predicted arithmetic mean exposure from the normalized exposure mixed model will be greater than the predicted 

arithmetic mean exposure from the linear mixed model for amounts of active ingredient below the threshold (left hand 

side of the graph). The predicted arithmetic mean exposure from the normalized exposure mixed model will be less 

than the predicted arithmetic mean exposure from the linear mixed model for amounts of active ingredient above the 

threshold (right hand side of the graph). Although these cases show a tendency for exposure estimates from the 

normalized exposure mixed model to under-predict exposure, the estimated slope is not very much greater than 1 for 

the inhalation concentration, and then it is clearly seen from the graphs that the two curves are numerically extremely 

close so that the under-prediction is very small at levels of active ingredient similar to those used in this study. 

Table 22. Threshold values for the amount of active ingredient. 

Exposure 

Route Clothing Slope 

Threshold Level (lb 

active ingredient) for 

Bottle 

Threshold Level (lb 

active ingredient) 

for Conventional 

Threshold Level (lb 

active ingredient) 

for Reduced Splash 
54

Exposure 

Route Clothing Slope 

Threshold Level (lb 

active ingredient) for 

Bottle 

Threshold Level (lb 

active ingredient) 

for Conventional 

Threshold Level (lb 

active ingredient) 

for Reduced Splash 

Dermal (mg) Long pants 

and long 

sleeves 

-0.28 1.14 1.43 0.38 

 Short pants 

and short 

sleeves 

-0.04 0.83 1.34 0.50 

 Long pants 

and short 

sleeves 

-0.26 1.07 1.42 0.37 

 Hands only -0.31 1.19 1.48 0.37 

Inhalation 

Concentration 

(mg/m3) 

 1.21 0.00025* 0.00271* 0.00073* 

Inhalation Dose 

(mg) 

 0.92 0.000062 0.00033 0.00015 

Inhalation 

8-hour TWA 

(mg/m3) 

 0.92 0.0000078 0.000041 0.000019 

*For this case, slope > 1 and so the normalized exposure mixed model under-predicts exposure for pounds of active 

ingredient above the threshold. 
55

Figure 23 
56

Figure 24 
57

Figure 25 
58

Figure 26 
59

Figure 27 
60

Figure 28 
61

Figure 29 
62

Figure 30 
63

Figure 31 
64

Figure 32 
65

Figure 33 
66

Figure 34 
67

Figure 35 
68

Figure 36 
69

Figure 37 
70

Figure 38 
71

Figure 39 
72

Figure 40 
73

Figure 41 
74

Figure 42 
75

Figure 43 

Alternative models for dermal exposure

As discussed above, the dermal exposure estimates show some unexpected patterns, with estimated arithmetic means 

that are higher for Long Dermal than for Long Short Dermal or higher for Long Short Dermal than for Short Dermal, 

and with some negative slopes or slopes very close to zero. Although the true arithmetic means must increase between 

Long Dermal, Long Short Dermal and Short Dermal (since the outer dosimeter values for the lower arm and lower leg 

are added), the estimated arithmetic means from the fitted models do not necessary increase. A negative slope is 

unexpected since that implies that the exposure decreases if the amount of active ingredient increases, which also seems 

counter-intuitive. To further investigate these findings we re-fitted the three original models after excluding some 

outlier values and also investigated alternative models for the slopes of the log-log-linear models. 

Three alternative sets of outliers were considered: 

• No outliers 

• Three outliers. These potential outliers are for Reduced Splash ME 1 in group 1a, Reduced Splash ME 7 in 

group 2, and Conventional Pour ME 6 in group 1b. These are three cases where the hands only exposure 

normalized by the amount of active ingredient is unusually high compared to other MEs in the same group. 

• Four outliers. These potential outliers are for Reduced Splash ME 1 in group 1a, Reduced Splash ME 7 in group 

2, Conventional Pour ME 6 in group 1b, and Conventional Pour ME 10 in group 2. The first three are cases 
76

where the hands only exposure normalized by the amount of active ingredient is unusually high compared to 

other MEs in the same group. The last case is where the hands only exposure is extremely low compared to the 

other hands only measurements in group 2 but the outer dosimeter for the lower arm is higher than the hands 

only measurement. 

Table 23 shows the arithmetic and geometric means of the unit exposure for each clothing scenario and group 

calculated using the empirical, log-normal simple random sampling, and mixed models after excluding these sets of 

outliers. For each group and data set, the arithmetic and geometric means from the empirical model (AMs and GMs) 

increase between Long Dermal, Long Short Dermal, and Short Dermal. For the lognormal model, the arithmetic mean 

AMu is estimated as GMs×exp(GSDs) where GSDs is the empirical geometric standard deviation. Although the GMs 

increases between Long Dermal, Long Short Dermal, and Short Dermal, the GSDs and hence the arithmetic mean GMu 

can decrease. The estimated arithmetic means from the lognormal model increase as expected between Long Dermal, 

Long Short Dermal, and Short Dermal when the four outliers are excluded. For the mixed model it is possible that 

neither the arithmetic mean AMm nor the geometric mean GMm increase as expected. The estimated geometric means 

from the lognormal model increase as expected when the three or four outliers are excluded, but the estimated 

arithmetic means did not consistently increase as expected. 

This statistical finding can be regarded as a statistical “quirk” of the fitted statistical models since the differences 

between the three dermal unit exposure arithmetic and geometric mean estimates are small when compared to their 

uncertainty (as illustrated in the wide parametric bootstrap confidence intervals displayed in Tables 9, 12, 13, and 14 

above). The dermal exposure for this liquid pour scenario is dominated by the hands only exposure, but the outer 

dosimeter values for the lower arm and lower leg vary considerably. 

Table 23. Dermal unit exposure (mg/lb AI) arithmetic means and geometric means using alternative statistical models 

and removing zero, three, or four outliers. 

Clothing Data Group Arithmetic Mean Geometric Mean 

 Empirical Lognormal Mixed Empirical Mixed 

 AMs AMu AMm GMs GMm 

Long Dermal No outliers Bottle 155.2511 158.0606 298.4676 116.1970 119.9586 

Long Short Dermal No outliers Bottle 155.8029 158.5404 280.7180 116.6646 121.5849 

Short Dermal No outliers Bottle 157.7836 160.7434 207.3503 118.5562 108.1348 

Long Dermal No outliers Conventional 8.3529 10.9082 9.9637 4.1123 4.0046 

Long Short Dermal No outliers Conventional 8.4623 10.0848 9.9085 4.4159 4.2916 

Short Dermal No outliers Conventional 9.0506 10.7192 9.0011 4.6348 4.6941 

Long Dermal No outliers Reduced Splash 3.7373 3.6006 3.1400 1.2447 1.2620 

Long Short Dermal No outliers Reduced Splash 3.7864 3.6543 3.0301 1.2967 1.3124 

Short Dermal No outliers Reduced Splash 4.2148 3.6551 3.9898 2.0312 2.0807 

Long Dermal Remove 3 outliers Bottle 94.4075 97.6548 177.5334 88.2638 88.5023 
77

Clothing Data Group Arithmetic Mean Geometric Mean 

 Empirical Lognormal Mixed Empirical Mixed 

 AMs AMu AMm GMs GMm 

Long Short Dermal Remove 3 outliers Bottle 94.7334 97.9490 166.1035 88.6254 89.0304 

Short Dermal Remove 3 outliers Bottle 96.4299 99.7846 142.2019 90.2199 89.7684 

Long Dermal Remove 3 outliers Conventional 6.4343 8.3406 7.0752 3.5275 3.5271 

Long Short Dermal Remove 3 outliers Conventional 6.5494 7.7556 7.1010 3.8070 3.8061 

Short Dermal Remove 3 outliers Conventional 6.8408 8.0949 6.3627 3.9736 4.0166 

Long Dermal Remove 3 outliers Reduced Splash 1.7623 2.0198 1.9827 0.9884 0.9884 

Long Short Dermal Remove 3 outliers Reduced Splash 1.8084 2.0722 1.9260 1.0325 1.0323 

Short Dermal Remove 3 outliers Reduced Splash 2.2127 2.2907 2.6401 1.6672 1.6666 

Long Dermal Remove 4 outliers Bottle 94.4075 97.6548 159.0276 88.2638 88.2638 

Long Short Dermal Remove 4 outliers Bottle 94.7334 97.9490 158.5748 88.6254 88.6254 

Short Dermal Remove 4 outliers Bottle 96.4299 99.7846 135.8073 90.2199 90.1188 

Long Dermal Remove 4 outliers Conventional 6.9103 8.0051 7.7983 4.3282 4.3282 

Long Short Dermal Remove 4 outliers Conventional 7.0070 8.1406 7.8506 4.3876 4.3876 

Short Dermal Remove 4 outliers Conventional 7.3203 8.4728 6.9460 4.5907 4.6092 

Long Dermal Remove 4 outliers Reduced Splash 1.7623 2.0198 1.7809 0.9884 0.9884 

Long Short Dermal Remove 4 outliers Reduced Splash 1.8084 2.0722 1.8475 1.0325 1.0325 

Short Dermal Remove 4 outliers Reduced Splash 2.2127 2.2907 2.5096 1.6672 1.6653 

The mixed log-log-linear model used to estimate the slopes was of the form: 

Log (Exposure) = Group Intercept + Slope1 × Log (Pounds of Active Ingredient) + Worker1 + Error1 (1) 

Worker1 is a normally distributed random effect variable with independent, identically distributed values for each 

worker, and Error1 is a normally distributed error variable with independent, identically distributed values for each 

total exposure measurement. The group intercept varies with the group. The slope, denoted here as Slope1, and the 

Worker1 variance, and Error1 variance are each assumed to be the same for each group. 

Since the mixed model produced negative and small slope estimates for the dermal exposures, we investigated the 

following alternative models: 
78

Log (Exposure) = Group Intercept + Group Slope2 × Log (Pounds of Active Ingredient) + Worker2 + Error2 (2) 

Worker2 is a normally distributed random effect variable with independent, identically distributed values for each 

worker, and Error2 is a normally distributed error variable with independent, identically distributed values for each 

total exposure measurement. The group intercept and group slope Slope2 each vary with the group. The slope, denoted 

here as Slope2, and the Worker2 variance, and Error2 variance are each assumed to be the same for each group. 

Log (Exposure) = Group Intercept + Group Slope3 × Log (Pounds of Active Ingredient) + Error3 (3) 

Error3 is a normally distributed error variable with independent, identically distributed values for each total exposure 

measurement. The group intercept, group slope Slope3, and Error3 variance each vary with the group. 

The difference between models 2 and 3 is that in model 2 the variances of worker and error are assumed to be the same 

across all there groups, but in model 3 there is no worker error and the error variances can be different for the different 

groups. Model 3 is exactly the same as assuming that for each group we have the simple linear regression model: 

Log (Exposure) = Intercept + Slope × Log (Pounds of Active Ingredient) + Error 

Table 24 shows the estimated slopes and 95% confidence intervals for these three models for each clothing scenario 

and group after excluding each of the three sets of outliers. If no outliers are removed, then all the estimated slopes are 

negative except for a small positive slope for model 3, Short Dermal, in the Reduced Splash group. Compared to model 

1, the group-specific slopes in models 2 and 3 have wider confidence intervals and are much more negative for the 

Bottle group and are more negative for Reduced Splash (except for model 3, Short Dermal). After excluding three or 

four outliers, the slopes are still negative for model 1, but the slopes become positive and very large (about 3) with very 

wide confidence intervals for Bottle and become small (about 0.2) for Conventional. After removing three or four 

outliers, the slopes in models 2 and 3 are about -0.5 and significantly lower than 1 for Reduced Splash Long Dermal 

and Long Short Dermal. 

For the Bottle and Conventional groups, after decreasing the amount of data (by removing outliers) and increasing the 

number of parameters (by allowing the slope to vary with the group), the confidence intervals for the slope become 

wide enough that neither the log-log-linearity with slope 1 assumption nor the independence assumption can be 

rejected. For Reduced Splash, the log-log-linearity with slope 1 assumption is rejected and the independence 

assumption is not rejected in all cases. The finding that these data support independence of exposure and the amount of 

active ingredient for dermal exposure is likely to be due to the fact that for this scenario, the bulk of the dermal 

exposure occurs due to accidental splashes and spills on the hands. 

Table 24. Dermal exposure (mg) versus pounds of active ingredient estimated log-log-linear slopes using alternative 

statistical models and removing zero, three, or four outliers. 

Clothing Data Group Slope1 Slope2 Slope3 

 Estimate Lower Upper Estimate Lower Upper Estimate Lower Upper 

Long Dermal No outliers Bottle -0.28 -1.06 0.49 -2.05 -14.03 9.92 -3.49 -13.47 6.50 

Long Short Dermal No outliers Bottle -0.26 -0.99 0.48 -2.04 -13.35 9.28 -3.49 -13.45 6.47 

Short Dermal No outliers Bottle -0.04 -0.68 0.60 -3.35 -13.14 6.44 -3.31 -13.37 6.76 

Long Dermal No outliers Conventional -0.28 -1.06 0.49 -0.09 -1.06 0.89 -0.07 -1.12 0.98 

Long Short Dermal No outliers Conventional -0.26 -0.99 0.48 -0.05 -0.97 0.87 -0.04 -0.99 0.91 
79

Clothing Data Group Slope1 Slope2 Slope3 

 Estimate Lower Upper Estimate Lower Upper Estimate Lower Upper 

Short Dermal No outliers Conventional -0.04 -0.68 0.60 -0.07 -0.87 0.73 -0.04 -1.00 0.91 

Long Dermal No outliers Reduced Splash -0.28 -1.06 0.49 -0.61 -1.84 0.63 -0.57 -1.90 0.76 

Long Short Dermal No outliers Reduced Splash -0.26 -0.99 0.48 -0.60 -1.77 0.57 -0.57 -1.88 0.74 

Short Dermal No outliers Reduced Splash -0.04 -0.68 0.60 -0.03 -1.04 0.97 0.04 -1.03 1.11 

Long Dermal Remove 3 outliers Bottle -0.14 -0.84 0.56 2.97 -12.27 18.20 2.97 -8.32 14.25 

Long Short Dermal Remove 3 outliers Bottle -0.13 -0.78 0.52 2.95 -11.15 17.05 2.95 -8.28 14.18 

Short Dermal Remove 3 outliers Bottle 0.14 -0.50 0.78 2.96 -11.02 16.94 3.28 -7.79 14.35 

Long Dermal Remove 3 outliers Conventional -0.14 -0.84 0.56 0.16 -0.81 1.12 0.16 -1.09 1.40 

Long Short Dermal Remove 3 outliers Conventional -0.13 -0.78 0.52 0.18 -0.71 1.08 0.18 -0.93 1.30 

Short Dermal Remove 3 outliers Conventional 0.14 -0.50 0.78 0.19 -0.70 1.07 0.19 -0.93 1.31 

Long Dermal Remove 3 outliers Reduced Splash -0.14 -0.84 0.56 -0.52 -1.58 0.54 -0.52 -1.48 0.43 

Long Short Dermal Remove 3 outliers Reduced Splash -0.13 -0.78 0.52 -0.52 -1.50 0.46 -0.52 -1.45 0.41 

Short Dermal Remove 3 outliers Reduced Splash 0.14 -0.50 0.78 0.08 -0.89 1.05 0.08 -0.61 0.78 

Long Dermal Remove 4 outliers Bottle -0.10 -0.73 0.53 2.97 -10.59 16.52 2.97 -8.32 14.25 

Long Short Dermal Remove 4 outliers Bottle -0.10 -0.72 0.52 2.95 -10.48 16.38 2.95 -8.28 14.18 

Short Dermal Remove 4 outliers Bottle 0.18 -0.42 0.78 3.28 -8.85 15.41 3.28 -7.79 14.35 

Long Dermal Remove 4 outliers Conventional -0.10 -0.73 0.53 0.24 -0.62 1.10 0.24 -0.81 1.29 

Long Short Dermal Remove 4 outliers Conventional -0.10 -0.72 0.52 0.24 -0.61 1.09 0.24 -0.81 1.29 

Short Dermal Remove 4 outliers Conventional 0.18 -0.42 0.78 0.25 -0.52 1.02 0.25 -0.80 1.30 

Long Dermal Remove 4 outliers Reduced Splash -0.10 -0.73 0.53 -0.52 -1.47 0.42 -0.52 -1.48 0.43 

Long Short Dermal Remove 4 outliers Reduced Splash -0.10 -0.72 0.52 -0.52 -1.46 0.41 -0.52 -1.45 0.41 

Short Dermal Remove 4 outliers Reduced Splash 0.18 -0.42 0.78 0.08 -0.76 0.93 0.08 -0.61 0.78