Estimating Upper Centile Pesticide 

Concentrations and Sample Size 

Requirement

Wenlin Chen, Syngenta Crop Protection, LLC

Paul Mosquin, RTI International

Roy W. Whitmore, RTI International

Paul Hendley, Syngenta Crop Protection, LLC
Introduction

 Use of available monitoring data to estimate potential 

pesticide peak concentrations or very high centiles (e.g. 

99th) provides a useful reality check for comparison with 

exposure model output in regulatory assessment.

 Technical challenges: 

 Certain data sets have relatively low annual sample 

frequency across many years for many sites. 

 Variably stratified monitoring (i.e. sampling timing is 

generally targeted and not simple random sampling) 

due to seasonal residue patterns and other variables.

2
Introduction

 Objective is to

 propose a survey sampling approach to account 

for complexities in pesticide monitoring datasets 

(e.g. large sample sizes but variable sampling 

frequency), and 

 apply the approach to estimate the upper centiles

of atrazine historical monitoring data from surface 

water Community Water Systems (CWS) as a 

case study.

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Outline

 Description of atrazine historical data sets

 Methods

 Analysis weights

 Effective sample size requirements

 Centile estimates and confidence intervals (CI’s)

 Simulation study

 Results 

 Discussion and conclusions

4
Description of Data Sets

 National Safe Drinking Water Act (SDWA) 

monitoring data set

 Nationwide program

 Data for case study between 1993 and 2008

 50,081 atrazine measurements for finished 

(drinking) water from 4404 surface water CWS

 Samples were typically scheduled quarterly

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Description of Data Sets

 Regional (Midwest corn belt) high sampling 

frequency data set (VMP/AMP) 

 Combined data of Syngenta Voluntary Monitoring 

Program (VMP),1993-2002; and Atrazine Monitoring 

Program (AMP), 2003-2009 used for the case study

 Primarily Midwest Corn belt. CWS selection based on 

atrazine SDWA monitoring history; 

 Weekly sampling typically from May through July (VMP) 

and April through July (AMP); biweekly other months;

 Finished and raw (source) water samples from more 

than 130 CWS with total over 46,000 measurements. 

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Method 

Evaluation by 

Simulation

Data sets and 

represented 

statistic (sub) 

population of 

data

Analysis 

weights 

Effective 

sample size

Centile

estimates and 

C.I.s

Methods

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Methods

 Analysis weights

 Number of days an individual sample “represents”.

 Time-interval weights

One half the time to the previous measurement and one half the 

time to the next measurement.

 Probability weights

Inverse of a known and non-zero probability a day is sampled.

 Stratified systematic sampling

Constant number of days between sampling events within a 

stratum.

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Methods

 Sample size requirements (For details: Mosquin et al., J. 

Environ. Qual., 2012)

 Tolerance intervals (Hahn and Meeker, 1991) 

 Relative Standard Error (RSE)

 Woodruff interval skewness criterion 

 Effective sample size

It is a sample size of a data set with monitoring design that is 

equivalent to simple random sampling. It equals the sample 

size of non simple random sampling discounted (i.e. 

divided) by a sampling design effect.

 Centile estimates and Woodruff confidence intervals

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Methods

 Simulation to evaluate method performance on 

less frequent monitoring

 “True” monitoring data populations (computer 

generated/not true monitoring data) 

 Artificial 50 or 500 site-years

 365-d values per site-year generated as log-normal random 

variables with seasonality.

 Two annual mean scenarios: 1) constant; 2) normally variable. 

 4 samples per site-year, 10,000 replications

 1 random sample each in Jan-Apr, May-Jun, JulAug, and Sep-Dec.

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Methods
Results

 Requisite sample size by tolerance interval method

Smallest effective sample size for the probability of containing the 100q-th centile

with a confidence level of 100(1- ) (Ref.: Hahn and Meeker, 1991) 

Confidence Level 

Centile ( )

90.0% 95.0% 97.5% 99.0% 99.9%

80.0% 16 32 64 161 1609

90.0% 22 45 91 230 2302

95.0% 29 59 119 299 2995

97.5% 36 72 146 368 3688

99.0% 44 90 182 459 4603

99.9% 66 135 273 688 6905

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For example, with effective sample size of 59, 299, 2995, there is 95% confidence 

that the existing monitored data contain the 95th, 99th and 99.9th centile 

concentrations, respectively.
Results

 Requisite sample size by Relative Standard Error

Smallest effective sample size such that RSE of the estimate of a population 

proportion will be no more than a pre-specified upper bound. 10% RSE= 

accurate estimates; 30% RSE = moderately precise estimates, and RSE of 

50% or more = minimal precision.

RSE upper 

bound, 

True Population Percentage

10.0% 5.0% 2.5% 1.0% 0.1%

50% 37 77 157 397 3997

40% 57 119 244 619 6244

30% 101 212 434 1101 11101

20% 226 476 976 2476 24976

10% 901 1901 3901 9901 99901

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For example, at moderate precision (30% RSE), the required smallest effective 

sample size is 212, 1101, and 11101, for the 95th, 99th, and 99.9th centile

estimates, respectively.

i.e., 99th

centile
Results

 Requisite sample size by Woodruff interval 

skewness criterion

Smallest effective sample size according to skewness of the binomial distribution 

used in the Woodruff confidence interval determination. Under simple random 

sampling, two-sided confidence intervals obtained for the Woodruff method 

are expected to have reasonable coverage provided that the binomial 

distribution associated with the centile does not have excessive skew. 

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For example, an effective sample size of 69, 389, and 3989 would provide a 

good coverage of the true population of 95th, 99th, and the 99.9th centiles, 

respectively, by the Woodruff confidence intervals. 
Results

 Simulation study

 Coverage Percent intervals containing the true target 

quantity

15

True

value /2 zone /2 zone

10,000 simulations 

and CI’s 
Results

 Simulation study

 Probability weights: estimates very close to true value and CI coverage 

around 95% except the 99.9th centile of 50 site-year set.

 Time-interval weights: estimates slightly larger than true value and onesided coverage close to 95% or better except the 99.9th centile of 50 siteyear set. 

Number 

Site-Years Centile

True 

Average of 

Population

Probability Weights Time-interval Weights

Estimated 

Centile

Coverage Twosided (%) Estimated 

Centile

Coverage 

Two-sided (%) 

Coverage 

One-sided (%) 

50

(total 200 

samples)

0.90 1.62 1.58 96 1.80 89 100

0.95 2.44 2.39 97 2.68 92 100

0.99 5.09 4.92 92 5.40 90 93

0.999 10.01 9.24 24 9.40 24 24

500

(total 2000 

samples)

0.90 1.62 1.59 94 1.81 30 100

0.95 2.44 2.41 95 2.71 52 100

0.99 5.09 5.19 96 5.73 83 100

0.999 10.01 11.60 92 12.52 90 93

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Results

 Atrazine data sets

 Unequal weighting effects and estimated effective 

sample sizes

Dataset

Water 

Sample 

Type

Number of 

CWS Years Number of Atrazine Measurements

Design 

Effect

Effective 

Sample 

Size

SDWA Finished 4,404 1993-2008 50,081 4.11 12,166

VMP/AMP

Finished 220 1993-2009 48,532 2.62 18,538

Raw 228 1993-2009 46,491 2.76 16,828

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Results

 Estimated centiles and their Woodruff confidence 

intervals for raw and finished water atrazine

measurements (ppb).

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* Numbers in parentheses are one-sided 95% confidence interval.
Discussion and Conclusions

 Atrazine SDWA, and VMP/AMP datasets have more 

than140,000 measurements in over 4400 CWS during the 

period 1993 to 2009, on which this case study is based. 

 Based on the Woodruff criterion method, minimum effective 

sample sizes to estimate confidence intervals for the 95th, 99th, 

and 99.9th centiles were 69, 389, and 3989, respectively. A 

simulation exercise showed these numbers to be conservative 

in the determined sample sizes.

 With effective sample sizes greater than values shown in the 

tolerance interval table, it can be stated, for example, that “there 

is 95% confidence that the existing monitored data include the 

99th centile analyte concentration”.

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Discussion and Conclusions

 Combined with requisite sample sizes, the proposed survey 

sampling method is useful for estimating quantities from 

monitoring programs where there is a large amount of data but 

limited data per site-year to estimate upper centiles of interest 

at a site-year level.

 Existing monitoring data from a range of sources (e.g. 

government, company and academia), assuming the 

underlining data population is understood, can together be 

used to greatly improve the understanding of the likely 

distribution of residues in water and these estimates can 

provide valuable reality checks for model output in regulatory 

assessment.

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End of slides

Thank you!