Developing a Sampling Plan Using Statistical Methods

ERDC TN-DOER-C15

July 2000

assumptions for standard (parametric) statistical methods, nonparametric methods are sometimes

useful. Nonparametric methods use the ranking of the data values, rather than the individual data

values themselves. No assumptions regarding the distribution of the data are required for nonpara-

metric methods (Mendenhall and Beaver 1994). Several of these methods do require a minimum

number of samples to be applicable, and these requirements should be reviewed during the sampling

planning stages. Among them are the Mann-Whitney test for comparison of the means and variances

of two independent samples; the Sign Test for Paired Observations, which can be used to determine

if values of a selected parameter are greater in one sample than in another (the nonparametric

paired t-test, which has a binomial distribution under certain conditions); and the Kruskal-Wallis

H-test, which is used for determining whether multiple samples come from the same population

(the nonparametric analysis of variance test, which has a chi-square distribution under certain

conditions).

The primary utility of parametric and nonparametric methods is to determine if there is a statistically

significant difference between samples or sample means. These tools may be useful in interpreting

the data and extending it to unsampled areas. Before getting to that point, however, a sampling plan

that will produce data lending itself to statistical analysis must be developed. The key questions in

developing a sampling plan are where to sample, how many samples to take, what size samples are

required, and what parameters to analyze. The first two questions can be addressed statistically.

The latter two are addressed in Olin-Estes and Palermo (2000a).

Developing a Sampling Plan Using Statistical Methods. Statistical packages have been

developed to assist in design of sampling plans and/or identification of hot spots that could be

adapted to determine the number and location of samples required to characterize a CDF. The

STATSS (Statistical Techniques Applied to Sediment Sampling), a guidance document prepared

for the U.S. Environmental Protection Agency, Region 5 (Lubin, Williams, and Lin 1995), describes

statistical considerations of sampling, and approaches for determining grid and sample size for

sampling sediments within a waterway. The Groundwater Modeling System (GMS) (Brigham

Young University 1999) is another statistically based package designed to facilitate definition of

subsurface contaminant plumes. The following is a general discussion of the underlying statistical

principles and data analysis methods that provide the framework for statistically based sampling.

The reader is referred to these statistical packages and references for more in-depth guidance in

applying these principles.

Where to sample. There are three basic sampling approaches:1

Judgmental approach.

Random approach.

Systematic approach.

A judgmental approach involves applying what is known about a site, and sampling in those areas

that appear most likely to be contaminated or otherwise of interest. The judgmental approach is

Personal communication, 9 October 1998, Dr. John H. Pardue, Civil and Environmental Engineering

Department, Louisiana State University, Baton Rouge.