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If this allocation leads to the same sample variances listed in Table 23.4, the variance of the
mean would be s 2 = 1.58 and the 95% confidence interval would be ±1.96 1.53 = ±2.5. This
y
is a reduction of about 10% without doing any additional work, except to make a better sampling
plan.

Comments

This chapter omits many useful sampling strategies. Fortunately there is a rich collection in other books.
Cochran (1977) and Cochran and Cox (1957) are the classic texts on sampling and experimental design.
Gilbert (1987) is the best book on environmental sampling and monitoring. He gives examples of
random sampling, stratified sampling, two- and three-stage sampling, systematic sampling, double sam-
pling, and locating hot spots. Two-stage sampling is also called subsampling. It is used when large field
samples are collected and one or more aliquots are selected from the field sample for analysis. This is
common with particulate materials. The subsampling introduces additional uncertainty into estimates of
means and variances. Three-stage sampling involves compositing field samples and then subsampling
for the composite for analysis. The compositing does some beneficial averaging.
Hahn and Meeker (1991) give examples and many useful tables for deriving sample size requirements
for confidence intervals for means, a normal distribution standard deviation, binomial proportions,
Poisson occurrence rates, tolerance bounds and intervals, and prediction intervals. This is a readable and
immensely practical and helpful book. Mendenhall et al. (1971) explain random sampling, stratified
sampling, ratio estimation, cluster sampling, systematic sampling, and two-stage cluster sampling.
This chapter was not written to provide a simple answer to the question, “What sample size do I
need?” There is no simple answer. The objective was to encourage asking a different question, “How
can the experiment be arranged so the standard error is reduced and better decisions will be made with
minimum work?”
Many kinds of sampling plans and experimental designs have been developed to give maximum
efficiency in special cases. A statistician can help us recognize what is special about a sampling problem
and then select the right sampling design. But the statistician must be asked to help before the data are
collected. Then all the tools of experimental design — replication, blocking, and randomization — can
be organized in your favor.

References

Cochran, W. G. (1977). Sampling Techniques, 3rd ed., New York, John Wiley.
Cochran, W. G. and G. M, Cox (1957). Experimental Designs, 2nd ed., New York, John Wiley.
Cohen, J. (1969). Statistical Power Analysis for the Behavioral Sciences, New York, New York Academy Press.
Fleiss, J. L. (1981). Statistical Methods for Rates and Proportions, New York, John Wiley.
Gibbons, R. D. (1994). Statistical Methods for Groundwater Monitoring, New York, John Wiley.
Gilbert, R.O. (1987). Statistical Methods for Environmental Pollution Monitoring, New York, Van Nostrand
Reinhold.
Hahn, G. A. and W. Q. Meeker (1991). Statistical Intervals: A Guide for Practitioners, New York, John Wiley.
Johnson, R. A. (2000). Probability and Statistics for Engineers, 6th ed., Englewood Cliffs, NJ, Prentice-Hall.
Kastenbaum, M. A., D. G. Hoel, and K. O. Bowman (1970). “Sample Size Requirements: One-Way Analysis
of Variance,” Biometrika, 57, 421–430.
Mendenhall, William, L. Ott, and R. L. Schaeffer (1971). Elementary Survey Sampling, Duxbury Press.
Mowery, P. D., J. A. Fava, and L. W. Clatlin (1985). “A Statistical Test Procedure for Effluent Toxicity Screening,”
Aquatic Toxicol. Haz. Assess., 7th Symp., ASTM STP 854.
Stein, J. and N. Dogansky (1999). “Sample Size Considerations for Assessing the Equivalence of Two Process
Means,” Qual. Eng., 12(1), 105–110.
U.S. EPA (1994). Guidance for the Data Quality Objectives Process, (EPA QA/G-4), Washington, D.C.,
Quality Assurance Management Staff.
© 2002 By CRC Press LLC