Page 231 - Statistics for Environmental Engineers

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26

Multiple Factor Analysis of Variance

KEY WORDS air pollution, dioxin, furan, incineration, samplers, ANOVA, analysis of variance, factorial
experiment, sampling error.

Environmental monitoring is expensive and complicated. Many factors may contribute variation to measured
values. An obvious source of variation is the sampling method. An important question is: “Do two samplers
give the same result?” This question may arise because a new sampler has come on the market, or because
a monitoring program needs to be expanded and there are not enough samplers of one kind available.
It might seem natural to compare the two (or more) available sampling methods under a fixed set of
conditions. This kind of experiment would estimate random error under only that specific combination
of conditions. The samplers, however, will be used under a variety of conditions. A sampler that is
effective under one condition may be weak under others. The error of one or both samplers might depend
on plant operation, weather, concentration level being measured, or other factors. The variance due to
laboratory measurements may be a significant part of the total variance. Interactions between sampling
methods and other possible sources of variation should be checked. The experimental design should take
into account all these factors.
Comparing two samplers under fixed conditions pursues the wrong goal. A better plan would be to
assess performance under a variety of conditions. It is important to learn whether variation between
samplers is large or small in comparison with variation due to laboratory analysis, operating conditions,
etc. A good experiment would provide an analysis of variance of all factors that might be important in
planning a sampling program.
It is incorrect to imagine that one data point provides one piece of information and therefore the informa-
tion content of a data set is determined entirely by the number of measurements. The amount of information
available from a fixed number of measurements increases dramatically if each observation contributes
to estimating more than one parameter (mean, factor effect, variance, etc.). An exciting application of
statistical experimental design is to make each observation do double duty or even triple or heavier duty.
However, any valid statistical analysis can only extract the information existing in the data at hand. This
content is largely determined by the experimental design and cannot be altered by the statistical analysis.
This chapter discusses an experimental design that was used to efficiently evaluate four factors that
were expected to be important in an air quality monitoring program. The experiment is based on a factorial
design (but not the two-level design discussed in Chapter 27). The method of computing the results is
not discussed because this can be done by commercial computer programs. Instead, discussion focuses
on how the four-factor analysis of variance is interpreted. References are given for the reader who wishes
to know how such experiments are designed and how the calculations are done (Scheffe, 1959).

Case Study: Sampling Dioxin and Furan Emissions from an Incinerator
Emission of dioxins and furans from waste incinerators has been under investigation in many countries.
It is important to learn whether different samplers (perhaps used at different incinerators or in different
cities or countries) affect the amount of dioxin or furan measured. It is also important to assess whether
differences, if any, are independent of other factors (such as incinerator loading rate and feed materials
which change from one sampling period to another).

© 2002 By CRC Press LLC