Statistics for Environmental Engineers

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Components of Variance


KEY WORDS analysis of variance, ANOVA, components of variance, composite sample, foundry waste, nested design, sampling cost, sample size, system sand.


A common problem arises when extreme variation is noted in routine measurements of a material. What are the important sources of variability? How much of the observed variability is caused by real differences in the material, how much is related to sampling, and how much is physical or chemical measurement error? A well-planned experiment and statistical analysis can answer these questions by breaking down the total observed variance into components that are attributed to specific sources.

Multiple Sources of Variation


When we wish to compare things it is important to collect the right data and use the appropriate estimate of error. An estimate of the appropriate error standard deviation can be obtained only from a design in which the operation we wish to test is repeated.


The kind of mistake that is easily made is illustrated by the following example. Three comparisons we might wish to make are (1) two testing methods, (2) two sampling methods, or (3) two processing methods. Table 25.1 lists some data that might have been collected to make these comparisons.


Two Testing Methods. Suppose we wish to compare two testing methods, A and B. Then we must compare, for example, ten determinations using test method A with ten determinations using test method B with all tests made on the same sample specimen.

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