Statistics for Environmental Engineers

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The ANOVA table for the laboratory data is given in Table 24.3. The F ratio is compared with the critical value F445a05= 2.59. The value of F = 6.81 found for this experiment is much larger than F445a052.59 so we conclude that the variation between laboratories has been inflated by real differences in the mean level of performance of the labs.

Knowing this result of the analysis of variance, a plausible conclusion would be that laboratory 4, having the lowest average, is different from the others. But laboratories 4 and 5 may both be different from the other three. Or laboratory 3 may also be different, but on the high side. Unfortunately, ANOVA does not tell us how many or which laboratories are different; we only know that they are not giving the same results.


When the ANOVA indicates differences between laboratories, additional questions arise.

1.    Which laboratories are different and which are the same? Making multiple pair-wise comparisons to answer this was discussed in Chapter 20.

2.    Which laboratories, if any, are giving correct results? Without knowing the true concentration of the samples analyzed, there is no answer to this question. We remind ourselves, however, that the performer who is different may be the champion!

3. Is a special program needed to bring all laboratories into conformance? Maybe the only needed step is to show the participating laboratories the results. Simply knowing there is a possible problem usually will stimulate improvement. Quality improvement depends more on collecting data and communicating the results than on fixing blame or identifying poor performers. This means that we do not always need to find out which laboratories are different. (Recall point 2.)

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