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L1592_frame_C24.fm Page 220 Tuesday, December 18, 2001 2:45 PM

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.)

A common question is: “Are the differences between labs large enough to have important consequences
in practice?” Importance and statistical significance are different concepts. Importance depends on the
actual use to which the measurements are put. Statistically significant differences are not always impor-
tant. We can change significance to nonsignificance by changing the probability level of the test (or by
using a different statistical procedure altogether). This obviously would not change the practical impor-
tance of a real difference in performance. Furthermore, the importance of a difference will exist whether
we have data to detect it or not.
Analysis of variance can be applied to problems having many factors. One such example, a four-way
ANOVA, is discussed in Chapter 26. Chapter 25 discusses the use of ANOVA to discover the relative
magnitude of several sources of variability in a sampling and measurement procedure. Box et al. (1978)
provide an interesting geometric interpretation of the analysis of variance.

References

Box, G. E. P., W. G. Hunter, and J. S. Hunter (1978). Statistics for Experimenters: An Introduction to Design,
Data Analysis, and Model Building, New York, Wiley Interscience.
Johnson, R. A. and D. W. Wichern (1992). Applied Multivariate Statistical Analysis, Englewood Cliffs, NJ,
Prentice-Hall.
Sokal, R. R. and F. J. Rohlf (1969). Biometry: The Principles and Practice of Statistics in Biological Research,
New York, W. H. Freeman and Co.

Exercises
24.1 Chromium Measurements. A large portion of chromium contaminated water was divided into
32 identical aliquots. Eight aliquots were sent to each of four laboratories and the following
data were produced. Are the laboratories making consistent measurements?

Lab 1 26.1 21.5 22.0 22.6 24.9 22.6 23.8 23.2
Lab 2 18.3 19.7 18.0 17.4 22.6 11.6 11.0 15.7
Lab 3 19.1 13.9 15.7 18.6 19.1 16.8 25.5 19.7
Lab 4 30.7 27.3 20.9 29.0 20.9 26.1 26.7 30.7

24.2 Aerated Lagoon. Conductivity measurements (µmho/cm) were taken at four different locations
in the aerated lagoon of a pulp and paper mill. The lagoon is supposed to be mixed by aerators
so the contents are homogeneous. Is the lagoon homogeneously mixed?

Location A Location B Location C Location D
620 630 680 560
600 670 660 620
630 710 710 600
590 640 670 610
650 680 630
660 680 640
630
590
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