Analysis of Variance

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Title: Analysis of Variance (ANOVA) Using MINITAB
Author: Keith M. Bower
Publication Source: Scientific Computing & Instrumentation, Vol. 17 No. 3, February 2000, pp 64-65

Abstract

General guidelines are provided for using and interpreting results from the ANOVA procedure. In particular, the example addresses:

(a) Anderson-Darling Normality test
(b) Test for equal variances
(c) General Linear Model
(d) Multiple comparison tests
(e) Analysis of residuals

Notes

The aim of this paper was to address the typical assumptions associated with performing the Analysis of Variance (ANOVA) procedure, in a rigorous manner. Importantly, I did not include a discussion of the randomization argument in favor of allowing the validity of the results obtained. The sole reason for this was that I wanted to present a relatively basic outline for more experienced practitioners (i.e. more of a "how to").

For a more rigorous discussion as to why there may be validity to the ANOVA results even if certain assumptions may be violated to a degree, see The Two-Sample t-Test and Randomization Test.

Regarding the inclusion of Tukey's Multiple Comparison Test, this was to try and introduce certain practitioners, who would be unfamiliar as to what the next step in the analysis should be, as to the progression. In hindsight, it may have been appropriate to provide some warnings against not using a series of two-sample t-tests to find differences, as well as addressing the flawed overlapping confidence interval argument.

For more information against the use of overlapping confidence intervals, see Some Misconceptions about Confidence Intervals.

Finally, it would also have been helpful to discuss the manner of choosing the comparisons prior to running the experiment, but that type of discussion was outside the scope of this paper.

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