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Published online by Cambridge University Press: 05 June 2012
Introduction
When you use a single factor ANOVA to examine the results of an experiment with three or more treatments, a significant result only indicates that one or more appear to come from populations with different means. It does not identify which particular treatment means appear to be from the same or different populations.
For example, a significant difference among the means of the three treatments A, B, and C can occur in several ways. Mean A may be greater (or less) than B and C; mean B may be greater (or less) than A and C; mean C may be greater (or less) than A and B; and, finally, means A, B, and C may all be different to each other.
If the treatments have been chosen as random representatives of all the possible treatments available (i.e. the factor is random so you have done a Model II ANOVA), you will not be interested in knowing which particular treatment means appear to be from the same or different populations because your hypothesis is more general. A significant result will reject the null hypothesis and show a difference, but that is all you will want to know.
In contrast, if the treatments have been specifically chosen (i.e. the factor is fixed so you have done a Model I ANOVA), you will be interested in knowing which treatment means appear to be from the same or different populations. There are several multiple comparison tests designed to do this.
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