Introduction to Analysis of Variance Procedures

Comparing Group Means

The F test for a classification factor that has more than two levels tells you whether the level effects are significantly different from each other, but it does not tell you which levels differ from which other levels.

If the level comparisons are expressed through differences of the arithmetic cell means, you can use the MEANS statement in the GLM and ANOVA procedures for comparison. If arithmetic means are not appropriate for comparison, for example, because your data are unbalanced or means need to be adjusted for other model effects, then you can use the LSMEANS statement in the GLIMMIX, GLM, and MIXED procedures for level comparisons.

If you have specific comparisons in mind, you can use the CONTRAST statement in these procedures to make these comparisons. However, if you make many comparisons that use some given significance level (0.05, for example), you are more likely to make a type 1 error (incorrectly rejecting a hypothesis that the means are equal) simply because you have more chances to make the error.

Multiple-comparison methods give you more detailed information about the differences among the means and enable you to control error rates for a multitude of comparisons. A variety of multiple-comparison methods are available with the MEANS statement in both the ANOVA and GLM procedures, as well as the LSMEANS statement in the GLIMMIX, GLM, and MIXED procedures. These are described in detail in the section Multiple Comparisons in Chapter 45: The GLM Procedure, and in Chapter 44: The GLIMMIX Procedure, and Chapter 65: The MIXED Procedure.