The previous chapter addressed the basic questions behind the analysis of variance and presented material that is critical to an understanding of what the analysis of variance is all about. This chapter builds on that material to discuss important measures of power and effect size, to expand on alternative ways of approaching comparisons among individual group means, to discuss the treatment of missing data, and to consider alternative approaches to the treatment of nonnormal data or heterogeneous variances. More than the usual focus is given to individual contrasts and their implications for power and effect size calculations, and less to the omnibus F and associated measures. This idea is certainly not new, but such suggestions in the literature have not always led to changes in practice.
The analysis of variance is a powerful tool that has served behavioral scientists well over the years. We know how to calculate power for various designs, we can derive effect size measures to provide meaningful interpretation to our results, and we have developed ways to work with missing observations and heterogeneous variances. However, most discussions of the analysis of variance focus on the omnibus F test, which considers all means simultaneously, or on traditional or innovative multiple comparison procedures focusing on all pairwise comparisons. One purpose of this chapter is to point out that we will do well to attend clearly and directly to those effects that we consider most important. That means that we need to derive our power estimates based on those contrasts rather than on the omnibus F; that we need to direct our attention to very specific and, it is hoped, few contrasts; and that we will do well to present effect size measures that speak to those contrasts.
The links that I reference are:
www.uvm.edu/~dhowell/AnovaChapter/FoaDoubled.dat
www.uvm.edu/~dhowell/AnovaChapter/JSLdep.sav
www.uvm.edu/~dhowell/AnovaChapter/AirportModified.dat