Abstract
This paper presents the foundations of contrast analysis as a method for examining change. Contrast analysis is a relatively high-powered, simple, and informative procedure for evaluating hypotheses about specific patterns of change. This paper reviews the general purpose and nature of contrast analysis, it discusses some of the advantages of contrast analysis as a method for examining change, it provides a conceptual overview of the relevant statistical procedures, it illustrates the approach by working through several examples, and it addresses important issues that should be considered when conducting and interpreting contrast analysis.
Acknowledgements
This work was supported by a grant from the National Institute of Health (R01-MH63908). I thank Erika Carlson, Kris Gauthier, and Eric Stone for their comments on this manuscript.
Notes
1. Although the current paper presents examples of contrast analysis for a study with five time points, contrast analysis is applicable to studies with any number of time points. In fact, contrast analysis is the implicit basis of some familiar techniques that involve only two time points, such as repeated-measures t tests and ANOVA designs with a two-level repeated-measures factor. Such techniques can be seen as contrast procedures in which the two contrast weights are +1 and −1.
2. An alternative approach to obtaining SSCONTRAST-NORM is by using “normalized” contrast weights in Step 1 of the contrast analysis procedure. A set of normalized contrast weights has a sums of squares value of 1.0. For example, the steady decline set of contrast weights in A1 have a SS value of 10: