Contrast Analysis

A standard analysis of variance (ANOVA) provides an F test, which is called an omnibus test because it reflects all possible differences between the means of the groups analyzed by the ANOVA. However, most experimenters want to draw conclusions more precise than “the experimental manipulation has an effect on participants’ behavior.” Precise conclusions can be obtained from contrast analysis because a contrast expresses a specific question about the pattern of results of an ANOVA. Specifically, a contrast corresponds to a prediction precise enough to be translated into a set of numbers called contrast coefficients, which reflect the prediction. The correlation between the contrast coefficients and the observed group means directly evaluates the similarity between the prediction and the results.

When performing a contrast analysis, one needs to distinguish whether the contrasts are planned or post hoc. Planned, or a priori, contrasts are selected before running the experiment. In general, they reflect the hypotheses the experimenter wants to test, and there are usually few of them. Post hoc, or a posteriori (after the fact), contrasts are decided after the experiment has been run. The goal of a posteriori contrasts is to ensure that unexpected results are reliable.

When performing a planned analysis involving several contrasts, one needs to evaluate whether these contrasts are mutually orthogonal or not. Two contrasts are orthogonal when their contrast coefficients are uncorrelated (i.e., their coefficient [Page 244]of correlation is zero). The number of possible orthogonal contrasts is one less than the number of levels of the independent variable.

All contrasts are evaluated by the same general procedure. First, the contrast is formalized as a set of contrast coefficients (also called contrast weights). Second, a specific F ratio (denoted Fψ) is computed. Finally, the probability associated with Fψ is evaluated. This last step changes with the type of analysis performed.