A New Look at Treatment Differences

Abstract

Quite frequently in the behavioral sciences, the raw data obtained from an experimental subject are a series of binary responses. In addition to the example of test item data we could include many questionnaire studies and psychological experiments involving discrimination, perception and the like. If the subjects are also classified on another variable, the design is similar to the split-plot design and is often called a two-factor repeated measures experiment by behavioral researchers. With continuous measurements which fit the normal model the analysis is fairly straightforward. Tests of the assumption of a patterned covariance matrix should be considered but results of Collier, et al., (1967) indicate that moderate departures do not seriously invalidate the usual tests of significance. For situations in which the researcher feels that this approach is unwarranted, a conservative test due to Greenhouse and Geisser (1959) or multivariate procedures described elsewhere e.g., Danford, et al., (1960); Cole and Grizzle (1966) are appropriate. For dichotomous data, however, the literature provides few clues to aid the researcher. Recent non-parametric results of Koch (1969) which are based on ranks, are not directly applicable for dichotomous data. Other than the use of total scores or separate tests of proportions for each response, the present writer knows of no methods which are used with any frequency by behavioral scientists. Robustness of variance ratio procedures suggests that the usual univariate F tests might also be useful with binary data. In fact, when Cochran (1950) introduced the Q statistic, he also presented data which