Contrasts and Correlations in Theory Assessment

Abstract

To describe a systematic quantitative approach to assessing the predictions made by competing theories using contrasts and correlational indices of effect sizes. We illustrate the use of the contrast F and t to compare and combine predictions when the raw data are continuous scores, and z contrasts when working with frequencies in 2 x k tables of counts. The traditional effect size correlation indicates the magnitude of the effect on individual scores of participants' assignment to particular conditions. The contrast correlation obtained from the contrast F or t is, in some cases, the easiest way of estimating the effect size correlation in designs using more than two groups. The alerting correlation is another way of appraising the predictive power of a contrast and can be used to compute the contrast F from published results when all we have are condition means and the omnibus F from an overall analysis of variance. Omnibus Fs, those with more than 1 df in the numerator, are rarely useful in data analytic work since they address unfocused questions, yielding only vague answers. Asking focused questions using contrasts increases the clarity of our questions and the clarity and statistical power of our answers.