OBJECTIVE: To describe a systematic quantitative approach to assessing the predictions made by competing theories using contrasts and correlational indices of effect sizes. METHODS: 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. RESULTS: 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. CONCLUSIONS: Asking focused questions using contrasts increases the clarity of our questions and the clarity and statistical power of our answers.
OBJECTIVE: To describe a systematic quantitative approach to assessing the predictions made by competing theories using contrasts and correlational indices of effect sizes. METHODS: 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. RESULTS: 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. CONCLUSIONS: Asking focused questions using contrasts increases the clarity of our questions and the clarity and statistical power of our answers.