SENSITIVITY OF THE T-TEST TO DIFFERENT MODELS OF INTERACTION - A REPLY

If the sample value of a linear contrast testing for interaction in a 2 x 2 design is near zero, this does not establish that there is no interaction in the population. A confidence interval for the population value of the interaction contrast specifies a range of plausible magnitudes of the interaction when the sample contrast is zero, and this range is remarkably wide when samples are small. In order to narrow the confidence interval, larger sample size must be employed. Sample size calculations should be done before the data are collected in a new study. Power pertains to a comparison of two hypothetical models of the data, one with pure additivity of effects and the other with a specific kind of interaction. Wise choice of parameters for the models is not made by copying parameter estimates from only one empirical study involving small samples, but instead the model should express the kind of interaction that would be psychologically interesting and relevant for theories of development.