Interactions and Specific Hypotheses

Abstract

A factor is an independent variable. A factorial design completely crosses two or more factors. It is an efficient design that simultaneously studies main effects of factors and their interactions. A distinction is made between factors that can be manipulated by researchers and factors that cannot be manipulated. Usually, the effects of manipulable factors are causally interpreted. Nonmanipulable factors are included for two different reasons, but they should not be dichotomized. First, to increase the precision of parameter estimates and the power of statistical tests. The nonmanipulable factor is included as a blocking variable in a randomized block design (if its values are known before participants are assigned to conditions) or as a covariate in the analysis of the data. Second, to study their relations with manipulable factors, but these relations should not be causally interpreted. The statistical analysis of factorial design data has to be tuned to the type of dependent variable (DV). Usually, ANOVA or ANCOVA are applied to (approximately) continuous DVs, but these methods make strong assumptions. Akritas et al.’s (J Am Stat Assoc 92:3375–3384, 1997) nonparametric method is more appropriate to analyze (approximately) continuous and ranked DVs. The preferred methods for dichotomous, nominal-categorical, and ordinal-categorical DVs are the logit, baseline-category, and cumulative logit models, respectively. Often, researchers apply omnibus statistical tests to factorial design data. These tests mainly fit into exploratory research. Confirmatory studies prespecify specific hypotheses. The proper methods to test these hypotheses are planned comparisons of conditions.