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A factorial design contains two or more independent variables and one dependent variable. The independent variables, often called factors, must be categorical. Groups for these variables are often called levels. The dependent variable must be continuous, measured on either an interval or a ratio scale.

Suppose a researcher is interested in determining if two categorical variables (treatment condition and gender) affect a continuous variable (achievement). The researcher decides to use a factorial design because he or she wants to examine population group means. A factorial analysis of variance will allow him or her to answer three questions. One question concerns the main effect of treatment: Do average achievement scores differ significantly across treatment conditions? Another question concerns the main effect of gender: Does the average achievement ...

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