One-Way and Factorial ANOVA


One-Way Analysis of Variance (ANOVA) is an extension form the t-test. Where the t-test only compares mean difference for two groups One-Way ANOVA compares several groups. For example, is adolescent substance use different among Whites, Blacks and Hispanics? Factorial ANOVA is an extension from One-Way ANOVA. Whereas One-Way ANOVA has only one independent variable, Factorial ANOVA has several independent variables. For instance, does an intervention program have different effects on Whites, Blacks and Hispanics? This study has two independent variables: treatment and ethnicity.

When several groups are compared, a subsequent test is often followed after a significant ANOVA to identify specific group difference. For example, is substance use different between Whites and Blacks, or between Blacks and Hispanics? In a Factorial ANOVA, the interaction effect is often the most interesting issue of the researcher. For instance, is the treatment more effective for Whites than for Blacks?

ANOVA is the most popular statistical procedure in applied research. One-Way and Factorial ANOVA are Between-Subjects ANOVA, because no repeated measures are involved. If each subject is measured several times, Repeated Measures ANOVA should be used.