Two-Way ANOVA Tests

Fundamentals of Social Statistics


The one-way ANOVA has a single independent variable (IV) which is usually a grouping variable, such as when an experimenter has a placebo and one or more experimental groups.  The two-way ANOVA allows for two independent variables.  In addition to examining the effect of the two factors, we can also examine the interaction of the two factors using the two-way ANOVA.

Each way in an ANOVA is a grouping variable.  Thus, a two-way ANOVA means that the subjects are classified by two variables, rather than by the one grouping variable in the one-way ANOVA.  The ways are also known as factors.  The effect of one grouping variable while not taking the other into account is known as a main effect.  With the two-way ANOVA, there are two main effects.

Sometimes, the main effect of one independent variable will depend on the level of the other dependent variable.  When this is the case, the two variables are said to have an interaction.

Key Terms

one-way analysis of variance (ANOVA), F statistic, ANOVA summary table, multiple comparison tests, post hoc tests, Type I error rate, Tukey Honestly Significant Difference (HSD), two-way ANOVA, main effect, interaction effect

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Last Modified:  02/12/2019

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