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Two-Way Between-Subjects ANOVA

Two-way between-subjects ANOVA is also known as between-subjects factorial ANOVA, completely randomized factorial ANOVA, two-way ANOVA, completely randomized factorial design with two treatments. It evaluates the effect of two independent variables (factors) on a response variable simultaneously. That is, it evaluates the variation among the differences between means for different levels of one factor over different levels of the other factor.


Two-Way Between-Subjects ANOVA Output

The default output includes the two-way ANOVA table. The additional output depends on selected options, and can include the two-way mean table, interaction plots, the test results for homogeneity of variance, and table reports for selected multiple comparisons/post-hoc tests.

The Default Output: Two-Way ANOVA Table

Testing for Homogeneity of Variance

Interaction Plots

The interaction plot is a graphical display of the effect of one factor at each level of the other factor. The error bars displayed on the interaction plots can represent:

Multiple Comparisons/Post-Hoc Tests

Simple comparisons (also know as pair-wise comparisons) accompanying two-way between-subjects ANOVA include:

When you select a multiple comparison/post-hoc test accompanying a two-way between ANOVA, the test will be performed for any item of the ANOVA table that has a p value less than or equal to the omnibus α.

The example below is the Newman-Keuls test result for the two-way between-subjects ANOVA example illustrated above. For more information regarding multiple comparisons, click here.

Supported Worksheet Layout

This ANOVA design requires (i) two categorical columns for storing levels of the design between-subjects factors (i.e., Factor A with p >= 2 levels, and Factor B with q >=2 levels), and (ii) a numeric column for storing the experimental scores (response values) from all of the pq independent groups.