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
- The source of variability: The between-groups variability (i) attributable to Factor A, (ii) attributable to Factor B, and (iii) attributable to AB interaction; the within-groups variability (i.e., error or residual variability)
- The sum of the squared deviations from the mean (Sum of Squares); the degrees of freedom (df); the Mean Square for each of the variability components
- The test statistic (F) and the p value
- The partial omega squared test result (testing strength of association)
This table displays:
Testing for Homogeneity of Variance
- Hartley's Fmax test
- Bartlett's chi-square test
For evaluating the homogeneity of variance assumption, Aabel provides:
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:
- Standard error of mean
- Standard Deviation
- Confidence Interval (including options of 90.0%, 95.0%, 97.5%, 99.0%)
Multiple Comparisons/Post-Hoc Tests
Simple comparisons (also know as pair-wise comparisons) accompanying two-way between-subjects ANOVA include:
- Tukey's HSD test (see the example above)
- Tukey B test on ordered means
- Fisher's LSD test
- The Newman-Keuls (Neuman-Keuls) test on ordered means
- Tukey Kramer test
- Scheffé test
- Bonferroni-Dunn test
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.