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Two-Way Mixed-Model ANOVA (Between-Within Design)

Two-way mixed model ANOVA is also known as Two-way Mixed factorial ANOVA and split-plot factorial design. This Design combines one independent sample factor (Factor A) and one correlated groups factor (Factor B), evaluating the main effects of the Factor A, Factor B, and the interaction (AB).

Two-Way Mixed-Model ANOVA Output

The default output includes the two-way ANOVA table. The additional output depends on selected options, and can include interaction plots, the results for sphericity test and corrections, and table reports for selected multiple comparisons tests.

The Default Output: Two-Way Mixed (Between-Within) ANOVA Table

Interaction Plots

Interaction plots are a graphical display of the effect of one factor at each level of the other factor. With no or insignificant interaction, the lines are approximately parallel (in the example below, the main effect is due to the pq condition "Low Temperature" x "High Humidity").

The error bars displayed on the interaction plots can represent:

Sphericity Evaluation (Haris W)

Greenhouse & Geisser and Huynd & Feldt Corrections

Multiple Comparisons/Post-Hoc Tests

Simple comparisons (also know as pair-wise comparisons) accompanying two-way mixed between-within ANOVA design 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

The example below is the Bonferroni-Dunn test result for the two-way mixed between-within ANOVA example illustrated above. For more information regarding multiple comparisons, click here.

Supported Worksheet Layout

For this ANOVA design, Aabel supports two different worksheet layouts.

  • The layout I allows storing the design experimental scores (response data) from all of the pq levels of the design factors (Factor A with p >= 2 levels, and Factor B with q >=2 levels) in a single numeric column, and uses the pq levels of the design factors to split the response data accordingly. In this layout, a subject occurs in multiple worksheet rows: hence, it is required to have a data column (numeric or categorical) with the subject ID.
  • The layout II requires storing the design experimental scores (response data) from each level of the within-subjects factor (Factor B) in a separate numeric column, and uses the p >= 2 levels of the between-subjects factor (Factor A) to split the response data accordingly.