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TwoWay MixedModel ANOVA (BetweenWithin Design)
Twoway mixed model ANOVA is also known as Twoway Mixed factorial ANOVA and splitplot 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).
TwoWay MixedModel ANOVA Output
The default output includes the twoway 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: TwoWay Mixed (BetweenWithin) ANOVA Table
 The source of variability: The betweensubjects variability (i) attributable to Factor A, and (ii) attributable to subjects within group error (Subjects WG); The withinsubjects variability (i) attributable to Factor B, (ii) attributable to AB interaction, and (iii) attributable to B x Subjects WG error
 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:
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:
 Standard error of mean
 Standard Deviation
 Confidence Interval (including options of 90.0%, 95.0%, 97.5%, 99.0%)
Sphericity Evaluation (Haris W)
 In factorial ANOVA with a mixed design Factor B represents multisample repeated measures. Accordingly, evaluating the tenability of sphericity assumption requires a multisample sphericity test, for which a variety of approaches have been made.
 Aabel uses the Harris approach [Harris, P. (1984); Kirk, R.E. (1995)] for testing the multisample sphericity assumption for Factor B.
Greenhouse & Geisser and Huynd & Feldt Corrections
 For sphericity corrections, Aabel provides Greenhouse & Geisser and Huynd & Feldt methods.
Multiple Comparisons/PostHoc TestsSimple comparisons (also know as pairwise comparisons) accompanying twoway mixed betweenwithin ANOVA design include:


The example below is the BonferroniDunn test result for the twoway mixed betweenwithin 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 withinsubjects factor (Factor B) in a separate numeric column, and uses the p >= 2 levels of the betweensubjects factor (Factor A) to split the response data accordingly.