ANOVA and ANCOVA (GLM)

Within-Subjects ANOVA (Repeated Measures): General Linear Model

• In the within-subjects design, we collect scores from every subject under all experimental conditions of the design. The overall analysis combines elements of both the between-subjects design and the within-subject design:
• For example, a two-factor within-subjects ANOVA combines elements of the between-subjects AxB design and the within-subjects AxS design, i.e., the main effects and the interaction are computed with the same procedures used for the between-subjects AxB design; the error terms are calculated using the AxS within-subjects design.
The Analysis Output

The analysis output including the default and optional ones can include:

• Multifactor cell means table
• Within-subjects ANOVA table
• Sphericity evaluations*:
• The Mauchly's Test Statistic (W)
• The Locally Best Invariant Test Statistic
• Correcting for Violations of Sphericity:
• The Greenhouse & Geisser epsilon
• The Huynh & Feldt epsilon and Lecoutre correction of Huynh & Feldt epsilon (if necessary)
• Corrections on degrees of freedom
• * Results are generated for both omnibus sphericity and local sphericity evaluations and corrections.

• Sphericity-corrected ANOVA test results
• Measures of Effect Size/Association
• Sphericity-corrected effect size
• Regression coefficients and model summary output
• Normality test on regression residuals of total model:
• D'Agostino-Pearson test
• Shapiro-Wilk test

This design requires:

• A numeric column (continuous variable) for storing the experimental scores
• n categorical columns, each of which with a minimum of two levels
• A a categorical column with the subject ID

Within-Subjects ANOVA Table: A Two-Way Example  Sphericity Evaluation Tests Results   Sphericity Corrections

The Epsilon Table Output (Greenhouse & Geisser, Huynh & Feldt, Lower Bound) Omnibus-Sphericity Corrected ANOVA Test Results Local-Sphericity Corrected ANOVA Test Results  Measures of Effect Size/Association Sphericity-Adjusted Noncentrality Parameter and Effect Size   The Regression Analysis Report Corresponding to ANOVA Test Results

Regression Coefficients and Model Summary Normality Tests on Regression Residuals  