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

The tables on this page are examples from a two-way design:

Within-Subjects ANOVA Table: A Two-Way Example

Within-Subjects ANOVA (General Linear Mdel): Test Results

Sphericity Evaluation Tests Results

Mauchly's Test of Sphericity

Locally Best Invariant Test of Sphericity

Sphericity Corrections

The Epsilon Table Output (Greenhouse & Geisser, Huynh & Feldt, Lower Bound)

Sphericity Corrections

Omnibus-Sphericity Corrected ANOVA Test Results

ANOVA Test Results Corrected for Omnibus Sphericity

Local-Sphericity Corrected ANOVA Test Results

ANOVA Test Results Corrected for Local Sphericity

Measures of Effect Size/Association

Eta, Eta Squared, Noncentrality Parameter, and Cohen's f

Sphericity-Adjusted Noncentrality Parameter and Effect Size

Effect Size Corrected for Omnibus Sphericity

Effect Size Corrected for Local Sphericity

The Regression Analysis Report Corresponding to ANOVA Test Results

Regression Coefficients and Model Summary

Within-Subjects ANOVA (General Linear Model): Regression Coefficients and Model Summary

Normality Tests on Regression Residuals

D'Agostino-Pearson Normality Test

Shapiro-Wilk Normality Test