ANOVA and ANCOVA (GLM)

Mixed Between-Within Subjects ANOVA: General Linear Model

  • n-Way mixed model combines one or more independent sample factor (between-subjects) and one or more correlated groups factor (repeated measures).
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)
    • Harris Multisample 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
  • 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
  • In mixed between-within design, multiple comparisons are provided to test differences among the levels of the between-subjects factor(s), and the the tests are being performed for the average across the levels of the within-subjects factors.
  • PMC for between-subjects factor(s) include:
    • Bonferroni-Dunn
    • Dunn-Sidak
    • Dunnett
    • Scheffé
    • Tukey-Kramer
    • Fisher's LSD
    • Tukey's HSD
    • Newman-Keul
    • Tukey B
    • Dunnett's C
    • Games-Howell

* Results are generated for both omnibus sphericity and local sphericity evaluations and corrections.

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

Between-Within Subjects ANOVA Table

Between-Within Design ANOVA (General Linear Mdel): Test Results

Sphericity Evaluation Tests Results

Mauchly's Test of Sphericity

Harris Multisample Test of Sphericity

Sphericity Corrections

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

Sphericity Corrections

Sphericity-Corrected ANOVA Test Results

ANOVA Test Results Corrected for Sphericity

Measures of Effect Size/Association

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

Sphericity-Adjusted Noncentrality Parameter and Effect Size

Sphericity-Corercted Effect Size

The Regression Analysis Report Corresponding to ANOVA Test Results

Regression Coefficients and Model Summary

Mixed Between-Within Subjects ANOVA: Regression Coefficients and Model Summary

Normality Tests on Regression Residuals

D'Agostino-Pearson Normality Test

Homoscedasticity Tests on Dependent Variable (Specific to Between-Subjects Factor)

Mauchly's Test of Sphericity

Harris Multisample Test of Sphericity