Repeated Measures/Mixed-Model ANOVA:

1. Repeated Measures/Mixed-Model ANOVA: SPSS Lab #4

2. MANOVA • Multivariate ANOVA (MANOVA) • Both 2+ IV’s and 2+ DV’s • SPSS won’t run with only 1 DV • Click “Analyze”  “General Linear Model”  “Multivariate…” • Same as “Univariate…” command, but lets you add 2+ DV’s • Multivariable ANOVA = Either 2+ IV’s or 2+ DV’s • Factorial ANOVA = 2+ IV’s

3. MANOVA • Assumptions • Same as one-way and factorial ANOVA • Independence of Observations • Normality • Use Shapiro-Wilk’s W or z-tests of individual skewness/kurtosis • MANOVA robust to violations of this with larger n’s, unless group sizes are unequal

4. MANOVA • Homoscedasticity • Use Box’s M and Levene’s Test • Box’s M tests for homoscedasticity in all DV’s at one (omnibus test) • MANOVA robust to violations of this unless group sizes are unequal • Correct using appropriate transformation

5. MANOVA • Multivariate Omnibus Tests • Univariate omnibus tests • Difference somewhere between levels of IV, when averaging across them • Multivariate omnibus tests • Difference somewhere between levels of IV on 1+ DV’s, when averaging across both levels and DV’s • Even more vague than univariate omnibus test • Several different tests • Pillai’s Trace most supported in research • Wilks’ λ (lambda) most popular • Do you interpret univariate tests without a significant omnibus test?

6. MANOVA

8. MANOVA • Follow-up inspection of univariate tests with multiple comparison procedures • Just like with “Univariate…” command

9. Analysis of Covariance (ANCOVA) • Same as ANOVA, but allows removal of variance attributable to a covariate • Used frequently if group differences are found on some IV • IV = treatment, Levels = treatment and control groups • Ideally, both groups differ ONLY on presence of treatment • If differ on something else, mean differences may be due to that instead of treatment

10. ANCOVA • IV = treatment, Levels = treatment and control groups • Ideally, both groups differ ONLY on presence of treatment • If differ on something else (i.e. gender ratio), mean differences may be due to that instead of treatment • Use “something else” as covariate to remove the effects of that variable

11. ANCOVA • Use same Analyze  General Linear Model  Univariate… (if only 1 DV) or Multivariate… (if 2+ DV’s) commands • Specify a “Covariate”

14. ANCOVA • Assumptions • Independence of Observations • Normality • Homoscedasticity • Same as (M)ANOVA

15. ANCOVA • Assumptions • Relationship between covariate and DV • Analyze  Correlate  Bivariate • Click covariate(s) and DV(s) into right box

16. ANCOVA • Assumptions • Relationship between covariate and DV • If no significant relationship is found, don’t use covariate • If multiple covariates are used, run 2 separate ANCOVA’s with related covariates and DV’s together • Relationship between IV and covariate is equal across levels of IV • If covariate x IV interaction is significant, than this assumption in violated • If violated, don’t use covariate

17. ANCOVA • Assumptions • Relationship between IV and covariate is linear • Examine best-fit line in scatterplots of DV and covariate within levels of IV

18. Repeated-Measures/Mixed-Model ANOVA • Repeated-Measures/Mixed-Model ANOVA • Click “Analyze”  “General Linear Model”  “Repeated Measures…” • “Within-Subject Factor” = IV for which same participants are included in all levels • I.e. IV = Time, Levels = Time 1, Time 2, etc. • Click “Add”, after all within-subjects factors are added click “Define” • Multivariate tests • Same as MANOVA

19. Repeated-Measures/Mixed-Model ANOVA

20. Repeated-Measures/Mixed-Model ANOVA • Mauchly’s W • Tests for sphericity or multivariate homogeneity of variances assumption • If significant, indicates violations of sphericity • However, very dependent on sample size – With few subjects, fails to detect violations (Type II Error) and with too many subjects detects violations too often (Type I Error)