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
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)