# Repeated Measures/Mixed-Model ANOVA:

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

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

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

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

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?

MANOVA

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

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

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

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

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

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

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

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

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

Repeated-Measures/Mixed-Model ANOVA

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)