Repeated MeasuresMixed Model ANOVA SPSS Lab 4 MANOVA

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

MANOVA p Multivariate ANOVA (MANOVA) n Both 2+ IV’s and 2+ DV’s p n Click “Analyze” “General Linear Model” “Multivariate…” p n n SPSS won’t run with only 1 DV 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 p Assumptions n n n Same as one-way and factorial ANOVA Independence of Observations Normality Use Shapiro-Wilk’s W or z-tests of individual skewness/kurtosis p MANOVA robust to violations of this with larger n’s, unless group sizes are unequal p

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

MANOVA p Multivariate Omnibus Tests n Univariate omnibus tests p n 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 p Even more vague than univariate omnibus test p Several different tests p § Pillai’s Trace most supported in research § Wilks’ λ (lambda) most popular p Do you interpret univariate tests without a significant omnibus test?

MANOVA

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

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

ANCOVA n n 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 p Use “something else” as covariate to remove the effects of that variable p

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

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

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

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

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

Repeated-Measures/Mixed-Model ANOVA p Repeated-Measures/Mixed-Model ANOVA n n 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. p Click “Add”, after all within-subjects factors are added click “Define” p n Multivariate tests p Same as MANOVA

Repeated-Measures/Mixed-Model ANOVA

Repeated-Measures/Mixed-Model ANOVA p Mauchly’s W n n Tests for sphericity or multivariate homogeneity of variances assumption If significant, indicates violations of sphericity p 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)