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

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Presentation on theme: "Repeated Measures/Mixed- Model ANOVA: SPSS Lab #4."— Presentation transcript:

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

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8  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”

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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  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)

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