2 MANOVA Multivariate ANOVA (MANOVA) Both 2+ IV’s and 2+ DV’s SPSS won’t run with only 1 DVClick “Analyze” “General Linear Model” “Multivariate…”Same as “Univariate…” command, but lets you add 2+ DV’sMultivariable ANOVA = Either 2+ IV’s or 2+ DV’sFactorial ANOVA = 2+ IV’s
3 MANOVA Assumptions Same as one-way and factorial ANOVA Independence of ObservationsNormalityUse Shapiro-Wilk’s W or z-tests of individual skewness/kurtosisMANOVA 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 unequalCorrect using appropriate transformation
5 MANOVA Multivariate Omnibus Tests Univariate omnibus tests Difference somewhere between levels of IV, when averaging across themMultivariate omnibus testsDifference somewhere between levels of IV on 1+ DV’s, when averaging across both levels and DV’sEven more vague than univariate omnibus testSeveral different testsPillai’s Trace most supported in researchWilks’ λ (lambda) most popularDo you interpret univariate tests without a significant omnibus test?
8 MANOVAFollow-up inspection of univariate tests with multiple comparison proceduresJust like with “Univariate…” command
9 Analysis of Covariance (ANCOVA) Same as ANOVA, but allows removal of variance attributable to a covariateUsed frequently if group differences are found on some IVIV = treatment, Levels = treatment and control groupsIdeally, both groups differ ONLY on presence of treatmentIf 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 treatmentIf differ on something else (i.e. gender ratio), mean differences may be due to that instead of treatmentUse “something else” as covariate to remove the effects of that variable
11 ANCOVAUse same Analyze General Linear Model Univariate… (if only 1 DV) or Multivariate… (if 2+ DV’s) commandsSpecify a “Covariate”
14 ANCOVA Assumptions Independence of Observations Normality HomoscedasticitySame as (M)ANOVA
15 ANCOVA Assumptions Relationship between covariate and DV Analyze Correlate BivariateClick 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 covariateIf multiple covariates are used, run 2 separate ANCOVA’s with related covariates and DV’s togetherRelationship between IV and covariate is equal across levels of IVIf covariate x IV interaction is significant, than this assumption in violatedIf 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 levelsI.e. IV = Time, Levels = Time 1, Time 2, etc.Click “Add”, after all within-subjects factors are added click “Define”Multivariate testsSame as MANOVA
20 Repeated-Measures/Mixed-Model ANOVA Mauchly’s WTests for sphericity or multivariate homogeneity of variances assumptionIf significant, indicates violations of sphericityHowever, 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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