Statistics for the Behavioral Sciences MANOVA Introduction Multivariate

Statistics for the Behavioral Sciences MANOVA Introduction Multivariate Analysis of Variance HDFS 7060 - Bubb, R. 1

MANOVA • Used to analyze 2 or more dependent variables • Extension of ANOVA • Omnibus test – all dependent variables simultaneously • Could do multiple ANOVA tests… • Inflates alpha (Type I error rate) • Bonferroni correction too conservative with more independent variables, levels, and dependent variables • Does not account for the relationship between DV’s HDFS 7060 - Bubb, R. 2

MANOVA • Assumptions are similar to between group ANOVA • DV’s assumed to be continuous (like ANOVA) • ANOVA assumes no measurement error for manifest variables • MANOVA assume measurement error for latent constructs HDFS 7060 - Bubb, R. 3

MANOVA • Multivariate tests • Pillai’s Trace • Most robust to violations of assumptions • Wilk’s Lambda and Hotelling’s Trace • Converge with larger sample sizes • Subject to assumption violations, but more Power when DV’s are uncorrelated • Roy’s Largest Root • Most Power when DV’s are correlated • But more Type I errors HDFS 7060 - Bubb, R. 4

MANOVA • If reject the null hypothesis with multivariate test: • At least one difference among the group means among the dependent variables • … but do not know which groups or DV’s • Typically, separate ANOVAs are calculated with post-hoc tests for groups • However, does not account for the relationship between DV’s • Descriptive discriminant analysis for DV relationship • However, does not compare group means, only variation • Conduct a one-way ANOVA on the discriminant scores • Use both HDFS 7060 - Bubb, R. 5