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MANOVA

# MANOVA - Statistics 101A Professor Esfandiari An example on...

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Statistics 101A Professor Esfandiari An example on multivariate of analysis of variance (MANOVA) I Overall comments about MANPOVA and how it differs fromANOVA Definition of MANOVA Technique used for assessing group differences across multiple metric dependent variables simultaneously, based on a set of categorical (non-metric) variables acting as independent variables Analysis of Variance (ANOVA): statistical technique used to determine whether samples from 2 or more groups come from populations with equal means. ANOVA employs one dependent measure, whereas MANOVA compares samples based on two or more dependent variables. Research considerations: An adequate sample must be used. Note that MANOVA requires greater sample sizes than ANOVA , overall and by group. The sample size must exceed certain thresholds in each cell. Recommended cell minimum is 20 observations in all cases and/or the number of samples in each cell should exceed the number of DV's. In some cases, treatments can be added after the initial data capture (post hoc). An example would be introducing a variable for gender, used as a blocking factor to increase homogeneity within your samples. ANOVA * Dependent Variable is normally distributed * Variances are equal for all treatment groups MANOVA * Independent observations * Variance/covariance matrices must be equal * Multivariate normal distribution

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Three steps to evaluate MANOVA results: * Evaluate covariates and interpret what effect they may have had * Assess the dependent variate and determine which dependent variables exhibited differences across groups * Identify which groups differ on a variable or on the entire variate. There are a variety of post hoc tests available to help with this step (Scheffe method, Tukey's HSD, Tukey's extension of LSD, Duncan's, etc.) or the researcher can make a priori or planned comparisons. Introduction Multivariate analysis of variance (MANOVA) is simply an ANOVA with several dependent variables. For example, we may conduct a study where we try two different textbooks, and we are interested in the students' improvements in math and physics. In that case, improvements in math and physics are the two dependent variables, and our hypothesis is that both together are affected by the difference in textbooks. A multivariate analysis of variance (MANOVA) could be used to test this hypothesis. Instead of a univariate F value, we would obtain a multivariate F value (Wilks' ) based on a comparison of the error variance/covariance matrix and the effect variance/covariance matrix. Although we only mention Wilks' here, there are other statistics that may be used, including Hotelling's trace and Pillai's criterion. The "covariance" here is included because the two measures are probably correlated and we must take this correlation into account when performing the significance test. Testing the multiple dependent variables is accomplished by creating new
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MANOVA - Statistics 101A Professor Esfandiari An example on...

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