A researcher assigns 33 subjects to 3 groups receiving dietary information via different modes: an online website, a nurse practitioner, or a video. The researcher measures 3 dependent variables related to the presentation: difficulty, usefulness, and importance. MANOVA is an appropriate analysis to determine if the modes of presentation have a significant effect on a combination of the dependent variables, while accounting for correlations between them. The researcher can use MANOVA to test whether the interactive website is superior to the other modes in conveying the information in a comprehensive yet cost-effective manner.
2. Multivariate analysis When there is more than one dependent variable, it is inappropriate to do a series of univariate tests. Multivariate analysis of variance (MANOVA) is an extension of analysis of variance, used with two or more dependent variables
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4. An extension of univariate ANOVA procedures to situations in which there are two or more related dependent variables (ANOVA analyses only a single DV at a time)
9. MANOVA works well in situations where there are moderate correlations between DVs. For very high or very low correlation in DVs, it is not suitable: if DVs are too correlated, there isn’t enough variance left over after the first DV is fit, and if DVs are uncorrelated, the multivariate test will lack power
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11. Anova vs. Manova Consider the following 2 group and 3 group scenarios, regarding two DVs Y1 and Y2 If we just look at the marginal distributions of the groups on each separate DV, the overlap suggests a statistically significant difference would be hard to come by for either DV However, considering the joint distributions of scores on Y1 and Y2 together (ellipses), we may see differences otherwise undetectable
12. Anova vs. Manova Now we can look for the greatest possible effect along some linear combination of Y1 and Y2 The linear combination of the DVs created makes the differences among group means on this new dimension look as large as possible
13. Anova vs. Manova So, by measuring multiple DVs you increase your chances for finding a group difference In this sense, in many cases such a test has more power than the univariate procedure, but this is not necessarily true as some seem to believe Also conducting multiple ANOVAs increases the chance for type 1 error and MANOVA can in some cases help control for the inflation
31. The F test from Box’s M statistics should be interpreted cautiously because it is a highly sensitive test of the violation of the multivariate normality assumption, particularly with large sample sizes.
53. Pillai’s criterion is considered more robust and should be used if sample size decreases, unequal cell sizes appear or homogeneity of covariances is violated
54. Roy’s gcris a more powerful test statistic if the researcher is confident that all assumptions are strictly met and the dependent measures are representative of a single dimension of effects
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56. It has the power of convergence (no single operationally defined dependent variable is likely to capture perfectly the conceptual variable of interest)
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58. It reduces error rate compared with performing a series of univariate tests