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Performance of the Roy-Bargmann Stepdown Procedure as a Follow Up to a Significant MANOVA

Performance of the Roy-Bargmann Stepdown Procedure as a Follow Up to a Significant MANOVA,W. Holmes Finch

Performance of the Roy-Bargmann Stepdown Procedure as a Follow Up to a Significant MANOVA   (Citations: 1)
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ultivariate Analysis of Variance (MANOVA) is a popular tool used by social science researchers and others, allowing for the analysis of multiple dependent variables with one or more independent factors. The null hypothesis being tested by MANOVA is µ1 = µ2 = µ3 where µk is the vector of means for group k. When this hypothesis is rejected due to a significant test statistic, researchers may be interested in to which groups or dependent variable(s) the result applies. Given that rejection of the very general null hypothesis of the MANOVA indicates that there is some difference among the k groups on one or more of the p dependent variables. In order to gain a more complete understanding of the nature of such a significant effect, a researcher may want to use a follow up analysis designed to illuminate the significant result in terms of group differences on the response variables (Tabachnick & Fidell, 2007; Stevens, 1996). A number of such approaches have been discussed in the literature, including the Simultaneous Test Procedure (STP) (Gabriel, 1968), Descriptive Discriminant Analysis (DDA) (Huberty, 1994), a Step Down procedure (SD) (Roy, 1958), two groups multivariate comparisons (Stevens, 1972) and the use of univariate Analysis of Variance (ANOVA). It should be noted that with the exception of the latter approach, all of these methods retain the general multivariate flavor of the original analysis, albeit in very different ways. Indeed, several authors (e.g. Stevens, 1996) argue that whatever follow up to MANOVA is finally used, it needs to be based upon a multivariate platform. Nonetheless, most researchers who make use of MANOVA will have specific questions regarding the nature, in terms of both the response variables and the groups, of the significant differences signaled by the multivariate analysis. This study was designed to examine the performance of one of these follow up methods that may be effective in characterizing a significant MANOVA result. Analysis of Variance (ANOVA) Perhaps the most straightforward approach to investigating a significant MANOVA result is through the application of individual univariate ANOVA analyses for each of the dependent variables separately. This approach is facilitated by common statistical software packages such as SAS and SPSS, which print the univariate results with the multivariate. Despite this ease of use, the use of univariate ANOVA in this way has generally been rejected as a viable alternative for following up a significant MANOVA result because, as Enders (2003) points out, the univariate ANOVA does not accurately maintain the nominal Type I error rate in most cases (generally being too conservative), even when a correction such as Bonferroni or Holm is used. Indeed, Maxwell (1992) found that using such alpha corrections with univariate ANOVA to maintain the nominal experiment-wise Type I error rate only works when either the MANOVA null hypothesis is totally false, the MANOVA null hypothesis is totally true or the MANOVA null hypothesis is false for all but one of the dependent variables. In all other cases, using ANOVA to investigate a significant MANOVA will yield an incorrect Type I error rate. Keselman, Huberty, Lix, et al
Published in 2007.
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