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Analysis of Variance
Discriminant Analysis
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Multivariate Analysis
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Performance of the RoyBargmann Stepdown Procedure as a Follow Up to a Significant MANOVA
Performance of the RoyBargmann Stepdown Procedure as a Follow Up to a Significant MANOVA,W. Holmes Finch
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Performance of the RoyBargmann Stepdown Procedure as a Follow Up to a Significant MANOVA
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Citations: 1
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W. Holmes Finch
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 experimentwise
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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Citation Context
(1)
...However, because of the high correlation between the two emotional factors, a Roy– Bargmann stepdown analysis was used (
Finch, 2007 ;
R oy & Bargmann, 1958 ;T abachnick &F idell,2007)...
Steve Guest
,
et al.
The development and validation of sensory and emotional scales of touc...
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The Annals of Mathematical Statistics
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Journal:
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Applied multivariate statistics for the social sciences
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J. Stevens
Published in 1996.
Comparison of the Usefulness of WithinGroup and Total Group Structure Coefficients for Identifying Variable Importance in Descriptive Discriminant Analysis Following a Significant MANOVA: Examination of the TwoGroup Case
(
Citations: 2
)
Mercedes K. Schneider
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Citations
(1)
The development and validation of sensory and emotional scales of touch perception
Steve Guest
,
Jean Marc Dessirier
,
Anahit Mehrabyan
,
Francis McGlone
,
Greg Essick
,
George Gescheider
,
Anne Fontana
,
Rui Xiong
,
Rochelle Ackerley
,
Kevin Blot
Journal:
Attention Perception & Psychophysics  ATTEN PERCEPT PSYCHOPHYS
, vol. 73, no. 2, pp. 531550, 2011