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at the multivariate test results, all the four multivariate tests reveal significant results and hence it is okay to conclude that group membership effects on the psychological aspects evaluated, even after the test effects of item difficulties are controlled on performance of people in the three areas.
Statistics for univariate comparisons of means are designs with only one dependent variable (DV). By comparison, statistics for multivariate comparisons of means have more than one dependent variable. The MANOVA may be either one-way (one IV) or factorial (more than one IV).
For these analyses, there is more than one DV. The different DVs, which are at least moderately correlated, are combined into a composite variable called a variate. The combined DVs serve to predict the between-group differences of the scores for the conditions of the IV.
A challenge arises in a research design that features only one IV with only 2 conditions. If a researcher desires to analyze two or more moderately correlated DVs rather than using a t-test with one DV, the multivariate Hotellings T2 can be used instead of separate t-tests for this situation. Instead of the null hypothesis for a t-test (M1 = M2), the null hypothesis for the Hotellings T2 is that the vectors of means for group A are the same as the vectors of means for group B. The value of Hotellings T2 can be transformed into four F-values: Wilks lambda, Pillais trace, Hotellings trace, and Roys largest root. When these F-values are significant at the alpha level determioned for the study (e.g., = .05), the researcher can reject the null hypothesis.
Usually the finding of significant multivariate effects is followed by analyses where the relationship between the IV(s) and each of the DVs is analyzed separately, using a univariate method to compare means (e.g., a t-test, a one-way ANOVA, a factorial ANOVA). Because there are multiple tests for multiple DVs, every test distorts the actual alpha level. That is, the
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(“SPSS for analyzing data with one IV and more than one DV & one-way Essay”, n.d.)
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(SPSS for Analyzing Data With One IV and More Than One DV & One-Way Essay)
“SPSS for Analyzing Data With One IV and More Than One DV & One-Way Essay”, n.d. https://studentshare.org/statistics/1615262-spss-for-analyzing-data-with-one-iv-and-more-than-one-dv-one-way-between-subjects-manova.
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