MANOVA Problem Set

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College of Doctoral Studies

RES-845: Module 8 Problem Set Solutions

Factorial (2 x 3) MANOVA

1.	Is there a sufficient correlation between the dependent variables to justify the use of MANOVA? YES! THE DEPENDENT VARIABLES ARE BOTH CONCEPTUALLY AND STATISTICALLY (r = .513) RELATED.
2.	Was the assumption of Equality of Covariance Matrices violated? Explain. NO! RESULT OF THE BOX'S TEST OF EQUALITY OF COVARIANCE MATRICES INDICATED NO VIOLATION (p = .463).
3.	Is there a statistically significant multivariate interaction effect? YES! Identify the dependent variable(s) of this interaction effect. EMOTION ONLY
4.	What would be the proper follow-up tests for a statistically significant interaction effect? CONDUCT TWO SEPARATE ONE-WAY ANOVAs WITH TREATMENT AS THE INDEPENDENT VARIABLE FOR MALES AND FEMALES. IF THE ONE-WAY ANOVAs REPORT A STATISTICALLY SIGNIFICANT OMNIBUS, THEN PERFORM THE APPROPRIATE POST-HOC.
5.	Identify the proper post hoc analyses for any statistically significant univariate effects. Explain your answer. THE LSD IS ONE OF THE PROPER POST-HOCS BECAUSE THE EQUAL VARIANCES ASSUMPTION IS NOT VIOLATED.
6.	Is there a statistically significant multivariate gender effect on the dependent variate? YES! BUT BECAUSE THERE IS AN INTERACTION EFFECT, THIS MAIN EFFECT IS OF LITTLE INTEREST.
7.	Why would a researcher conduct a MANOVA instead of several ANOVAs? THERE ARE AT LEAST TWO REASONS TO CONDUCT A MANOVA INSTEAD OF A SERIES OF ANOVAs. (1) MANOVA IS A MORE POWERFUL STATISTICAL TECHNIQUE (I.E., IT IS BETTER ABLE TO DETECT DIFFERENCES IF THEY REALLY EXIST), (2) MANOVA CONTROLS FOR AN INFLATED TYPE I ERROR.
8.	Write a Results section for this research.

Correlations

General Linear Model

Box's Test of Equality of Covariance Matricesa

Multivariate Tests c

Levene's Test of Equality of Error Variances a