Deck 6: Multivariate Analysis of Variance: Single Factor, Factorial, and Repeated Measures Designs

Question 1

A researcher wants to determine the mean difference in a composite outcome consisting of three continuous subscales based on a categorical independent variable. Which one of the following is an appropriate statistical procedure for doing this?

A) one-way MANOVA
B) two-way MANOVA
C) three-way MANOVA
D) repeated measures MANOVA

Answer 1

A
Explanation: There are three continuous dependent outcomes and one categorical independent variable, thus appropriate for a one-way MANOVA.

Question 2

A researcher conducts a 3 (factor A) x 4 (factor B) MANOVA with two dependent variables. The p value for Roy's largest root is .14 for factor A, .05 for factor B, and .22 for AxB, and the significance level is .10. Which one of the following is suggested?

A) Nonstatistically significant main effect for factor A. Statistically significant main effect for factor B and interaction effect
B) Nonstatistically significant main effect for factor A and the and interaction effect. Statistically significant main effect for factor B
C) The assumption of equal variance-covariances has been met
D) The assumption of equal variance-covariances has not been met

Answer 2

B
Explanation: Only factor B is statistically significant (p = .05) at alpha of .10

Question 3

Partial eta squared for a statistically significant main effect is .02 and the alpha level is .05. Which of the following is a correct interpretation of this value?

A) The results are statistically significant
B) The results are not statistically significant
C) There is a large effect
D) There is a small effect

Answer 3

D
Explanation: Per Cohen's (1988) interpretations, partial eta squared of .02 is generally considered a small effect.

Question 4

The omnibus test of multivariate normality has an observed probability of .15. The significance level is .01. What can be interpreted from this?

A) The assumption of linearity has been met
B) The assumption of multivariate normality is reasonable
C) The results are statistically significant
D) There is evidence of a violation of multivariate skew

Question 5

Scores on balance beam, uneven bars, and floor exercises are tracked in years 1 and 2 for competitive gymnasts. For which procedure is this data most likely a prospect?

A) one-way MANOVA
B) two-way MANOVA
C) three-way MANOVA
D) repeated measures MANOVA

Question 6

Which one of the following is NOT an omnibus test for MANOVA when approached as a doubly multivariate model?

A) Hotelling's trace
B) Mauchly's test
C) Pillai's trace
D) Roy's largest root

Question 7

Which one of the following omnibus test for MANOVA should be used under ideal conditions?

A) Hotelling's trace
B) Mauchly's test
C) Pillai's trace
D) Roy's largest root

Question 8

Wilks's generalized correlation ratio is which one of the following?

A) evidence of linearity
B) indicator for multivariate normality
C) measure of effect size
D) omnibus test for model fit

Question 9

In generating repeated measures MANOVA, you have alpha of .10 and Box's test p value of .01. What can be interpreted by this finding?

A) linearity can be assumed
B) the assumption of equal-variance covariance has not been met
C) the overall model is statistically significant
D) there is a very small effect

Question 10

A researcher conducting a doubly multivariate repeated measures MANOVA would NOT need to be considered with which one of the following assumptions?

A) balanced design
B) linearity
C) homogeneity of variance/covariance
D) multivariate normality of the dependent variables