Deck 6: Multivariate Analysis of Variance and Covariance

Question 1

Multivariate analysis of variance (MANOVA) is designed to test the significance of group differences with several dependent variables.

Answer 1

True

Question 2

At a minimum, the DVs should have some degree of linearity and share a common conceptual meaning.

Answer 2

True

Question 3

Using more than one DV when comparing treatments or groups based on differing characteristics is good because any worthwhile treatment or substantial characteristic will always affect participants in more than one way.

Answer 3

False

Question 4

MANOVA tests whether mean differences among k groups on a combination of DVs are unlikely to have occurred by chance.

Question 5

The new DV formed in MANOVA is, in fact, a nonlinear combination of the original measured DVs, combined in such a way as to maximize the group differences.

Question 6

The new DV formed in MANOVA is created by developing a linear equation where each measured DV has an associated weight and, when combined and summed, creates maximum separation of group means with respect to the new DV.

Question 7

A factorial MANOVA is a design that involves multiple IVs as well as multiple DVs.

Question 8

One advantage of using MANOVA, as opposed to doing a couple of ANOVAs, is the slight improvement in the chances of discovering what actually changes as a result of the differing treatments or characteristics.

Question 9

A second advantage of using MANOVA is that it consistently reveals differences not shown in separate ANOVAs.

Question 10

A third advantage of using MANOVA is that the overall Type I error rate is increased.

Question 11

MANOVA incorporates the interconnections of DVs into the analysis.

Question 12

The results of MANOVA are sometimes ambiguous with respect to the effects of the IVs on individual DVs.

Question 13

The calculations for MANOVA are based on scalar algebra.

Question 14

The most commonly used test statistic for MANOVA is Roy's Largest Root.

Question 15

Wilks' Lambda (Ʌ) is an inverse criterion, which means that the smaller the value of Ʌ, the less evidence for treatment effects or group differences.

Question 16

In conducting a MANOVA, one first tests the overall multivariate hypothesis.

Question 17

If the null hypothesis is retained, it is common practice to stop the interpretation of the analysis at this point and conclude that the treatments or conditions have no effect on the DVs.

Question 18

One of the assumptions of MANOVA is that the observations within each sample must be randomly sampled and must be dependent on each other.

Question 19

A second MANOVA assumption is that the observations on at least one DV must follow a multivariate normal distribution in the group.

Question 20

A third MANOVA assumption is that the relationships among all pairs of DVs for each cell in the data matrix must be normal.

Question 21

Multivariate Analysis of Covariance (MANCOVA) is essentially a combination of MANOVA and ANCOVA.

Question 22

MANCOVA asks if there are statistically significant mean differences among groups after adjusting the newly created DV for differences on one or more covariates.

Question 23

In MANCOVA, the effects of the covariates are added to the analysis, leaving the researcher with a clearer picture of the true effects of the IVs on the multiple DVs.

Question 24

The null hypothesis being tested in MANCOVA is that the adjusted population mean vectors are not equal.

Question 25

An assumption in MANCOVA is that linear relationships need not exist between all pairs of DVs, all pairs of covariates, and all DV-covariates in each cell.

Question 26

Initial assessments of normality with MANCOVA is done through the inspection of:

A) Histograms.
B) Boxplots.
C) Normal Q-Q plots.
D) All of the above.

Question 27

A violation of the assumption of homogeneity of regression slopes (as well as regression planes and hyperplanes) in MANCOVA is an indication that:

A) There is a covariate by treatment (IV) interaction.
B) There is a covariate by DV interaction.
C) Neither (a) nor (b) is correct.
D) Both (a) and (b) are correct.

Question 28

Examining group means (before and after covariate adjustment) for each DV in MANCOVA can assist in determining how groups differed for each DV because:

A) MANCOVA provides post hoc analyses.
B) MANCOVA does not provide post hoc analyses.
C) MANCOVA provides post hoc analyses when there is only one covariate.
D) MANCOVA provides post hoc analyses when there is only one factor.

Question 29

In summary, the first step in interpreting the MANCOVA results is to evaluate the preliminary MANCOVA results that include:

A) Box's test.
B) Test for homogeneity of regression slopes.
C) Box's test and the test for homogeneity of regression slopes.
D) F ratio.

Question 30

If Box's test is not significant when interpreting MANCOVA, which of the following test statistics should be used when interpreting the homogeneity of regression slopes and the subsequent multivariate tests?

A) Wilks' Lambda.
B) Pillai's Trace.
C) Hotelling's Trace.
D) All of the above.