Deck 17: Multivariate Analysis of Variance Manova

Question 1

Which of the following characteristics are associated with a MANOVA? (You may select more than one option.)

A) Two or more dependent variables
B) One or more independent variables
C) One dependent variable
D) Discriminant analysis is used as the follow-up test.

Answer 1

A, B AND D

Question 2

Which of the following descriptions best reflects the results from the MANOVA?

A) The significance values are all the same so any of the test statistics could be used.
B) Use Hotelling's trace as it accounts for a significant Box test result.
C) Use Roy's largest root as it is the most powerful test.
D) Use Wilks's lambda as it is the most conservative test.

Answer 2

B

Question 3

Based on the results presented in Q18, what would be the most appropriate test statistic to use?

A) Pillai-Bartlett trace
B) Hotelling's T²
C) Wilks's lambda
D) Roy's largest root

Answer 3

B

Question 4

Which of the following is the most appropriate explanation of the total cross-product (CP_R)?

A) An evaluation of the collective relationship between the two dependent variables
B) The influence of the experimental manipulation on the relationship between the dependent variables
C) The degree of influence individual differences in participant performance have on the relationship between the dependent variables
D) The level of influence group means have on the relationship between the dependent variables

Question 5

Cross-product calculations are used to perform the MANOVA analysis, but what is the ANOVA equivalent?

A) Sum of squares
B) Levene's test
C) Crosstabulation
D) Root mean squared

Question 6

Which of the following is not an assumption of MANOVA?

A) Observations should be statistically independent
B) Random sampling from a given population
C) Measured at an ordinal level
D) Homogeneity of covariate matrices

Question 7

What factors are most likely to strengthen the power of a MANOVA? (You may select more than one option.)

A) Effect size is large
B) One outcome variable that exhibits a large group difference whilst a second has a small or no group difference
C) High correlation between dependent variables
D) All of the above

Question 8

Which of the following is the most appropriate explanation of the total cross-product (CP_M)?

A) An evaluation of the collective relationship between the two dependent variables
B) The influence of the experimental manipulation on the relationship between the dependent variables
C) The degree of influence individual differences in participant performance have on the relationship between the dependent variables
D) The level of influence group means have on the relationship between the dependent variables

Question 9

Why might you wish to avoid using multiple ANOVAs to examine different outcome variables? (You may select more than one option.)

A) Increased likelihood of making Type I error
B) Increased likelihood of making Type II error
C) Relationship between the outcome variables is ignored
D) Groups that differ along only one dimension

Question 10

If multiple ANOVAs are used to follow up on a significant MANOVA result, what should be applied to the calculation to protect against Type I error?

A) Bonferroni adjustment
B) Tukey post hoc test
C) Shapiro-Wilk test
D) B and C

Question 11

How many levels are there to the independent variable?

A) 1
B) 2
C) 3
D) 4

Question 12

Examine the data below on state and trait sport confidence inventory (Vealey, 1986). How many dependent variables are being measured?

A) 2
B) 3
C) 4
D) 5

Question 13

How many independent variables are there?

A) 1
B) 2
C) 3
D) 4

Question 14

Because a MANOVA works on the basis of using several values to assess statistical significance it achieves this by converting dependent variables (e.g. trait and state anxiety) into underlying dimensions (i.e. discriminant function). What are the linear combinations of the dependent variables known as? (You may select more than one option.)

A) Variates
B) Factors
C) Eigenvectors
D) Vectors

Question 15

What can be ascertained from the following Box test results?

A) A significant result which suggests that the assumption of homogeneity has been violated.
B) A significant result which suggests that the assumption of homogeneity has not been violated.
C) A non-significant result which suggests that the assumption of homogeneity has been violated.
D) A non-significant result which suggests that the assumption of homogeneity has not been violated.

Question 16

What does the result from Q20 tell us?

A) An athlete's level of competition has a significant effect on state and trait anxiety.
B) The elite athletes differed from the sub-elite athletes on trait anxiety.
C) The elite athletes differed from the county athletes on state anxiety.
D) The sub-elite athletes differed from the sub-elite athletes on trait and state anxiety.

Question 17

Analyse the anxiety data in elite, sub-elite and county kayakers (see Q5). Calculate the CP_M based on the data provided below.

A) -696.13
B) +696.13
C) -347.13
D) 347.13

Question 18

Which of the following is the most appropriate explanation of the total cross-product (CP_T)?

A) An evaluation of the collective relationship between the two dependent variables
B) The influence of the experimental manipulation on the relationship between the dependent variables
C) The degree of influence individual differences in participant performance have on the relationship between the dependent variables
D) The level of influence group means have on the relationship between the dependent variables

Question 19

If test assumptions are violated, which non-parametric test should be performed?

A) None of the tests are appropriate
B) Friedman's test
C) McNemur's test
D) Mann-Whitney test

Question 20

Calculate the CP_R value based on the value above and assuming that the CP_T value equals 1630.27.

A) 2326.4
B) 934.14
C) 1283.13
D) 1977.41

Question 21

Analyse the data using a MANOVA and a simple contrast. What was the corresponding significance value between elite and sub-elite athletes?

A) p = .044
B) p = .006
C) p = .424
D) p = .473

Question 22

Having obtained a significant result from a MANOVA, how would the data be examined further?

A) Multiple one-way ANOVA
B) Multiple correlations
C) Serial chi-square tests
D) Serial Kolmogorov-Smirnov tests

Question 23

Examine the following table. Which of the following statements best describes the data presented?

A) State anxiety differed significantly between levels of competition, but trait anxiety did not.
B) Trait anxiety differed significantly between levels of competition, but state anxiety did not.
C) Both state and trait anxiety differed significantly between levels of competition.
D) Neither state and trait anxiety differed significantly between levels of competition.

Question 24

Why might you wish to run a discrimant analysis as opposed to an ANOVA following a MANOVA?

A) It allows the investigator to examine the nature of the relationship between two variables.
B) To reinforce the findings of the ANOVA.
C) It permits the investigator to check the distribution of the data and relate it to the dependent variables.
D) A discriminant analysis should be used in its own right and not used to supplement a MANOVA.

Question 25

Run a discriminant analysis on the data. How much variance is accounted for by the first dependent variable?

A) 100%
B) 75%
C) 50%
D) 25%