Deck 12: Glm 1: Comparing Several Independent Means

Question 1

Analyse the cycling time-trial data below. Thirty-two elite cyclists were randomly allocated into one of four groups. Without using SPSS, calculate the mean and total for each group. The groups were as follows
i. Received caffeine and were told it was
ii. Received caffeine and were told it was not
iii. Received no caffeine and were told it was not
iv. Received no caffeine but were told it was
Group 1-
v. Mean: 45.9 km
vi. Total:367 km
Group 2
vii. Mean:39.9 km
Viii. Total:319 km
Group 3
ix. Mean:38.9 km
x. Total:311 km
Group 4
xi. Mean:46.8 km
xii. Total:374 km
How would you calculate the total sum of squares?

A) SST = SSW + SSB
B) SST = SSW - SSB
C) SST = SSB / SSW
D) SST = SSB × SSW

Answer 1

SST = SSW + SSB

Question 2

An ANOVA works on the basis of comparing systematic and systematic variance, but how is this achieved?

A) Systematic variance / unsystematic variance
B) Systematic variance × unsystematic variance
C) Unsystematic variance / systematic variance
D) Unsystematic variance - systematic variance

Answer 2

Systematic variance / unsystematic variance

Question 3

If the value for F-statistic in Q15 were to decrease, what would happen to the p-value?

A) Decrease - become more significant.
B) Increase - become less significant.
C) The p-value is unaffected by the F-statistic
D) The p-value could increase or decrease depending on the between- and within-groups degrees of freedom.

Answer 3

Increase - become less significant.

Question 4

How would you calculate the between sum of squares?

A) SSB = SST - SSW
B) SSB = SST + SSW
C) SSB = SSW / SST
D) SSB = SSW × SST

Question 5

Based on the answers provided in Q7, calculate the between sum of squares for the time-trial data.

A) 392.1
B) 377.7
C) 364.2 d .369.9

Question 6

Based on the information presented in Q15, what can be assumed from the result?

A) There is a significant difference somewhere between the four groups but the location of the differences is not known.
B) There are no significant differences between the four groups.
C) Significant differences are only located between those that received caffeine and those that did not receive caffeine.
D) Significant differences were identified between all of the groups.

Question 7

Using an F-distribution table, locate the critical value required to produce a p-value equal to .05.

A) 2.95
B) 2.71
C) 2.56
D) 2.46

Question 8

What is the correct expression for the one-way ANOVA based on the information presented in the table below?

A) F_{(3, 28)} = 9.83, p < .001
B) F_{(3, 28)} = 9.83, p = .000
C) F_{(3, 28)} = .001, p < 9.83
D) F_{(3, 28)} = .001, p = 9.83

Question 9

Analysis of variance (ANOVA) performs which type of test?

A) F-test
B) t-test
C) z-test
D) xy-test

Question 10

What type of research design does a one-way ANOVA adopt?

A) Independent-groups design
B) Repeated-measures design
C) Within-groups design
D) Mixed model design

Question 11

Examine the Levene's test table. What can be deduced from the finding?

A) The Levene's test is not significant and therefore the null hypothesis is rejected.
B) The Levene's test is not significant and therefore the null hypothesis is accepted.
C) The Levene's test is significant and therefore the null hypothesis is rejected.
D) The Levene's test is significant and therefore the null hypothesis is accepted.

Question 12

Does an ANOVA test identify specifically where the differences exist between the groups?

A) No
B) Yes
C) Yes, provided the data are normally distributed
D) Yes, provided the data are not normally distributed

Question 13

If a one-way ANOVA is considered a parametric test, what is its non-parametric equivalent?

A) Kruskal-Wallis ANOVA
B) Friedman's ANOVA
C) Roy's largest root
D) There is no non-parametric equivalent, therefore multiple Mann-Whitney tests should be used.

Question 14

Suppose you decided to run multiple independent t-tests as opposed to a one-way ANOVA and subsequent contrasts and/or post hoc tests. How should you correct for the p-value?

A) Apply a Bonferroni correction.
B) No adjustment to the p-value is necessary.
C) You should never use multiple t-tests.
D) Conduct a Levene's adjustment.

Question 15

Based on the answers provided in Q7, calculate the within sum of squares for the time-trial data.

A) 372.1
B) 389.7
C) 401.7
D) 456.8

Question 16

What is the purpose of a post hoc test?

A) It identifies where differences between the study groups exist.
B) It identifies the overall appropriateness of the ANOVA model.
C) It identifies differences between and within study groups.
D) It identifies where differences within the study group exist.

Question 17

Based on the answers provided in Q7, calculate the total sum of squares for the time-trial data.

A) 764.2
B) 746.2
C) 801.3
D) 822.6

Question 18

Calculate the η² (eta squared) value based on the sum of squares between groups and the sum of squares within groups.

A) .7
B) .5
C) .3
D) .1

Question 19

For an ANOVA to be used, what is the minimum number of data sets required?

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

Question 20

When would it be appropriate to use the planned comparisons instead of the post hoc tests to identify differences in the time-trial groups?

A) When specific hypotheses have been generated before the experiment.
B) Comparisons should always be run with post hoc tests.
C) Comparisons should be run in place of post hoc tests when no hypothesis has been planned prior to the experiment.
D) Neither post hoc tests or comparisons are really necessary, as they only provide supplementary information.

Question 21

Suppose you decided to run multiple independent t-tests as opposed to a one-way ANOVA and subsequent contrasts and/or post hoc tests. How should you correct for the p-value?

A) Apply a Bonferroni correction.
B) No adjustment to the p-value is necessary.
C) You should never use multiple t-tests.
D) Conduct a Levene's adjustment.

Question 22

Analyse the cycling time-trial data below. Thirty-two elite cyclists were randomly allocated into one of four groups. Without using SPSS, calculate the mean and total for each group. The groups were as follows
i. Received caffeine and were told it was
ii. Received caffeine and were told it was not
iii. Received no caffeine and were told it was not
iv. Received no caffeine but were told it was
Group 1-
v. Mean: 45.9 km
vi. Total:367 km
Group 2
vii. Mean:39.9 km
Viii. Total:319 km
Group 3
ix. Mean:38.9 km
x. Total:311 km
Group 4
xi. Mean:46.8 km
xii. Total:374 km
How would you calculate the total sum of squares?

A) SST = SSW + SSB
B) SST = SSW - SSB
C) SST = SSB / SSW
D) SST = SSB × SSW

Question 23

If the value for F-statistic in Q15 were to decrease, what would happen to the p-value?

A) Decrease - become more significant.
B) Increase - become less significant.
C) The p-value is unaffected by the F-statistic
D) The p-value could increase or decrease depending on the between- and within-groups degrees of freedom.

Question 24

For an ANOVA to be used, what is the minimum number of data sets required?

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

Question 25

An ANOVA works on the basis of comparing systematic and systematic variance, but how is this achieved?

A) Systematic variance / unsystematic variance
B) Systematic variance × unsystematic variance
C) Unsystematic variance / systematic variance
D) Unsystematic variance - systematic variance

Question 26

What type of research design does a one-way ANOVA adopt?

A) Independent-groups design
B) Repeated-measures design
C) Within-groups design
D) Mixed model design

Question 27

Analysis of variance (ANOVA) performs which type of test?

A) F-test
B) t-test
C) z-test
D) xy-test

Question 28

What is the purpose of a post hoc test?

A) It identifies where differences between the study groups exist.
B) It identifies the overall appropriateness of the ANOVA model.
C) It identifies differences between and within study groups.
D) It identifies where differences within the study group exist.

Question 29

Based on the answers provided in Q7, calculate the between sum of squares for the time-trial data.

A) 392.1
B) 377.7
C) 364.2 d .369.9

Question 30

Calculate the η² (eta squared) value based on the sum of squares between groups and the sum of squares within groups.

A) .7
B) .5
C) .3
D) .1

Question 31

Examine the Levene's test table. What can be deduced from the finding?

A) The Levene's test is not significant and therefore the null hypothesis is rejected.
B) The Levene's test is not significant and therefore the null hypothesis is accepted.
C) The Levene's test is significant and therefore the null hypothesis is rejected.
D) The Levene's test is significant and therefore the null hypothesis is accepted.

Question 32

Based on the information presented in Q15, what can be assumed from the result?

A) There is a significant difference somewhere between the four groups but the location of the differences is not known.
B) There are no significant differences between the four groups.
C) Significant differences are only located between those that received caffeine and those that did not receive caffeine.
D) Significant differences were identified between all of the groups.

Question 33

How would you calculate the between sum of squares?

A) SSB = SST - SSW
B) SSB = SST + SSW
C) SSB = SSW / SST
D) SSB = SSW × SST

Question 34

When would it be appropriate to use the planned comparisons instead of the post hoc tests to identify differences in the time-trial groups?

A) When specific hypotheses have been generated before the experiment.
B) Comparisons should always be run with post hoc tests.
C) Comparisons should be run in place of post hoc tests when no hypothesis has been planned prior to the experiment.
D) Neither post hoc tests or comparisons are really necessary, as they only provide supplementary information.

Question 35

If a one-way ANOVA is considered a parametric test, what is its non-parametric equivalent?

A) Kruskal-Wallis ANOVA
B) Friedman's ANOVA
C) Roy's largest root
D) There is no non-parametric equivalent, therefore multiple Mann-Whitney tests should be used.

Question 36

Based on the answers provided in Q7, calculate the within sum of squares for the time-trial data.

A) 372.1
B) 389.7
C) 401.7
D) 456.8

Question 37

Using an F-distribution table, locate the critical value required to produce a p-value equal to .05.

A) 2.95
B) 2.71
C) 2.56
D) 2.46

Question 38

Based on the answers provided in Q7, calculate the total sum of squares for the time-trial data.

A) 764.2
B) 746.2
C) 801.3
D) 822.6

Question 39

Does an ANOVA test identify specifically where the differences exist between the groups?

A) No
B) Yes
C) Yes, provided the data are normally distributed
D) Yes, provided the data are not normally distributed

Question 40

What is the correct expression for the one-way ANOVA based on the information presented in the table below?

A) F_{(3, 28)} = 9.83, p < .001
B) F_{(3, 28)} = 9.83, p = .000
C) F_{(3, 28)} = .001, p < 9.83
D) F_{(3, 28)} = .001, p = 9.83

Question 41

How would you describe this effect?

A) Large effect
B) Medium effect
C) Small effect
D) Very small effect