Deck 12: Multiple Comparison Procedures

Question 1

How many possible pairwise contrasts are there if J = 5?

A) 5
B) 10
C) 15
D) 20

Answer 1

B

Question 2

Which of the following linear combinations of population means is a legitimate contrast?

A) $\mu$ ₁- $\mu$ ₂/2+ $\mu$ ₃/2
B) ( $\mu$ ₁+ $\mu$ ₂)/2+ $\mu$ ₃
C) $\mu$ ₁+ $\mu$ ₂)/2- $\mu$ ₃
D) $\mu$ ₁- $\mu$ ₂- $\mu$ ₃

Answer 2

$\mu$ ₁+ $\mu$ ₂)/2- $\mu$ ₃

Question 3

If J = 3, which of the following sets of contrasts is orthogonal?

A) $\mu$ ₁- $\mu$ ₂, $\mu$ ₁- $\mu$ ₃
B) $\mu$ ₂+ $\mu$ ₃, $\mu$ ₂- $\mu$ ₃
C) $\mu$ ₁- $\mu$ ₃, $\mu$ ₁( $\mu$ ₂+ $\mu$ ₃)/2
D) $\mu$ ₁- $\mu$ ₃, $\mu$ ₂-( $\mu$ ₁+ $\mu$ ₃)/2

Answer 3

$\mu$ ₁- $\mu$ ₃, $\mu$ ₂-( $\mu$ ₁+ $\mu$ ₃)/2

Question 4

When a one-factor fixed-effects ANOVA results in a nonsignificant F ratio for J = 4, one should follow-up the ANOVA with which one of the following post-hoc procedures?

A) Scheffe' method
B) Tukey HSD method
C) Fisher LSD method
D) None of the above

Question 5

Applying the Dunn procedure, the per contrast alpha is calculated to be 0.01 for five contrasts. What is the nominal family-wise error rate?

A) .002
B) .005
C) .01
D) .05

Question 6

For any pairwise MCP, holding the number of groups and df_with constant, as the $\alpha$ level increases, the critical value will

A) increase.
B) decrease.
C) not change.
D) increase or decrease depending on which MCP is used.

Question 7

Which of the following statements about post hoc tests is true?

A) We should always do post hoc tests following an omnibus ANOVA F test.
B) We should always do post hoc tests following a significant ANOVA F test.
C) With post hoc comparisons, we can only conduct pairwise tests.
D) We should always do post hoc tests following a significant ANOVA F test and
When J > 2.

Question 8

Which of the following statements about trend analysis is true?

A) The independent variable should not be on the nominal scale.
B) If the factor has 3 levels, we can test the linear trend, the quadratic trend, and the
Cubic trend.
C) The set of contrasts are not necessarily orthogonal.
D) If there is a significant linear trend, there cannot be a significant quadratic trend.

Question 9

For pairwise post hoc contrasts with unequal group variances, which of the following MCPs is most appropriate?

A) Scheffe'
B) Kaiser-Bowden
C) Tukey HSD
D) Games-Howell

Question 10

A researcher used Fisher's LSD to test three contrasts: $\mu$ ₁- $\mu$ ₂, $\mu$ ₁- $\mu$ ₃, $\mu$ ₁-( $\mu$ ₂+ $\mu$ ₃)/2. Evaluate this practice.

A) This practice is problematic because Fisher's LSD is always too liberal.
B) This practice is problematic because Fisher's LSD can only be used to test simple contrasts.
C) This practice is problematic because the contrasts are not orthogonal.
D) I do not see any problem with this practice. It is great!

Question 11

Which one of the following procedures does not assume equal group variances?

A) Scheffe'
B) Kaiser-Bowden
C) Tukey HSD
D) Tukey-Kramer

Question 12

Which of the following is not an assumption of Tukey HSD?

A) equal sample sizes (n)
B) equal group variances
C) equal group means
D) all of the above are assumptions for the test.

Question 13

Following a significant omnibus ANOVA F test, Scheffe; MCP is conducted. Which of the following results is never possible?

A) Only one pairwise contrast is significant.
B) Only one complex contrast is significant.
C) None of the pairwise contrasts is significant.
D) None of the linear contrasts is significant.

Question 14

If 5 orthogonal contrasts can be tested, what is the number of levels of the independent variable?

A) 1
B) 4
C) 5
D) 6

Question 15

Which of the following procedures can be used to test complex contrasts?

A) Tukey HSD
B) Dunnett's method
C) Fisher's LSD
D) Scheffe' method

Question 16

In a study of different instructional methods, if the researcher is only interested in comparing the scores of the class taught by the traditional method against each of the classes taught by the alternative methods, which procedure should she use?

A) Dunnett method
B) Dunn (Bonferroni) method
C) Tukey HSD
D) Trend analysis

Question 17

In the same study described in item 16, if the researcher is now interested in comparing the scores of the class taught by the traditional method against the average of the classes taught by all the alternative methods, which procedure should she use?

A) Dunnett method
B) Dunn (Bonferroni) method
C) Tukey HSD
D) Trend analysis

Question 18

The same researcher now wants to examine if student scores will increase as the instructional time increases. She randomly assigned 60 students to three classes. Each class spent 4 hours, 5 hours, and 6 hours per day respectively on instruction. Then she compared the average scores of the three classes. Which procedure is the most appropriate for this research question?

A) Dunnett method
B) Dunn (Bonferroni) method
C) Tukey HSD
D) Trend analysis

Question 19

In the study described in item 18, the researcher finds out that student scores increase significantly when instructional time increases, so she predicts that scores will be even higher if the instructional time is 12 hours per day. Evaluate the prediction.

A) The prediction is problematic because 4, 5, 6, and 12 are not equally spaced.
B) The prediction is problematic because the classes with longer instructional time
May not have the same number of students.
C) The prediction is problematic because we have no way of knowing what the trend is
Outside of the range of 4 to 6 hours of instructional time.
D) The prediction is accurate because it is based on empirical evidence.

Question 20

After a significant F test, two different pairwise comparison procedures were used to detect the differences between 5 group means. Procedure A detected one significant contrast, whereas procedure B showed that all contrasts are significant. Which procedure is more powerful?

A) procedure A
B) procedure B
C) equally powerful
D) cannot be determined based on the information given

Question 21

In post hoc pairwise comparisons, if procedure A yields wider confidence intervals than procedure B does, which procedure is more powerful?

A) procedure A
B) procedure B
C) equally powerful
D) cannot be determined based on the information given

Question 22

After a significant F test, a researcher used the Scheffe' method to test all pairwise contrasts and found that all contrasts are significant. He then repeated MCP with the Tukey method. What would he find?

A) All pairwise contrasts are significant.
B) Fewer number of contrasts are significant.
C) None of the pairwise contrasts are significant.
D) Anything is possible.

Question 23

If J = 4, which of the following statements is true?

A) You should always do a priori comparisons before an ANOVA.
B) You should always do post hoc tests after an ANOVA.
C) You should always do post hoc tests to determine why H₀ was rejected.
D) You should always do post hoc tests to determine why H₀ was not rejected.

Question 24

In an experiment, $\bar{Y}_{1}$ =10, $\bar{Y}_{2}$ =20, and $\bar{Y}_{3}$ =40. Tukey HSD shows that $\mu$ ₂- $\mu$ ₁ is a significant contrast. What will you find out about $\mu$ ₃- $\mu$ ₁ and $\mu$ ₃- $\mu$ ₂ if the same procedure and same $\alpha$ level are used?

A) Only $\mu$ ₃- $\mu$ ₁ is significant.
B) Only $\mu$ ₃- $\mu$ ₂ is significant.
C) Both contrasts are significant.
D) None of the contrasts are necessarily significant.

Question 25

In an experiment, $\bar{Y}_{1}$ =10, $\bar{Y}_{2}$ =200, and $\bar{Y}_{3}$ =4000. Which pairwise contrast will necessarily be significant?

A) $\mu$ ₂- $\mu$ ₁
B) $\mu$ ₃- $\mu$ ₁
C) $\mu$ ₃- $\mu$ ₂
D) None of the contrasts will necessarily be significant.

Question 26

A one-factor fixed-effects ANOVA is performed on data for 5 groups of unequal sizes, and H₀ is rejected at the .05 level of significance. Using the Scheffe' procedure, test the contrast that
$\bar{Y}_{.1}-\frac{P_{s 2}+P_{s 3}}{2}$ at the .05 level of significance given the following information:
df_with = 30, $\bar{Y}_{.1}$ = 5, n₁ = 6, $\bar{Y}_{.2}$ = 7.5, n₂ = 6, $\bar{Y}_{.3}$ = 8.5, n₃ = 6, and MS_with = 9.

Question 27

A one-factor fixed-effects ANOVA is performed on data from three groups of equal size (n = 15) and equal variances, and H₀ is rejected at the .05 level. The following values were computed: MS_with = 60 and the sample means are $\bar{Y}_{.1}$ = 25, $\bar{Y}_{.2}$ = 20, and $\bar{Y}_{.3}$ = 12. Use the Tukey HSD method to test all possible pairwise contrasts ( $\alpha$ = .05).

Question 28

Dr Guinea Pigg would like to test if the amount of caffeine intake would affect how well laboratory rats performed on a specific task. He randomly assigned 40 rats to five groups (n = 8). Each rat walked the same maze after drinking caffeinated water. The amount of caffeine the rats took and the number of mistakes they made in walking the maze were recorded in the following table.
$\begin{array}{crrrrr}\hline \text { Dosage } & 10 \mathrm{mg} & 20 \mathrm{mg} & 30 \mathrm{mg} & 40 \mathrm{mg} & 50 \mathrm{mg} \\\hline & 16 & 16 & 2 & 5 & 7 \\& 5 & 10 & 9 & 8 & 12 \\\text { Number of } & 11 & 7 & 11 & 1 & 14 \\\text { mistakes } & 23 & 12 & 13 & 5 & 16 \\& 18 & 7 & 10 & 8 & 11 \\& 12 & 4 & 13 & 11 & 9 \\& 12 & 23 & 9 & 9 & 19 \\& 19 & 13 & 9 & 9 & 24 \\\hline\end{array}$ Using the data, conduct a trend analysis to test if there is any linear, quadratic, or cubic trend ( $\alpha$ = .05).

Question 29

In the experiment described in Question 3, if instead of a planned test, Dr Guinea Pigg conducted an omnibus ANOVA F test at $\alpha$ = .05 and found out that there was significant difference between the group means. Suppose the group variances are equal. Use the Tukey method to test all possible pairwise contrasts.

Question 30

Consider the situation where there are J = 3 groups of subjects. Answer the following
questions:
a. Construct a set of orthogonal contrasts and show that they are orthogonal.
b. Construct a set of contrasts for Dunnett's test (use group 1 as the reference group).
Are these contrasts orthogonal? Why?
c. Construct a set of contrasts for pairwise comparisons. Are these contrasts orthogonal? Why?