Question 1

How many possible pairwise contrasts are there if J = 5?
A) 5
B) 10
C) 15
D) 20

Accepted Answer

The number of possible pairwise contrasts for J items is given by the formula J*(J-1)/2. For J = 5, this equals 5*(5-1)/2 = 10.

Question 2

Which of the following linear combinations of population means is a legitimate contrast? A) $\mu$S1U1B11S1U1B0-$\mu$S1U1B12S1U1B0/2+$\mu$S1U1B13S1U1B0/2 B) ($\mu$S1U1B11S1U1B0+$\mu$S1U1B12S1U1B0)/2+$\mu$S1U1B13S1U1B0 C) $\mu$S1U1B11S1U1B0+$\mu$S1U1B12S1U1B0)/2-$\mu$S1U1B13S1U1B0 D) $\mu$S1U1B11S1U1B0-$\mu$S1U1B12S1U1B0-$\mu$S1U1B13S1U1B0

Accepted Answer

C

Question 3

If J = 3, which of the following sets of contrasts is orthogonal?
A) $\mu$S1U1B11S1U1B0-$\mu$S1U1B12S1U1B0,$\mu$S1U1B11S1U1B0-$\mu$S1U1B13S1U1B0
B) $\mu$S1U1B12S1U1B0+$\mu$S1U1B13S1U1B0,$\mu$S1U1B12S1U1B0-$\mu$S1U1B13S1U1B0
C) $\mu$S1U1B11S1U1B0-$\mu$S1U1B13S1U1B0,$\mu$S1U1B11S1U1B0($\mu$S1U1B12S1U1B0+$\mu$S1U1B13S1U1B0)/2
D) $\mu$S1U1B11S1U1B0-$\mu$S1U1B13S1U1B0,$\mu$S1U1B12S1U1B0-($\mu$S1U1B11S1U1B0+$\mu$S1U1B13S1U1B0)/2

Accepted Answer

D

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

Accepted Answer

When a one-factor fixed-effects ANOVA results in a nonsignificant F ratio, it indicates that there is no statistically significant difference among the group means. Therefore, there is no need for post-hoc comparisons, making "None of the above" the correct choice. Post-hoc procedures like Scheffe', Tukey HSD, and Fisher LSD are used to identify specific group differences after a significant ANOVA result.

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

Accepted Answer

The nominal family-wise error rate is calculated as 1 - (1 - per contrast alpha)^number of contrasts. For this scenario, it would be 1 - (1 - 0.01)^5, which is approximately 0.05, indicating the overall risk of making at least one Type I error across all contrasts.

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.

Accepted Answer

As the significance level ($\alpha$) increases, the critical value decreases because you are more willing to accept a higher rate of Type I error, thus requiring a lower threshold to reject the null hypothesis.

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.

Accepted Answer

Post hoc tests are conducted after a significant ANOVA F test when there are more than two groups (J > 2) to determine which specific group differences are significant.

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.

Accepted Answer

Trend analysis requires the independent variable to be on an interval or ratio scale, not nominal, to assess trends like linear or quadratic.

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

Accepted Answer

The Games-Howell procedure is most appropriate for pairwise post hoc contrasts when there are unequal variances among groups, as it does not assume homogeneity of variances.

Question 10

A researcher used Fisher's LSD to test three contrasts: $\mu$S1U1B11S1U1B0-$\mu$S1U1B12S1U1B0,$\mu$S1U1B11S1U1B0-$\mu$S1U1B13S1U1B0,$\mu$S1U1B11S1U1B0-($\mu$S1U1B12S1U1B0+$\mu$S1U1B13S1U1B0)/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!

Accepted Answer

Fisher's LSD (Least Significant Difference) test is designed for simple pairwise comparisons, not for testing complex or multiple contrasts simultaneously. It assumes independence among the tests, which might not hold in the case of multiple or complex contrasts.

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

Accepted Answer

The Kaiser-Bowden procedure does not assume equal group variances, unlike the other procedures listed.

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.

Accepted Answer

Tukey's HSD (Honestly Significant Difference) test assumes equal sample sizes and equal group variances, but it does not assume equal group means. In fact, it is used to find which means are significantly different from each other.

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.

Accepted Answer

Scheffe's method is designed to test all possible contrasts, including complex ones. If the omnibus ANOVA is significant, at least one contrast (pairwise or complex) should be significant, making option D impossible.

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

Accepted Answer

The number of orthogonal contrasts that can be tested is one less than the number of levels of the independent variable, so if 5 orthogonal contrasts can be tested, there must be 6 levels of the independent variable.

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

Accepted Answer

Scheffe's method is specifically designed for testing complex contrasts, allowing for the comparison of any linear combination of group means, making it more flexible and suitable for complex hypothesis testing compared to the other methods listed, which are more limited in their application.

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

Accepted Answer

The Dunnett method is specifically designed for comparing a control group (in this case, the class taught by the traditional method) against each of several treatment groups (the classes taught by alternative methods) without inflating the Type I error rate. This makes it the appropriate choice for the scenario described.

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

Accepted Answer

The answer of In the same study described in item...

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

Accepted Answer

Trend analysis is the most appropriate procedure for examining if student scores increase as the instructional time increases because it specifically looks at the relationship between variables (in this case, instructional time and scores) to determine if there is a consistent trend or pattern over the conditions (different hours of instruction).

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.

Accepted Answer

The prediction is problematic because it extrapolates beyond the observed range of 4 to 6 hours, assuming the trend continues without evidence for instructional times as high as 12 hours.

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

Accepted Answer

Procedure B is more powerful because it detected more significant contrasts, indicating a greater ability to identify differences between group means.

Quiz 12: Multiple Comparison Procedures

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

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

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

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?

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?

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

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

Which of the following statements about trend analysis is true?

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

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.

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

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

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

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

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

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?

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?

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.

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?