Test Bank Answers Hypothesis Testing ANOVA Chapter.12 3e

Test Bank

1. A researcher wants to do an analysis with an independent variable that is categorical and has three classes. The dependent variable is continuous. Which test is appropriate?

A. χ²

B. dependent samples t test

C. ANOVA

D. independent samples t test

2. A professor’s research assistant has a penchant for cutting corners. Due to the rather complex nature of the ANOVA test, the professor has asked the assistant to perform, he has opted, instead, to simply run a series of t tests. Why might this be a bad decision for our assistant?

A. The between-group variance will decrease as the t tests are performed, making it seem as though a relation exists when none, in fact, does.

B. The familywise error rate will increase, making the work fraught with unacceptably high levels of error.

C. The levels of Type II error will increase rapidly, making the analyses meaningless.

D. The within-group variance will decrease to such low levels the validity of the work will come into question.

3. Which of the following are the types of variances analyzed by an ANOVA?

A. standard error and mean error

B. external and internal

C. intergroup and intragroup

D. between-group and within-group

4. Which of the following is the statistic for the ANOVA?

A. F

B. X²

C. μ

D. Σ

5. What is the theoretical probability distribution for ANOVA?

A. X² distribution

B. F distribution

C. z distribution

D. t distribution

6. When true differences between groups substantially outweigh the random fluctuations present within each group, the ANOVA statistic ______.

A. will be zero

B. will be small

C. will be negative

D. will be large

7. When between-group variance is small relative to within-group variance, the ANOVA statistic will ______.

A. be small

B. be zero

C. be negative

D. be large

8. In ANOVA, the null hypothesis is rejected when ______.

A. the X² statistic exceeds the critical value

B. the F statistic exceeds the critical value

C. the z statistic exceeds the critical value

D. the t statistic exceeds the critical value

9. Which of the following is the correct H₀ for the ANOVA?

A. H₀: t_obt > t_crit

B. H₀: µ μ₁ = µμ₂ = µμ₃

C. H₀: Z_obt > Z_crit

D. H₀: X²_crit > X²_obt

10. Which of the following is the correct H₁ for the ANOVA?

A. H₁: t_obt ≠ t_crit

B. H₁: Z_obt ≥ Z_crit

C. H₁: someµ μ_i ≠ some µ_j

D. H₁: X²_crit ≥ X²_obt

11. Post hoc tests are ______.

A. conducted prior to an ANOVA to determine whether the within-group variance is larger than the between-group variance

B. conducted when the null is rejected in ANOVA in order to determine the number and location of differences between groups

C. conducted during the actual ANOVA calculations to determine if the between-group variance is large enough to be considered significant in the rejection of the null hypothesis

D. conducted when the alternative hypothesis is retained to determine if the within-group variance is large enough to be considered significant in the rejection of the null hypothesis

12. The theoretical probability distribution for the ANOVA is bounded on the left at ______.

A. zero

B. −1

C. 1

D. none of the above; the ANOVA probability distribution is not bounded

13. In ANOVA, the acronym MS denotes ______.

A. sum of squares

B. mean sum

C. mean squares

D. grand mean

14. The ratio of between-group variance to within-group variance is also known as ______?

A. X² statistic

B. z statistic

C. F statistic

D. t statistic

15. Ω² ______.

A. can be left as a proportion or presented as a percent

B. is always expressed as a proportion

C. is always expressed as a percent

D. is expressed as a proportion when the mean square is above 1.00

16. A test that compares each group to all others in a series of two-variable hypothesis tests is ______.

A. Ω²

B. λ

C. Tukey’s honest significant difference (HSD)

D. mean sum of squares

17. The HSD test is conceptually similar to a series of t tests but has one important difference. What is it that makes the HSD distinct from a series of t tests?

A. It eliminates the need for the sum of squares.

B. It sidesteps the necessity of calculating the standard error.

C. It sidesteps the problems associated with Type II errors.

D. It sidesteps the problem of familywise error.

18. The HSD test is also known as ______.

A. the Holmes significance difference

B. Tukey’s honest significant difference (HSD)

C. λ’s homed statistical difference

D. λ’s honest statistical difference

19. If the null is rejected in an ANOVA, which of the following tests would a researcher run if he or she was interested in the magnitude of the relationship between the independent and dependent variables?

A. Ω²

B. λ

C. mean sum of squares

D. the Holmes significance difference

20. Ω² is bounded by ______.

A. −1 and 1

B. 0 and −1

C. 0 and 1

D. There is no limit to the Ω² statistic.

21. ANOVA relies upon a theoretical distribution whose curve shape ______.

A. is determined by the sample size

B. is determined by the population size

C. is determined by the mean square and sum of squares

D. is determined by the degrees of freedom and the α level

22. What are the limits to the number of classes that can be successfully analyzed using ANOVA?

A. 1 only

B. 2 only

C. 3 only

D. There is no limit to the number of classes that can be analyzed by an ANOVA.

23. ______ is a measure of association for ANOVA that is expressed as the proportion of the total variability in the sample that is due to between-group differences.

A. Ω²

B. Bonferroni

C. Tukey’s HSD

D. λ

24. What is a commonly used test used to determine the number and location of differences between groups?

A. λ

B. Ω²

C. Tukey’s HSD

D. ANOVA

25. Between-groups sum of squares is denoted how in an ANOVA?

A. SS_G

B. SS_B

C. SS_(BG)

D. SS_D

26. Due to the fact that the ANOVA fails to indicate which group(s) stands out from the rest, researchers must conduct ______.

A. t tests

B. F tests

C. post hoc tests

D. none of these

27. In calculating the degrees of freedom in the ANOVA, ______ is the symbol used to represent the number of groups.

A. k

B. g

C. F

D. none of these

28. The grand mean in an ANOVA is symbolized by ______.

A. x

B. F

C.

D. none of these

29. SS_t denotes ______ in an ANOVA.

A. sum of squares within

B. sum of squares between

C. total sum of squares

D. none of these

30. “There are significant mean differences in the arrest rates of low, middle, and upper class individuals” is an example of what kind of hypothesis?

A. null hypothesis

B. directional hypothesis

C. nondirectional hypothesis

D. None of these

31. “There are no significant mean differences in the arrest rates of low, middle, and upper class individuals” is an example of what kind of hypothesis?

A. null hypothesis

B. directional hypothesis

C. nondirectional hypothesis

D. none of these

32. Which of the following distributions are bounded on the left at zero (meaning that it only has positive values).

A. z distribution

B. t distribution

C. F distribution

D. all of these

33. Which of the following test is customarily performed if significant mean differences are detected after an ANOVA test?

A. F test

B. t test

C. χ² test

D. post hoc test

34. Which of the following is a post hoc test?

A. Ω²

B. Bonferroni

C. Tukey’s honest significant difference

D. all of these

35. Which post hoc test is interpreted as the proportion of the variability in the dependent variable that is attributable to the independent variable?

A. Ω²

B. Bonferroni

C. Tukey’s honest significant difference

D. all of these

1. It is considered appropriate for a researcher to perform the analysis of variance test using a continuous dependent variable.

2. The ANOVA is based upon an examination of variances.

3. Due to the complexity of the ANOVA, researchers can, if they so choose, opt to perform a series of t tests to expedite their calculations.

4. In ANOVA, there are three types of variances analyzed.

5. Within-group variance is driven by random variations between people or objects in the group and is a measure of error.

6. The ANOVA statistic indicates neither the number of differences nor the specific group(s) that stand out from the others.

7. In ANOVA, degrees of freedom are based on sample size, similar to t tests.

8. df_B = k – 1 is the formula for the calculation of the degrees of freedom between groups in an ANOVA.

9. In the ANOVA’s theoretical distribution, the critical region is always found in the left-hand tail of the curve.

10. In ANOVA, it is possible to have negative values for the sums of squares and the mean squares.

11. Larger values of indicate stronger independent variable-dependent variable relationships.

12. Rejection of the null hypothesis in an HSD means that there is a significant difference between the means.

13. The Bonferroni test minimizes Type I errors in favor of Type II.

14. The Bonferroni test has been criticized for being too conservative.

15. The best method of obtaining a more holistic picture of your data is to use both the HSD and Bonferroni test.

16. The ANOVA is appropriate for a categorical variable with at least two classes.

17. The increase in the likelihood of a Type 1 error that results from running repeated statistical tests on a single sample is referred to as family-wise error.

18. The extent to which a set of groups or classes are similar to or different from one another, or in other words, a measure of the true group effect, is called between-group variance.

19. The amount of diversity that exists among the people or objects in a single group or class is referred to as within-group variance.

20. The X² statistic is a ratio that compares the amount of variance between groups to that within groups.

1. A researcher conducted an ANOVA and arrived at a result of F_obt = −2.34. She knows immediately that she made a mistake in her calculations. How does she know this?

2. What are the two formulas for degrees of freedom in ANOVA?

3. Explain why a researcher would opt for an ANOVA instead of a series of t tests.

4. What is the decision rule in ANOVA always phrased in terms of F_obt being greater than F_crit for the null to be rejected? That is, why is the ANOVA decision rule different from the t test decision rule in that the null is never rejected if F_obt is less than F_crit?

5. The hospitality industry in a particular state is worried about crimes against theme park visitors, so a researcher is hired to find out whether larceny rates differ across the different amusement parks in the state. Take the data he has obtained on three parks and conduct an ANOVA to see if there is any statistically significant difference between the parks in terms of larcenies.

Potter Park Fern Park Cypress Park

15 2 1

12 4 0

9 9 16

10 11 4

5 6

α = .05