Test Bank ANOVA 3 Means Analysis Chapter 11

Chapter 11: Hypothesis Involving Three or More Population Me

Learning Objective: 11.1. Explain why multiple t-tests are not appropriate when an independent variable has more than two categories.

Cognitive Domain: Knowledge

Answer Location: The logic of analysis of variance

Difficulty Level: Easy

2. A problem with conducting multiple t-tests on more than two sample means is ______.

a. we are assuming that the samples are independent

b. the samples may not differ enough

c. we are assuming that the samples are dependent

d. we may not know each groups variance

Learning Objective: 11.1. Explain why multiple t-tests are not appropriate when an independent variable has more than two categories.

Cognitive Domain: Knowledge

Answer Location: The problem with using a t-test with three or more means

Difficulty Level: Medium

3. A problem with conducting multiple t-tests on more than two sample means is ______.

a. the alpha level increases with each test making it easier to commit a Type I error

b. the alpha level decreases with each test making it easier to commit a Type I error

c. the alpha level increases with each test making it easier to commit a Type II error

d. the alpha level decreases with each test making it easier to commit a Type II error

Learning Objective: 11.1. Explain why multiple t-tests are not appropriate when an independent variable has more than two categories.

Cognitive Domain: Knowledge

Answer Location: The problem with using a t-test with three or more means

Difficulty Level: Medium

4. ANOVA is based on ______.

a. comparing the means within groups with the means between groups

b. comparing the proportions within groups with the proportions between groups

c. comparing the alpha levels within groups with the alpha levels between groups

d. comparing the variance within groups with the variance between groups

Learning Objective: 11.2. Describe the importance of the variance in testing the difference between means.

Cognitive Domain: Knowledge

Answer Location: The logic of analysis of variance

Difficulty Level: Easy

5. A researcher hypothesizes that offenders who do not receive services in prison will have higher number of arrests after release than those who participate in program A. Those who participate in program A and B will have lower numbers of arrests post-release than those who only participate in program A and those who receive no services. In conducting an ANOVA with this data, how would the null hypotheses be stated?

a. H0: all three means are equal

b. H0: not all means are equal

c. H0: all three mean are different

d. H0: two means are equal

Learning Objective: 11.2. Describe the importance of the variance in testing the difference between means.

Cognitive Domain: Knowledge

Answer Location: Conducting a hypothesis test with ANOVA

Difficulty Level: Easy

6. The statistical test of ANOVA, the F-test, examines ______.

a. the variance between groups divided by the variance within groups

b. the variance within groups divided by the variance between groups

c. the summation of all the samples average mean divided by the number of samples

d. the standard deviation between groups divided by the standard deviation within groups

Learning Objective: 11.2. Describe the importance of the variance in testing the difference between means.

Cognitive Domain: Knowledge

Answer Location: Types of variance: Total, between-groups, and within-group

Difficulty Level: Easy

7. Total variability is ______.

a. the difference between a groups mean and the grand mean

b. the difference between all groups mean and the grand mean

c. the difference between an individual score and the grand mean

d. the summation of each groups variance

Learning Objective: 11.3. Identify and interpret the total-, between-, and within-group sum of squares and their relationship to testing the difference between means.

Cognitive Domain: Comprehension

Answer Location: Types of variance: Total, between-groups, and within-group

Difficulty Level: Medium

8. Between-groups variability is ______.

a. the difference between each group mean

b. the difference between each group mean divided by the number of groups

c. the difference between the group mean and the grand mean

d. the difference between each group mean divided by the total sample size

Learning Objective: 11.3. Identify and interpret the total-, between-, and within-group sum of squares and their relationship to testing the difference between means.

Cognitive Domain: Comprehension

Answer Location: Types of variance: Total, between-groups, and within-group

Difficulty Level: Medium

9. ______ variability may be thought of as error.

a. Between-group

b. Within-group

c. Total

d. Eta squared

Learning Objective: 11.3. Identify and interpret the total-, between-, and within-group sum of squares and their relationship to testing the difference between means.

Cognitive Domain: Comprehension

Answer Location: Types of variance: Total, between-groups, and within-group

Difficulty Level: Medium

10. ______ variability may be thought of as the treatment or differences we are interested in.

a. Between-group

b. Within-group

c. Total

d. Eta squared

Learning Objective: 11.3. Identify and interpret the total-, between-, and within-group sum of squares and their relationship to testing the difference between means.

Cognitive Domain: Comprehension

Answer Location: Types of variance: Total, between-groups, and within-group

Difficulty Level: Medium

11. To find the within-group degrees of freedom, one must ______.

a. subtract 1 from the number of groups

b. subtract the number of groups from the total number of observations

c. subtract 1 from the total number of observations

d. divide each groups mean by the within-groups sum of squares and then divide the result by the total number of groups.

Learning Objective: 11.3. Identify and interpret the total-, between-, and within-group sum of squares and their relationship to testing the difference between means.

Cognitive Domain: Comprehension

Answer Location: Types of variance: Total, between-groups, and within-group

Difficulty Level: Easy

12. To find the between-group degrees of freedom, one must ______.

a. subtract 1 from the number of groups

b. subtract the number of groups from the total number of observations

c. subtract 1 from the total number of observations

d. divide each groups mean by the within-groups sum of squares and then divide the result by the total number of groups.

Learning Objective: 11.3. Identify and interpret the total-, between-, and within-group sum of squares and their relationship to testing the difference between means.

Cognitive Domain: Comprehension

Answer Location: Types of variance: Total, between-groups, and within-group

Difficulty Level: Easy

13. To find the total degrees of freedom, one must ______.

a. subtract 1 from the number of groups

b. subtract the number of groups from the total number of observations

c. subtract 1 from the total number of observations

d. divide each groups mean by the within-groups sum of squares and then divide the result by the total number of groups.

Learning Objective: 11.3. Identify and interpret the total-, between-, and within-group sum of squares and their relationship to testing the difference between means.

Cognitive Domain: Comprehension

Answer Location: Types of variance: Total, between-groups, and within-group

Difficulty Level: Easy

14. Which test allows for the researcher to identify which means are significantly different from each other?

a. ANOVA

b. Tukey’s HSD

c. Eta squared

d. F statistic

Learning Objective: 11.5. Describe the purpose of John Tukey’s Honest Significance Difference (HSD) test.

Cognitive Domain: Knowledge

Answer Location: Tukey’s honest significance difference (HSD) test

Difficulty Level: Easy

15. Which of the following eta squared results would indicate a strong relationship between the dependent and independent variable?

a. .19

b. .29

c. .49

d. .79

Learning Objective: 11.6. State the difference between measures of association and the analysis of variance (ANOVA) hypothesis test.

Cognitive Domain: Knowledge

Answer Location: Eta squared (correlation ratio)

Difficulty Level: Easy

True/False

16. ANOVAs are useful for independent variables that have more than two values because this test assumes that the samples means are independent.

Learning Objective: 11.1. Explain why multiple t-tests are not appropriate when an independent variable has more than two categories.

Cognitive Domain: Knowledge

Answer Location: The logic of analysis of variance

Difficulty Level: Easy

17. The denominator of the formula for the F-ratio is concerned with the difference between groups.

Learning Objective: 11.3. Identify and interpret the total-, between-, and within-group sum of squares and their relationship to testing the difference between means.

Cognitive Domain: Knowledge

Answer Location: Types of variance: Total, between-groups, and within-group

Difficulty Level: Easy

18. Tukey’s HSD allows for the researcher to compare individual group means with each other to identify which ones are significantly different.

Learning Objective: 11.5. Describe the purpose of John Tukey’s Honest Significance Difference (HSD) test.

Cognitive Domain: Knowledge

Answer Location: Tukey’s honest significance difference (HSD) test

Difficulty Level: Easy

19. The eta squared allows a researcher to measure the strength of the relationship between the independent and dependent variable.

Learning Objective: 11.6. State the difference between measures of association and the analysis of variance (ANOVA) hypothesis test.

Cognitive Domain: Knowledge

Answer Location: Eta squared (correlation ratio)

Difficulty Level: Easy

20. If you add the between- and within-groups sum of square, you will get the total sum of squares.

Learning Objective: 11.3. Identify and interpret the total-, between-, and within-group sum of squares and their relationship to testing the difference between means.

Cognitive Domain: Knowledge

Answer Location: Types of variance: Total, between-groups, and within-group

Difficulty Level: Easy

21. If you subtract the within-groups sum of squares from the total sum of squares you will get the between-groups sum of squares.

Learning Objective: 11.3. Identify and interpret the total-, between-, and within-group sum of squares and their relationship to testing the difference between means.

Cognitive Domain: Knowledge

Answer Location: Types of variance: Total, between-groups, and within-group

Difficulty Level: Easy

22. If you subtract the between-groups sum of squares from the total sum of squares you will get the within-groups sum of squares.

Learning Objective: 11.3. Identify and interpret the total-, between-, and within-group sum of squares and their relationship to testing the difference between means.

Cognitive Domain: Knowledge

Answer Location: Types of variance: Total, between-groups, and within-group

Difficulty Level: Easy

23. The variance for both within- and between-groups is obtained by dividing each groups sum of squares by its respective degrees of freedom.

Learning Objective: 11.3. Identify and interpret the total-, between-, and within-group sum of squares and their relationship to testing the difference between means.

Cognitive Domain: Knowledge

Answer Location: Types of variance: Total, between-groups, and within-group

Difficulty Level: Easy

24. Rejecting the null hypothesis of equal means suggests that each and every group mean is different from one another.

Learning Objective: 11.3. Identify and interpret the total-, between-, and within-group sum of squares and their relationship to testing the difference between means; 11. 5. Describe the purpose of John Tukey’s Honest Significance Difference (HSD) test.

Cognitive Domain: Knowledge

Answer Location: Types of variance: Total, between-groups, and within-group; Tukey’s honest significance difference (HSD) test

Difficulty Level: Medium

Essay

25). Explain why an ANOVA is required for more than two groups as compared to multiple t-tests. Be sure to describe the assumption of t-tests and implications for Type I error.

Learning Objective: 11.1. Explain why multiple t-tests are not appropriate when an independent variable has more than two categories.

Cognitive Domain: Application

Answer Location: The logic of analysis of variance

Difficulty Level: Hard