Statistics salkind 4e test bank ch13

Chapter 13: Two Groups Too Many? Try Analysis of Variance
Test Bank
MULTIPLE CHOICE
1. Who is responsible for the invention of the F statistic?
a. Pearson Fisher
b. Karl Pearson
c. R. A. Fisher
d. R. A. Pearson
ANS:
REF:
OBJ:
COG:

C
PTS: 1
DIF: Easy
Introduction to Analysis of Variance
What analysis of variance is and when it is appropriate to use
Knowledge

2. The ANOVA is like an extension of the _______.
a. t-test
b. F-test
c. Correlation
d. Regression
ANS:
REF:
OBJ:
COG:

A

PTS: 1
DIF: Easy
Introduction to Analysis of Variance
What analysis of variance is and when it is appropriate to use
Knowledge

3. The ANOVA uses the _______.
a. F-test
b. t-test
c. p-test
d. r-test
ANS:
REF:
OBJ:
COG:

A
PTS: 1
DIF: Easy
Introduction to Analysis of Variance
What analysis of variance is and when it is appropriate to use
Knowledge

4. A simple analysis of variance is used to study participants who are tested _______.
a. Only once
b. Only twice
c. Once or more
d. Twice or more
ANS: A
PTS: 1

DIF: Easy
REF: The Path to Wisdom and Knowledge


OBJ: What analysis of variance is and when it is appropriate to use
COG: Knowledge
5. The ANOVA can be used to test the differences _______.
a. Between two groups only
b. Between two or more groups
c. Within a single group
d. Among three groups only
ANS:
REF:
OBJ:
COG:

B
PTS: 1
DIF: Easy
Introduction to Analysis of Variance
What analysis of variance is and when it is appropriate to use
Knowledge

6. A simple analysis of variance includes _______ factor(s) or treatment variables in the

analysis.
a. Only one
b. Only two
c. Three or more
d. One or more

ANS:
REF:
OBJ:
COG:

A
PTS: 1
DIF: Easy
Different Flavors of ANOVA
What analysis of variance is and when it is appropriate to use
Knowledge

7. A simple analysis of variance is also called _______.
a. The two-way analysis of variance
b. Factorial ANOVA
c. Correlational ANOVA
d. The one-way analysis of variance
ANS:
REF:
OBJ:
COG:

D
PTS: 1
DIF: Easy
Different Flavors of ANOVA
What analysis of variance is and when it is appropriate to use
Knowledge

8. A factorial ANOVA includes _______ treatment factor(s).

a. More than one
b. Only one
c. Only two
d. Only three or more
ANS:
REF:
OBJ:
COG:

A
PTS: 1
DIF: Easy
Different Flavors of ANOVA
What analysis of variance is and when it is appropriate to use
Knowledge


9. An omnibus test tests _______.
a. Overall differences
b. Specific comparisons
c. Very large samples
d. Very small populations
ANS: A
PTS: 1
REF: Computing the F-Test Statistic
COG: Knowledge

DIF: Medium
OBJ: How to compute and interpret the F statistic

10. The ANOVA is a(n) _______.
a. Omnibus test
b. Correlational test
c. Regressional analysis
d. Factorial correlation
ANS: A
PTS: 1
REF: Computing the F-Test Statistic
COG: Knowledge

DIF: Medium
OBJ: How to compute and interpret the F statistic

11. Which of the following is the same as t2 when examining the difference between two groups?
a. F
b. T
c. Cohen’s d
d. F2
ANS: A
PTS: 1
REF: Computing the F-Test Statistic
COG: Knowledge

DIF: Medium
OBJ: How to compute and interpret the F statistic

12. When your research questions calls for you to examine the differences in group means among

three or more groups, which of the following would be the appropriate procedure?
a. Pearson correlation

b. Dependent-sample t-test
c. Regression
d. Analysis of variance
ANS:
REF:
OBJ:
COG:

D
PTS: 1
DIF: Easy
Introduction to Analysis of Variance
What analysis of variance is and when it is appropriate to use
Knowledge

13. What type of ANOVA is used when there is only one type of treatment or grouping factor

with more than two levels?
a. One way


b. Two way
c. Three way
d. Four way
ANS:
REF:
OBJ:
COG:

A

PTS: 1
DIF: Easy
Different Flavors of ANOVA
What analysis of variance is and when it is appropriate to use
Knowledge

14. Which of the following would be an example of a design that examines the effects of gender

and socioeconomic status (i.e., high, medium, and low) on a test of student achievement?
a. Simple ANOVA
b. One-way ANOVA
c. 2  3 ANOVA
d. 3  3 ANOVA
ANS:
REF:
OBJ:
COG:

C
PTS: 1
DIF: Medium
Different Flavors of ANOVA
What analysis of variance is and when it is appropriate to use
Comprehension

15. Which of the following would be an example of a design that examines the effects of gender

and region of residence (e.g., Northeast, South, Midwest, and West)?
a. Simple ANOVA
b. One-way ANOVA

c. 2  2 ANOVA
d. 2  4 ANOVA
ANS:
REF:
OBJ:
COG:

D
PTS: 1
DIF: Medium
Different Flavors of ANOVA
What analysis of variance is and when it is appropriate to use
Comprehension

16. Which of the following would be an example of a design that examines the effects of region

of residence (e.g., Northeast, South, Midwest, and West) and income (i.e., low, medium, and
high)?
a. Simple ANOVA
b. One-way ANOVA
c. 3  3 ANOVA
d. 4  3 ANOVA
ANS:
REF:
OBJ:
COG:

D
PTS: 1
DIF: Medium

Different Flavors of ANOVA
What analysis of variance is and when it is appropriate to use
Comprehension


17. If you wanted to examine whether the degree of parental involvement differs based on

students’ grade in school (i.e., first, second, third, etc.), what is the dependent variable of
interest?
a. Grade level
b. Students
c. Parents
d. Degree of parent involvement
ANS:
REF:
OBJ:
COG:

D
PTS: 1
DIF: Medium
Different Flavors of ANOVA
What analysis of variance is and when it is appropriate to use
Comprehension

18. If you wanted to examine whether the degree of parental involvement differs based on

students’ grade in school (i.e., first, second, third, etc.), what is the independent variable of
interest?
a. Grade level

b. Students
c. Parents
d. Degree of parent involvement
ANS:
REF:
OBJ:
COG:

A
PTS: 1
DIF: Medium
Different Flavors of ANOVA
What analysis of variance is and when it is appropriate to use
Comprehension

19. Which of the following is the formula for computing the F statistic?
a. F = MSbetween ÷ MSwithin
b. F = SSbetween ÷ SSwithin
c. F = MSwithin ÷ MSbetween
d. F = SSwithin ÷ SSbetween
ANS: A
PTS: 1
REF: Computing the F-Test Statistic
COG: Knowledge

DIF: Medium
OBJ: How to compute and interpret the F statistic

20. The variability between groups is due to _______.
a. Chance

b. The grouping factor
c. The F ratio
d. The level of the dependent variable
ANS: B
PTS: 1
REF: Computing the F-Test Statistic
COG: Knowledge

DIF: Medium
OBJ: How to compute and interpret the F statistic


21. The variability within groups is due to _______.
a. Chance
b. The grouping factor
c. The F ratio
d. The level of the dependent variable
ANS: A
PTS: 1
REF: Computing the F-Test Statistic
COG: Knowledge

DIF: Medium
OBJ: How to compute and interpret the F statistic

22. In order to increase the value of the F statistic, which of the following must occur?
a. MSwithin > MSbetween
b. MSwithin = MSbetween
c. MSwithin < MSbetween
d. Ratio = 1

ANS: C
PTS: 1
REF: Computing the F-Test Statistic
COG: Comprehension

DIF: Medium
OBJ: How to compute and interpret the F statistic

23. What is the first step in the computation of the F statistic?
a. Setting the level of risk
b. Selecting the appropriate test
c. Computing the obtained value
d. Stating the null and research hypotheses
ANS: D
PTS: 1
REF: Computing the F-Test Statistic
COG: Knowledge

DIF: Easy
OBJ: How to compute and interpret the F statistic

24. Computing the between-group variance first calls for summing the difference between grand

mean (means of all scores) and the group means. This is known as the _______.
a. MSwithin
b. SSwithin
c. SSbetween
d. MSbetween
ANS: C
PTS: 1

REF: Computing the F-Test Statistic
COG: Comprehension

DIF: Medium
OBJ: How to compute and interpret the F statistic

25. When you compute the sum of the differences between each individual score and the group

mean, you have calculated the _______.
a. MSwithin
b. SSwithin
c. MSbetween


d. SSbetween
ANS: B
PTS: 1
REF: Computing the F-Test Statistic
COG: Comprehension

DIF: Medium
OBJ: How to compute and interpret the F statistic

26. When computing the degrees of freedom for ANOVA, how is the within-group estimate

calculated?
a. n - 1
b. k - 1
c. N - k
d. (n – 1) ÷ k

ANS: C
PTS: 1
REF: Computing the F-Test Statistic
COG: Comprehension

DIF: Medium
OBJ: How to compute and interpret the F statistic

27. When computing the degrees of freedom for ANOVA, how is the between-group estimate

calculated?
a. n - 1
b. k - 1
c. N - k
d. (n – 1) ÷ k
ANS: B
PTS: 1
REF: Computing the F-Test Statistic
COG: Comprehension

DIF: Medium
OBJ: How to compute and interpret the F statistic

28. When interpreting F(2, 27) = 8.80, p < .05, how many groups were examined?
a. 30
b. 27
c. 3
d. 2
ANS: C
PTS: 1

DIF: Medium
REF: So How Do I Interpret F(2, 27) = 8.80, p < .05?
OBJ: How to compute and interpret the F statistic

COG: Application

29. When interpreting F(2, 27) = 8.80, p < .05, what is the within-groups df?
a. 30
b. 27
c. 3
d. 2
ANS: B
PTS: 1
DIF: Medium
REF: So How Do I Interpret F(2, 27) = 8.80, p < .05?
OBJ: How to compute and interpret the F statistic

COG: Application


30. When interpreting F(2, 27) = 8.80, p < .05, what is the total sample size examined?
a. 30
b. 29
c. 3
d. 2
ANS: A
PTS: 1
DIF: Medium
REF: So How Do I Interpret F(2, 27) = 8.80, p < .05?
OBJ: How to compute and interpret the F statistic

COG: Application

31. When interpreting F(2, 27) = 8.80, p < .05, what is the between-groups df?
a. 30
b. 27
c. 3
d. 2
ANS: D
PTS: 1
DIF: Medium
REF: So How Do I Interpret F(2, 27) = 8.80, p < .05?
OBJ: How to compute and interpret the F statistic

COG: Application

32. Using ANOVA, a null hypothesis could look like this:
a. H0 : µ1 = µ2 = µ3
b. H0 : µ1 > µ2 > µ3
c. H0 : µ1 = µ2 > µ3
d.
ANS: A
PTS: 1
REF: Computing the F-Test Statistic
COG: Comprehension

DIF: Medium
OBJ: How to compute and interpret the F statistic

33. Using ANOVA, an alternative or research hypothesis could look like this:

a. H0 : µ1 = µ2 = µ3
b. H0 : µ1 > µ2 > µ3
c. H0 : µ1 = µ2 > µ3
d.
ANS: D
PTS: 1
REF: Computing the F-Test Statistic
COG: Comprehension

DIF: Medium
OBJ: How to compute and interpret the F statistic

34. If the amount of variability due to within-group differences is equal to the amount of

variability due to between-group differences, your F value will be equal to _______.
a. 0
b. 1
c. -1


d. 2
ANS: B
PTS: 1
REF: Computing the F-Test Statistic
COG: Comprehension

DIF: Medium
OBJ: How to compute and interpret the F statistic

35. In a 4  3 factorial design, there are how many levels of the first grouping factor?

a. 3
b. 4
c. 7
d. 12
ANS:
REF:
OBJ:
COG:

B
PTS: 1
DIF: Medium
Different Flavors of ANOVA
What analysis of variance is and when it is appropriate to use
Comprehension

36. In a 4  3 factorial design, there are how many levels of the second grouping factor?
a. 3
b. 4
c. 7
d. 12
ANS:
REF:
OBJ:
COG:

A
PTS: 1
DIF: Medium
Different Flavors of ANOVA

What analysis of variance is and when it is appropriate to use
Comprehension

37. In a 5  4 factorial ANOVA design, how many possible group assignments for subjects are

there?
a. 5
b. 20
c. 4
d. 9
ANS:
REF:
OBJ:
COG:

B
PTS: 1
DIF: Medium
Different Flavors of ANOVA
What analysis of variance is and when it is appropriate to use
Comprehension

38. In a 4  3 factorial ANOVA design, how many possible group assignments for subjects are

there?
a. 3
b. 4
c. 7
d. 12

ANS:
REF:
OBJ:
COG:

D
PTS: 1
DIF: Medium
Different Flavors of ANOVA
What analysis of variance is and when it is appropriate to use
Comprehension

39. If your MSbetween is higher than your MSwithin, your F value will be _______.
a. Higher
b. Lower
c. The same
d. Zero
ANS: A
PTS: 1
REF: Computing the F-Test Statistic
COG: Comprehension

DIF: Medium
OBJ: How to compute and interpret the F statistic

40. If your MSbetween is lower than your MSwithin, your F value will be _______.
a. Higher
b. Lower
c. The same

d. Zero
ANS: B
PTS: 1
REF: Computing the F-Test Statistic
COG: Comprehension

DIF: Medium
OBJ: How to compute and interpret the F statistic

41. If your MSwithin is higher than your MSbetween, your F value will be _______.
a. Higher
b. Lower
c. The same
d. One
ANS: B
PTS: 1
REF: Computing the F-Test Statistic
COG: Comprehension

DIF: Medium
OBJ: How to compute and interpret the F statistic

42. If your MSwithin is lower than your MSbetween, your F value will be _______.
a. Higher
b. Lower
c. The same
d. One
ANS: A
PTS: 1
REF: Computing the F-Test Statistic

COG: Comprehension

DIF: Medium
OBJ: How to compute and interpret the F statistic


43. A research study is investigating the effects of studying French one, two, or three hours

weekly between fourth graders and ninth graders. How would this factorial design be best
described?
a. 2  3
b. 3  2
c. 3  3
d. 6  3
ANS:
REF:
OBJ:
COG:

B
PTS: 1
DIF: Medium
Different Flavors of ANOVA
What analysis of variance is and when it is appropriate to use
Comprehension

44. ANOVA first tests for an overall difference between the means. This is known as what type of

test?
a. Omnibus

b. Pluribus
c. Omnivorous
d. Omnibor
ANS: A
PTS: 1
REF: Computing the F-Test Statistic
COG: Comprehension

DIF: Medium
OBJ: How to compute and interpret the F statistic

45. All of the following ANOVA options are available within Excel’s Data Analysis tools

EXCEPT this:
a. ANOVA: single factor
b. ANOVA: two factor with replication
c. ANOVA: comprehensive factor
d. ANOVA: two factor without replication
ANS: C
PTS: 1
DIF: Easy
REF: Using the Amazing Data Analysis Tools to Compute the F Value
OBJ: How to use the F.TEST and F.DIST function
COG: Knowledge
46. If you perform multiple t-tests, which of the following is true?
a. The risk of Type I error increases.
b. The risk of Type I error decreases.
c. The risk of Type I error is not impacted.
d. There is a 10% chance of committing a Type I error.
ANS: A

PTS: 1
DIF: Medium
REF: So How Do I Interpret F(2, 27) = 8.80, p < .05?
OBJ: How to compute and interpret the F statistic

COG: Comprehension


47. Talking about the direction of specific differences in ANOVA would not make any sense

because it is a(n) _______ test.
a. Monobus
b. Multibus
c. Omnibus
d. Octobus
ANS: C
PTS: 1
REF: Computing the F-Test Statistic
COG: Comprehension

DIF: Medium
OBJ: How to compute and interpret the F statistic

48. In ANOVA, the variance due to differences in performance is separated into variance that is

due to differences between individuals _______ groups and variance due to differences
_______ groups.
a. Within; between
b. Above; between
c. Above; within

d. Over; between
ANS: A
PTS: 1
REF: Computing the F-Test Statistic
COG: Knowledge

DIF: Medium
OBJ: How to compute and interpret the F statistic

49. A researcher wants to create an intervention to improve the well-being of first-semester

graduate students, so she gives one group of students specific doses of rocky road ice cream,
the next group of students specific doses of licorice, and the third group of students specific
doses of chewy fruit-flavored candies for their treatments. To analyze the differences in
well-being between the types of “treatment,” she would use a(n) _______.
a. Dependent-samples t-test
b. Analysis of variance
c. Independent-samples t-test
d. Repeated-measures analysis of variance
ANS:
REF:
OBJ:
COG:

B
PTS: 1
DIF: Medium
Different Flavors of ANOVA
What analysis of variance is and when it is appropriate to use
Application

TRUE/FALSE
1. There are three ANOVA options within the Excel data analysis tools.
ANS: T
PTS: 1
DIF: Easy
REF: Using the Amazing Data Analysis Tools to Compute the F Value
OBJ: How to use the F.TEST and F.DIST function
COG: Knowledge


2. There are several types of ANOVA.
ANS:
REF:
OBJ:
COG:

T
PTS: 1
DIF: Easy
Different Flavors of ANOVA
What analysis of variance is and when it is appropriate to use
Knowledge

3. The simple analysis of variance, or one-way analysis of variance, includes only one factor or

treatment variable in the analysis.
ANS:
REF:
OBJ:

COG:

T
PTS: 1
DIF: Medium
Different Flavors of ANOVA
What analysis of variance is and when it is appropriate to use
Comprehension

4. ANOVA constitutes a pairwise comparison.
ANS: F
PTS: 1
REF: Computing the F-Test Statistic
COG: Comprehension

DIF: Medium
OBJ: How to compute and interpret the F statistic

5. Pairwise comparisons can be used in order to determine whether there are significant

differences between specific groups.
ANS: T
PTS: 1
REF: Computing the F-Test Statistic
COG: Comprehension

DIF: Medium
OBJ: How to compute and interpret the F statistic

6. The analysis of variance tests the difference between three or more means.

ANS:
REF:
OBJ:
COG:

T
PTS: 1
DIF: Easy
Introduction to Analysis of Variance
What analysis of variance is and when it is appropriate to use
Knowledge

7. Factorial design is a simpler type of ANOVA in which there is only one treatment factor

being explored.
ANS:
REF:
OBJ:
COG:

F
PTS: 1
DIF: Medium
Different Flavors of ANOVA
What analysis of variance is and when it is appropriate to use
Comprehension

8. All F-tests are nondirectional.
ANS: T
PTS: 1

REF: Computing the F-Test Statistic
COG: Comprehension

DIF: Medium
OBJ: How to compute and interpret the F statistic


SHORT ANSWER
1. What is the sum of squares total?
ANS:

The sum of squares total is equal to the sum of the between-group and within-group sum of
squares.
PTS: 1
DIF: Medium
REF: Computing the F-Test Statistic
OBJ: How to compute and interpret the F statistic
COG: Knowledge
2. If the total sample size was 50, and there were three groups examined, what is the

between-groups degrees of freedom?
ANS:

2
PTS: 1
DIF: Medium
REF: Computing the F-Test Statistic
OBJ: How to compute and interpret the F statistic
COG: Application
3. If the total sample size was 50, and there were three groups examined, what is the

within-groups degrees of freedom?
ANS:

47
PTS: 1
DIF: Medium
REF: Computing the F-Test Statistic
OBJ: How to compute and interpret the F statistic
COG: Application
4. What is the MSbetween value?
ANS:

The MSbetween value is the average of the between-groups sum of squares. It is calculated by
dividing the between-groups sum of squares by the between-groups degrees of freedom (k 1).
PTS: 1
DIF: Hard
REF: Computing the F-Test Statistic
OBJ: How to compute and interpret the F statistic
COG: Comprehension
5. What is the MSwithin value?
ANS:

The MSwithin value is the average of the within-groups sum of squares. It is calculated by
dividing the within-groups sum of squares by the within-groups degrees of freedom (N - k).
PTS: 1
DIF: Hard
REF: Computing the F-Test Statistic
OBJ: How to compute and interpret the F statistic
COG: Comprehension

6. What is the F value?
ANS:

The F value is test statistic needed to evaluate the hypothesis that there are overall differences
between groups.
PTS: 1
DIF: Medium
REF: Computing the F-Test Statistic
OBJ: How to compute and interpret the F statistic
COG: Comprehension
7. Why is this statistical technique called analysis of variance?
ANS:

The technique is called analysis of variance because the variance due to differences in
performance or scores is separated into variance that is due to differences between individual
scores within groups and variance due to differences between groups.
PTS: 1
DIF: Hard
REF: Introduction to Analysis of Variance
OBJ: What analysis of variance is and when it is appropriate to use
COG: Comprehension
8. How is ANOVA similar to and different from a t-test?
ANS:

ANOVA is similar to a t-test in that the differences between means are examined. ANOVA is
different in that more than two means are examined.
PTS: 1
DIF: Medium

REF: Computing the F-Test Statistic
OBJ: How to compute and interpret the F statistic
COG: Analysis
9. How would you interpret the equation: H0 : µ1 = µ2 = µ3?
ANS:

The above equation is a null hypothesis indicating that there is no overall difference between
means for the three different groups.
PTS: 1
DIF: Medium
REF: Computing the F-Test Statistic
OBJ: How to compute and interpret the F statistic
COG: Comprehension
10. How would you interpret the equation:

?

ANS:

The above equation is a research hypothesis indicating that there is an overall difference
between means in the three groups being tested. The hypothesis is nondirectional because it
does not posit where the differences are.
PTS: 1
DIF: Medium
REF: Computing the F-Test Statistic
OBJ: How to compute and interpret the F statistic
COG: Comprehension


11. What is an omnibus test? Provide an example of an omnibus test.

ANS:

An omnibus test refers to a test that examines the overall differences between means.
ANOVA is an omnibus test.
PTS: 1
DIF: Medium
REF: Computing the F-Test Statistic
OBJ: How to compute and interpret the F statistic
COG: Comprehension
12. What is the F ratio?
ANS:

The F ratio is a ratio of the variability between groups to the variability within groups.
PTS: 1
DIF: Medium
REF: Computing the F-Test Statistic
OBJ: How to compute and interpret the F statistic
COG: Comprehension
13. What does the between-group sum of squares assess? What does the within-group sum of

squares assess?
ANS:

Between-group sum of squares looks at how different each group’s mean is from the overall
mean. Within-group sum of squares looks at how different each score in the group is from the
mean of that group.
PTS: 1
DIF: Medium
REF: Computing the F-Test Statistic
OBJ: How to compute and interpret the F statistic

COG: Analysis
14. Draw a table outlining the following example of a 3  3 factorial design: A researcher wants

to study jumping rope (skips per minute) for fifth, sixth, and seventh graders who practice 15
minutes, 30 minutes, or 60 minutes daily.
ANS:

The table might look like this:
Fifth graders
15 minutes
30 minutes
60 minutes

Sixth graders

Seventh graders

PTS: 1
DIF: Medium
REF: Different Flavors of ANOVA
OBJ: What analysis of variance is and when it is appropriate to use
COG: Comprehension
15. Why is it best not to perform multiple t-tests on the same data?
ANS:


When you perform multiple t-tests, you increase the Type I error rate to higher than an
acceptable rate.
PTS: 1
DIF: Medium

REF: So How Do I Interpret F(2, 27) = 8.80, p < .05?
OBJ: How to compute and interpret the F statistic
COG: Comprehension