Chapter 5: Ice Cream and Crime: Computing Correlation Coefficients
Test Bank
MULTIPLE CHOICE
1. Who is responsible for the invention of the Pearson product–moment correlation coefficient?
a. Pearson Fisher
b. Karl Pearson
c. Karl Fisher
d. Fisher Pearson
ANS: B
PTS: 1
REF: What Are Correlations All About?
COG: Knowledge

DIF: Easy
OBJ: What correlations are and how they work

2. When interested in examining how one variable changes in relation to another, which of the

following descriptive statistics would you want to use?
a. Mean
b. Variance
c. Correlation
d. Standard Deviation
ANS: C
PTS: 1
REF: What Are Correlations All About?
COG: Knowledge

DIF: Easy
OBJ: What correlations are and how they work



ANS: B
PTS: 1
REF: What Are Correlations All About?
COG: Knowledge

DIF: Medium
OBJ: What correlations are and how they work

6. Which of the following illustrates the range of possible values of Pearson’s product–moment

correlation coefficient?
a. -.01 to .01
b. -1.0 to 1.0
c. -2.0 to 2.0
d. -3.0 to 3.0
ANS: B
PTS: 1
DIF: Easy
REF: Types of Correlation Coefficients: Flavor 1 and Flavor 2
OBJ: How to interpret the value of the correlation coefficient

COG: Knowledge

7. If variables change in the same direction, what type of correlation is this called?
a. Positive correlation
b. Negative correlation
c. Positive causation
d. Negative causation
ANS: A


COG: Knowledge

10. Pearson’s product–moment correlation coefficient is represented by the following letter:
a. r
b. p
c. c
d. z
ANS: A
PTS: 1
DIF: Easy
REF: Types of Correlation Coefficients: Flavor 1 and Flavor 2


OBJ: What correlations are and how they work

COG: Knowledge

11. What would you use to visually represent a correlation?
a. Histogram
b. Polygon
c. Line graph
d. Scatterplot
ANS: D
PTS: 1
DIF: Easy
REF: A Visual Picture of a Correlation: The Scatterplot
OBJ: What correlations are and how they work

COG: Knowledge


14. If the correlation between variables is .70, what percentage of the variance is shared variance?
a. 70%
b. 51%
c. 49%
d. 30%
ANS: C
PTS: 1
DIF: Medium
REF: A Determined Effort: Squaring the Correlation Coefficient
OBJ: How to interpret the value of the correlation coefficient
COG: Application
15. If the correlation between variables is .70, what percentage of the variance is not shared

variance?
a. 70%
b. 51%
c. 49%
d. 30%
ANS: B
PTS: 1
DIF: Medium
REF: A Determined Effort: Squaring the Correlation Coefficient


OBJ: How to interpret the value of the correlation coefficient

COG: Application

16. If the correlation between variables is .80, what is the coefficient of determination?


REF: Using-Your-Thumb Rule
COG: Application

19. Which of the following correlations would be interpreted a strong relationship?
a. .39
b. .59
c. .79
d. .89
ANS: C
PTS: 1
DIF: Medium
OBJ: How to interpret the value of the correlation coefficient

REF: Using-Your-Thumb Rule
COG: Application

20. Which of the following correlations would be interpreted a moderate relationship?
a. .25
b. .35
c. .45
d. .65
ANS: C
PTS: 1
DIF: Medium
OBJ: How to interpret the value of the correlation coefficient

REF: Using-Your-Thumb Rule
COG: Application


b. -.22
c. .19
d. -.96
ANS: C
PTS: 1
DIF: Medium
OBJ: How to interpret the value of the correlation coefficient

REF: Using-Your-Thumb Rule
COG: Application

24. This is another word for a positive correlation:
a. Inverse correlation
b. Negative correlation
c. Strong correlation
d. Direct correlation
ANS: D
PTS: 1
DIF: Easy
REF: Types of Correlation Coefficients: Flavor 1 and Flavor 2
OBJ: What correlations are and how they work

COG: Knowledge

25. This is another word for a negative correlation:
a. Direct correlation
b. Weak correlation
c. Strong correlation
d. Indirect correlation
ANS: D

DIF: Easy
REF: Using Excel to Create a Scatterplot
OBJ: What correlations are and how they work

COG: Comprehension

28. The coefficient of determination is equal to
a. The square of the Pearson product–moment correlation coefficient
b. The square of the phi coefficient
c. The square root of the Pearson product–moment correlation coefficient
d. The square root of the phi coefficient
ANS: A
PTS: 1
DIF: Medium
REF: A Determined Effort: Squaring the Correlation Coefficient
OBJ: How to interpret the value of the correlation coefficient
COG: Knowledge
29. The amount of unexplained variance in a relationship between two variables is called

_______.
a. Coefficient of determination
b. Coefficient of alienation
c. Pearson’s product–moment correlation coefficient
d. Phi coefficient
ANS: B
PTS: 1
DIF: Medium
REF: A Determined Effort: Squaring the Correlation Coefficient
OBJ: How to interpret the value of the correlation coefficient
COG: Knowledge

a. A line sloping upward
b. A line sloping downward
c. A horizontal line
d. A vertical line
ANS: C
PTS: 1
DIF: Medium
REF: A Visual Picture of a Correlation: The Scatterplot
OBJ: What correlations are and how they work

COG: Application

33. This is used to summarize the correlations between a set of variables:
a. Scatterplot
b. Correlation
c. Correlation matrix
d. Scatterplot matrix
ANS: C
PTS: 1
DIF: Medium
REF: Bunches of Correlations: The Correlation Matrix
OBJ: Using the Correlation tool in the Data Analysis tools to compute a correlation and a correlation
matrix COG:
Knowledge
34. If the range of one or both of the variables is restricted, the correlation will be _______.
a. Strengthened
b. Reduced
c. The same
d. It cannot be determined.
ANS: B

REF: Other Cool Correlations
OBJ: What other types of correlations exist and when to use them
COG: Comprehension


37. If you wanted to compute the correlation between two ordinal-level variables, which type of

correlation should you use?
a. Point biserial
b. Phi
c. Spearman rank
d. Pearson
ANS: C
PTS: 1
DIF: Medium
REF: Other Cool Correlations
OBJ: What other types of correlations exist and when to use them
COG: Comprehension
38. If you wanted to compute the correlation between one nominal-level variable and one

interval-level variable, which type of correlation should you use?
a. Point biserial
b. Phi
c. Spearman rank
d. Pearson
ANS: A
PTS: 1
DIF: Medium
REF: Other Cool Correlations
OBJ: What other types of correlations exist and when to use them

c. Correlation coefficient
d. Psi index
ANS: C
PTS: 1
REF: What Are Correlations All About?

DIF: Medium


OBJ: How to interpret the value of the correlation coefficient

COG: Knowledge

42. The Pearson product–moment correlation examines the relationship between what type of

variables?
a. Discontinuous
b. Continuous
c. Nominal level
d. Large
ANS: B
PTS: 1
REF: What Are Correlations All About?
COG: Knowledge

DIF: Medium
OBJ: What correlations are and how they work

43. This measure is equal to the percentage of variance in one variable that is accounted for by the


d. No correlation
ANS: C
PTS: 1
DIF: Medium
REF: Types of Correlation Coefficients: Flavor 1 and Flavor 2
OBJ: What correlations are and how they work

COG: Knowledge

46. If X decreases in value as Y decreases, what type of correlation exists?
a. Positive correlation
b. Negative correlation
c. Neutral correlation
d. No correlation
ANS: A
PTS: 1
DIF: Medium
REF: Types of Correlation Coefficients: Flavor 1 and Flavor 2
OBJ: What correlations are and how they work

COG: Knowledge


47. If X increases in value as Y increases, what type of correlation exists?
a. Positive correlation
b. Negative correlation
c. No correlation
d. Inverse correlation
ANS: A
PTS: 1

DIF: Medium
REF: Types of Correlation Coefficients: Flavor 1 and Flavor 2
OBJ: What correlations are and how they work

COG: Application

50. If X increases in value as Y increases in value, what type of correlation exists?
a. Positive correlation
b. Absolute correlation
c. Negative correlation
d. Nonabsolute correlation
ANS: A
PTS: 1
DIF: Medium
REF: Types of Correlation Coefficients: Flavor 1 and Flavor 2
OBJ: What correlations are and how they work

COG: Comprehension

51. If X decreases in value as Y increases in value, what type of correlation exists?
a. Positive correlation
b. Absolute correlation
c. Negative correlation
d. Nonabsolute correlation
ANS: C
PTS: 1
DIF: Medium
REF: Types of Correlation Coefficients: Flavor 1 and Flavor 2
OBJ: What correlations are and how they work



COG: Knowledge

4. Correlation coefficients describe every individual person in your data set.
ANS: F
PTS: 1
DIF: Easy
REF: Types of Correlation Coefficients: Flavor 1 and Flavor 2
OBJ: What correlations are and how they work

COG: Knowledge

5. The coefficient of determination is more precise than using a correlation coefficient alone.
ANS: T
PTS: 1
DIF: Medium
REF: A Determined Effort: Squaring the Correlation Coefficient
OBJ: How to interpret the value of the correlation coefficient
COG: Comprehension
6. If two variables are correlated, this implies that one variable causes the other.
ANS: F
PTS: 1
DIF: Medium
REF: As More Ice Cream Is Eaten, the Crime Rate Goes Up (or Association Versus Causality)
OBJ: What correlations are and how they work
COG: Comprehension
7. In certain cases, Pearson’s product–moment correlation coefficient can have values greater

than 1.
ANS: F


If variables change in the same direction, then there is a direct (or positive) correlation. If
variables change in opposite directions, then there is an indirect (or negative) correlation.
PTS: 1
DIF: Medium
REF: Types of Correlation Coefficients: Flavor 1 and Flavor 2
OBJ: What correlations are and how they work

COG: Comprehension

2. Is a correlation of 0.6 stronger than a correlation of -0.9? Why or why not?
ANS:

A correlation of -0.9 is stronger than a correlation of 0.6 because the absolute value of the
correlation reflects the strength of the correlation.
PTS: 1
DIF: Medium
REF: Types of Correlation Coefficients: Flavor 1 and Flavor 2
OBJ: How to interpret the value of the correlation coefficient

COG: Application

3. A correlation coefficient comparing exercise and body mass is -.67. What does this say about

the relationship between exercise and weight?
ANS:

If exercise / body mass = -.67, then there is a strong indirect or negative relationship; greater
exercise is associated with less body mass.
PTS: 1

PTS: 1
DIF: Medium
REF: Computing a Simple Correlation Coefficient
OBJ: How to compute a single correlation coefficient
COG: Comprehension
6. What is the purpose of a scatterplot?
ANS:

The shape of the plotted data points on a scatterplot or scattergram can indicate if the
relationship between the variables is positive (direct), negative (indirect), if there is no
relationship, or if the relationship is curvilinear.
PTS: 1
DIF: Medium
REF: A Visual Picture of a Correlation: The Scatterplot
OBJ: What correlations are and how they work
COG: Comprehension
7. Why will you rarely find a perfect correlation between any two variables?
ANS:

You will rarely find a perfect correlation between any two variables because few variables are
exactly alike.
PTS: 1
DIF: Medium
REF: A Visual Picture of a Correlation: The Scatterplot
OBJ: What correlations are and how they work
COG: Comprehension
8. Give an example of two variables that may have a curvilinear relationship instead of a linear

one.
ANS:

OBJ: What correlations are and how they work

COG: Comprehension

11. What is a correlation coefficient, and what is its range?
ANS:

A correlation coefficient is a numerical index that reflects the relationship between two
variables. The value of the correlation coefficient ranges from -1.0 to +1.0.
PTS: 1
DIF: Medium
REF: Types of Correlation Coefficients: Flavor 1 and Flavor 2
OBJ: How to interpret the value of the correlation coefficient

COG: Knowledge

12. Under what circumstances would you use the phi coefficient?
ANS:

X = nominal variable and Y = nominal variable
PTS: 1
DIF: Medium
REF: Other Cool Correlations
OBJ: What other types of correlations exist and when to use them
COG: Comprehension
13. Under what circumstances would you use the Pearson correlation?
ANS:

X = interval variable and Y = interval variable
PTS: 1

REF: Other Cool Correlations
OBJ: What other types of correlations exist and when to use them
COG: Comprehension
17. In order to calculate a Pearson’s r between the hours college students study in a week and

their GPAs, it would be best to have the students report their cumulative GPA as a number out
to the hundredths rather than as pre-established categories (A = 4, B = 3, C = 2, D = 1, F = 0).
Please explain why that is.
ANS:

Pearson’s correlations need to be conducted with continuous variables, and the numerical
equivalent of a letter grade is categorical data.
PTS: 1
DIF: Medium
REF: Other Cool Correlations
OBJ: What correlations are and how they work
COG: Application
18. A sample of typical undergraduate students is very likely to have a range of GPAs from 0.0 to

4.0, whereas graduate students are often required to have good grades (e.g., from 3.0 to 4.0).
Please explain what influence these two different ranges of GPA would have on any
correlations calculated on these two separate groups of students.
ANS:

Correlations reflect the amount of variability that is shared between two variables and what
they have in common. The graduate students’ GPAs do not vary nearly as much as the
undergraduate students (the data are more restricted), so correlations using the graduate
students’ GPAs are more likely to be close to zero than correlations using the undergraduates’
GPAs.
PTS: 1

PTS: 1
DIF: Hard
REF: Using Excel to Create a Scatterplot
OBJ: What correlations are and how they work
COG: Application