Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

SECTION 15.1 | Introduction 487
15.1 Introduction
LEARNING OBJECTIVE
1. Describe the information provided by the sign (+/–) and the numerical value of a
correlation.
Correlation is a statistical technique that is used to measure and describe the relationship
between two variables. Usually the two variables are simply observed as they exist naturally
in the environment—there is no attempt to control or manipulate the variables. For example, a
researcher could check high school records (with permission) to obtain a measure of each student’s
academic performance, and then survey each family to obtain a measure of income. The
resulting data could be used to determine whether there is relationship between high school
grades and family income. Notice that the researcher is not manipulating any student’s grade
or any family’s income, but is simply observing what occurs naturally. You also should notice
that a correlation requires two scores for each individual (one score from each of the two
variables). These scores normally are identified as X and Y. The pairs of scores can be listed in
a table, or they can be presented graphically in a scatter plot (Figure 15.2). In the scatter plot,
the values for the X variable are listed on the horizontal axis and the Y values are listed on the
vertical axis. Each individual is represented by a single point in the graph so that the horizontal
position corresponds to the individual’s X value and the vertical position corresponds to the
Y value. The value of a scatter plot is that it allows you to see any patterns or trends that exist
in the data. The scores in Figure 15.2, for example, show a clear relationship between family
income and student grades: as income increases, grades also increase.
■ The Characteristics of a Relationship
A correlation is a numerical value that describes and measures three characteristics of the
relationship between X and Y. These three characteristics are as follows
1. The Direction of the Relationship The sign of the correlation, positive or
negative, describes the direction of the relationship.
Person
A
B
C
D
E
F
G
H
I
J
K
L
M
N
Family
Income
(in $1000)
31
38
42
44
49
56
58
65
70
90
92
106
135
174
Student’s
Average
Grade
72
86
81
78
85
80
91
89
94
83
90
97
89
95
Student’s average grade
100
95
90
85
80
75
70
30 55 70 90 110 130 150 170 190
Family income (in $1000)
FIGURE 15.2
Correlational data showing the relationship between family income (X) and student grades (Y) for a sample of n = 14 high
school students. The scores are listed in order from lowest to highest family income and are shown in a scatter plot.