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

SECTION 15.3 | Using and Interpreting the Pearson Correlation 499
■ Outliers
An outlier is an individual with X and/or Y values that are substantially different (larger or
smaller) from the values obtained for the other individuals in the data set. The data point
of a single outlier can have a dramatic influence on the value obtained for the correlation.
This effect is illustrated in Figure 15.7. Figure 15.7(a) shows a set of n = 5 data points for
which the correlation between the X and Y variables is nearly zero (actually r = –0.08).
In Figure 15.7(b), one extreme data point (14, 12) has been added to the original data set.
When this outlier is included in the analysis, a strong, positive correlation emerges (now
r = + 0.85). Note that the single outlier drastically alters the value for the correlation
and thereby can affect one’s interpretation of the relationship between variables X and Y.
Without the outlier, one would conclude there is no relationship between the two variables.
With the extreme data point, r = +0.85 implies a strong relationship with Y increasing
consistently as X increases. The problem of outliers is a good reason for looking at a scatter
plot, instead of simply basing your interpretation on the numerical value of the correlation.
If you only “go by the numbers,” you might overlook the fact that one extreme data point
inflated the size of the correlation.
■ Correlation and the Strength of the Relationship
A correlation measures the degree of relationship between two variables on a scale from
0–1.00. Although this number provides a measure of the degree of relationship, many
researchers prefer to square the correlation and use the resulting value to measure the
strength of the relationship.
(a)
12
(b)
12
Y values
10
8
6
r = –0.08
Y values
10
8
6
r = 0.85
4
4
2
2
2 4 6 8 10 12 14
2 4 6 8 10 12 14
X values
X values
Original Data
Subject X Y
A
B
C
D
E
1
3
6
4
5
3
5
4
1
2
Data with Outlier Included
Subject X Y
A
B
C
D
E
F
1
3
6
4
5
14
3
5
4
1
2
12
FIGURE 15.7
A demonstration of how one extreme data point (an outlier) can influence the value of a correlation.