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

498 CHAPTER 15 | Correlation
60
Number of serious crimes
50
40
30
20
FIGURE 15.5
Hypothetical data showing the
logical relationship between
the number of churches and
the number of serious crimes
for a sample of U.S. cities.
10
0 10 20
30 40 50 60 70
Number of churches
■ Correlation and Restricted Range
Whenever a correlation is computed from scores that do not represent the full range of possible
values, you should be cautious in interpreting the correlation. Suppose, for example,
you are interested in the relationship between IQ and creativity. If you select a sample of
your fellow college students, your data probably will represent only a limited range of IQ
scores (most likely from 110–130). The correlation within this restricted range could be
completely different from the correlation that would be obtained from a full range of IQ
scores. For example, Figure 15.6 shows a strong positive relationship between X and Y
when the entire range of scores is considered. However, this relationship is obscured when
the data are limited to a restricted range.
To be safe, you should not generalize any correlation beyond the range of data represented
in the sample. For a correlation to provide an accurate description for the general
population, there should be a wide range of X and Y values in the data.
FIGURE 15.6
In this example, the full range of X and
Y values shows a strong, positive correlation,
but the restricted range of scores
produces a correlation near zero.
Y values
X values
X values restricted
to a limited range