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

504 CHAPTER 15 | Correlation
17
16
15
Z = 3
Large Cities
Number of Crimes
14
13
12
11
10
9
8
7
6
5
4
Z = 2
Medium Cities
3
2
Z = 1
Small Cities
1
1 2 3 4 5 6 7 8 9
Number of Churches
10 11 12 13 14 15 16 17
FIGURE 15.10
Hypothetical data showing the logical relationship between the number of churches and the number of crimes for three
groups of cities: those with small populations (Z = 1), those with medium populations (Z = 2), and those with large
populations (Z = 3).
the five cities with small populations, few churches, and little crime. The five points in the
upper right corner represent the five cities with large populations, many churches and a lot
of crime. The partial correlation controls population size by mathematically equalizing the
populations for all 15 cities. Population is increased for the five small cities, which also
increases churches and crime. Similarly, population is decreased for the five large cities,
which also decreases churches and crime. In Figure 15.10, imagine the five points in the
bottom left moving up and to the right so they overlap with the points in the center. At the
same time, the five points in the upper right move down and to the left so they also overlap
the points in the center. When population is equalized, the resulting set of 15 cities is shown
in Figure 15.11. Note that controlling the population appears to have eliminated the relationship
between churches and crime. This appearance is verified by the correlation for the
15 data points in Figure 15.11, which is r = 0, exactly the same as the partial correlation.