Russel-Research-Method-in-Anthropology

634 Chapter 20
9
8
7
Assaults
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5
4
3
2
–5 5 15 25 35 45 55 65 75 85 95 99+
Temperature (F)
Figure 20.6. The relationship between temperature and the rate of assault is nonlinear.
SOURCE: E. G. Cohn and J. Rotton, ‘‘Assault as a Function of Time and Temperature: A Moderator-Variable
Time-Series Analysis,’’ Journal of Personality and Social Psychology, Vol. 72, pp. 1322–1334. 1997 by the
American Psychological Association. Reprinted with permission.
U.S. cities. Then it begins to drop. Figure 20.6, from Cohn and Rotton (1997),
shows the dramatic pattern. The reasons for this pattern are very complex, but
it is clear from figure 20.6 that a simple, linear correlation is inadequate to
describe what’s going on.
If you get a very weak r for two variables that you believe, from theory or
from field research, are strongly related, then draw a scatterplot and check it
out. Scatterplots are available in all the major statistical packages and they are,
as you saw in figure 20.1, packed with information. For sheer intuitive power,
there is nothing like them.
Figure 20.7a, for example, is the same plot we saw in figure 20.1d of infant
mortality and per capita gross domestic product in 2000 for the 50 countries
in table 19.8. I’ve repeated the figure here because I want you to see it next to
figure 20.7b, which is a plot of infant mortality and the natural logarithm of
PCGDP.
The correlation between the original variables in figure 20.7a is –0.60. This
indicates a negative relation, but the scatterplot clearly shows that the relation
is not linear. Transforming each value of PCGDP into its natural logarithm
has the effect of making the distribution more normal, but it changes the interpretation
of the graph.
In figure 20.7b, the correlation is now a very strong 0.84, but countries
at the bottom, with $100 dollars in per capita domestic product, have to raise
their PCGDP by a factor of 10 in order to cut their infant mortality rate in
half. At $1,000 per year, countries only have to raise their per capita income