Russel-Research-Method-in-Anthropology

Bivariate Analysis: Testing Relations 639
really want to understand what makes the data messy in the first place? In
general, you cannot achieve understanding of messiness by cleaning things
up. Still, as in all aspects of research, be ready to break this rule, too, when
you think you’ll learn something by doing so.
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Violent crimes in the United States (for all
states and Washington, D.C.), per 100,000
population, by average annual pay, 1997.
Figure 20.9. The effect of outliers.
Violent crimes in the United States (for all
states, without Washington, D.C.), per
100,000 population, by average annual pay,
1997.
Figure 20.9a shows the relation between (1) the number of violent crimes
per 100,000 people in each of the 50 U.S. states and Washington, D.C., in
1997 and (2) the average annual pay for people in the 50 states plus Washington,
D.C. Figure 20.9b shows exactly the same thing, but without including
the data from Washington, D.C. The correlation between the two variables
with D.C. in the picture is .44. When we leave out the data for D.C., the correlation
sinks to .19.
That’s because the violent crime rate in Washington, D.C., was an appalling
2,024 per 100,000 population in 1997, and the average annual pay there was
$46,775. For the 50 states in the United States, the next highest violent crime
rate, in Florida, was half that of D.C., and the next highest average pay, in
Connecticut, was 17% lower than that in D.C.
The sizes of the dots in figures 20.9a and b indicate the influence each data
point has on the correlation—that is, how much the correlation would change
if you took each data point out of the calculation. The legend for this little
trick is between the figures. That huge circle in the upper-right of figure 20.9a
is Washington, D.C. To repeat: Pearson’s r for the two variables in figure 20.9a
is 0.442 and for figure 20.9b, without D.C., it’s 0.190. Now, that’s an outlier.