Russel-Research-Method-in-Anthropology

632 Chapter 20
.26. This means that in fewer than five tests in a hundred would we expect to
find the correlation smaller than .14 or larger than .26. In other words, we are
95% confident that the true r for the population (written , which is the Greek
letter rho) is somewhere between .14 and .26.
By contrast, the 95% confidence limits for an r of .30 in a random sample
of 30 is not significant at all; the true correlation could be 0, and our sample
statistic of .30 could be the result of sampling error.
The 95% confidence limits for an r of .40 in a random sample of 30 is statistically
significant. We can be 95% certain that the true correlation in the population
() is no less than .05 and no larger than .67. This is a statistically significant
finding, but not much to go on insofar as external validity is
concerned. You’ll notice that with large samples (like 1,000), even very small
correlations are significant at the .01 level.
On the other hand, just because a statistical value is significant doesn’t
mean that it’s important or useful in understanding how the world works.
Looking at the lower half of table 20.18, we see that even an r value of .40 is
statistically insignificant when the sample is as small as 30. If you look at the
spread in the confidence limits for both halves of table 20.18, you will notice
something very interesting: A sample of 1,000 offers some advantage over a
sample of 400 for bivariate tests, but the difference is small and the costs of
the larger sample could be very high, especially if you’re collecting all your
own data.
Recall from chapter 7, on sampling, that in order to halve the confidence
interval you have to quadruple the sample size. Where the unit cost of data is
high—as in research based on direct observation of behavior or on face-toface
interviews—the point of diminishing returns on sample size is reached
quickly. Where the unit cost of data is low—as it is with mailed questionnaires
or with telephone surveys—a larger sample is worth trying for.
Nonlinear Relations
And now for something different. All the examples I’ve used so far have
been for linear relations where the best-fitting ‘‘curve’’ on a bivariate scatterplot
is a straight line. A lot of really interesting relations, however, are nonlinear.
Smits et al. (1998) measured the strength of association between the educational
level of spouses in 65 countries and how that relates to industrialization.
Figure 20.5 shows what they found. It’s the relation between per capita energy
consumption (a measure of industrialization and hence of economic development)
and the amount of educational homogamy in those 65 countries.