Russel-Research-Method-in-Anthropology

184 Chapter 7
in a Mexican village to determine how many have ever worked illegally in the
United States. How many of those men do you need to interview to ensure a
95% probability sample, with a 5% confidence interval? Answer: Since we
have no idea what the percentage is that we’re trying to estimate, we set P and
Q at .5 each in formula 7.5. Solving for n (sample size), we get:
n (1.96) 2 (.5)(.5)/(.05) 2 384.16
which we round up to 385. Then we apply the finite population correction:
n
385
1(384/540) 225
This is still a hefty percentage of the 540 people in the population, but it’s
a lot smaller than the 385 called for by the standard formula.
Settling for Bigger Confidence Intervals
If we were willing to settle for a 10% confidence interval, we’d need only
82 people in this example, but the trade-off would be substantial. If 65 out of
225, or 29%, reported that they had worked illegally in the United States, we
would be 68% confident that from 24% to 34% really did, and 95% confident
that 19% to 39% did. But if 24 out of 82 (the same 29%) reported having
participated in extreme sports, we’d be 68% confident that the true figure was
between 19% and 39%, and 95% confident that it was between 9% and 49%.
With a spread like that, you wouldn’t want to bet much on the sample statistic
of 29%.
If it weren’t for ethnography, this would be a major problem in taking samples
from small populations—the kind we often study in anthropology. If
you’ve been doing ethnography in a community of 1,500 people for 6 months,
however, you may feel comfortable taking a confidence interval of 10%
because you are personally (not statistically) confident that your intuition
about the group will help you interpret the results of a small sample.
Another Catch
All of this discussion has been about estimating single parameters, whether
proportions or means. You will often want to measure the interaction among
several variables at once. Suppose you study a population of wealthy, middleclass,
and poor people. That’s three kinds of people. Now add two sexes, male
and female (that makes six kinds of people) and two colors, black and white
(that makes 12 kinds). If you want to know how all those independent vari-