Russel-Research-Method-in-Anthropology

584 Chapter 19
describe a set of data. But in comparative perspective, they help us produce
theory; that is, they help us develop ideas about what causes things, and what
those things, in turn, cause. We’ll compare cases when we get to bivariate
analysis in the chapter coming up next.
The Logic of Hypothesis Testing
One thing we can do, however, is test whether the mean of a sample of data,
x, is likely to represent the mean of the population, , from which the sample
was drawn. We’ll test whether the mean of FEMILLIT in table 19.7 is likely
to represent the mean of the population of 50 countries. To do this, we will
use the logic of hypothesis testing. This logic is used very widely—not just in
the social sciences, but in all probabilistic sciences, including meteorology
and genetics, for example.
The key to this logic is the statement that we can test whether the mean of
the sample is likely to represent the mean of the population. Here’s how the
logic works.
1. First, we set up a null hypothesis, written H 0 , which states that there is no difference
between the sample mean and the mean of the population from which the
sample was drawn.
2. Then we set up the research hypothesis (also called the alternative hypothesis),
written H 1 , which states that, in fact, the sample mean and the mean of the
population from which the sample was drawn are different.
3. Next, we decide whether the research hypothesis is only about magnitude or is
directional. IfH 1 is only about magnitude—that is, it’s nondirectional—then it
can be stated just as it was in (2) above: The sample mean and the mean of the
population from which the sample was drawn are different. Period.
If H 1 is directional, then it has to be stated differently: The sample mean is
[bigger than] [smaller than] the mean of the population from which the sample
was drawn.
This decision determines whether we will use a one-tailed or a two-tailed
test of the null hypothesis.
To understand the concept of one-tailed and two-tailed tests, suppose you
have a bell curve that represents the distribution of means from many samples
of a population. Sample means are like any other variable. Each sample has a
mean, and if you took thousands of samples from a population you’d get a
distribution of means (or proportions). Some would be large, some small, and
some exactly the same as the true mean of the population. The distribution