Russel-Research-Method-in-Anthropology

Sampling 155
off base in our thinking. Separating the population into gender strata might
just be creating unnecessary work. Worse, it might introduce unknown error.
If your guess about age and gender being related to desired number of children
is wrong, then using table 6.1 to create a sampling design will just make it
harder for you to discover your error.
Here are the rules on stratification: (1) If differences on a dependent variable
are large across strata like age, sex, ethnic group, and so on, then stratifying
a sample is a great idea. (2) If differences are small, then stratifying just
adds unnecessary work. (3) If you are uncertain about the independent variables
that could be at work in affecting your dependent variable, then leave
well enough alone and don’t stratify the sample. You can always stratify the
data you collect and test various stratification schemes in the analysis instead
of in the sampling.
Disproportionate Sampling
Disproportionate stratified random sampling is appropriate whenever an
important subpopulation is likely to be underrepresented in a simple random
sample or in a stratified random sample. Suppose you are doing a study of
factors affecting grade-point averages among college students. You suspect
that the independent variable called ‘‘race’’ has some effect on the dependent
variable.
Suppose further that 5% of the student population is African American and
that you have time and money to interview 400 students out of a population
of 8,000. If you took 10,000 samples of 400 each from the population (replacing
the 400 each time, of course), then the average number of African Americans
in all the samples would approach 20—that is, 5% of the sample.
But you are going to take one sample of 400. It might contain exactly 20
(5%) African Americans; on the other hand, it might contain just 5 (1.25%)
African Americans. To ensure that you have enough data on African American
students and on white students, you put the African Americans and the Whites
into separate strata and draw two random samples of 200 each. The African
Americans are disproportionately sampled by a factor of 10 (200 instead of
the expected 20).
Native Americans comprise just 8/10 of 1% of the population of the United
States. If you take a thousand samples of 1,000 Americans at random, you
expect to run into about eight Native Americans, on average, across all the
samples. (Some samples will have no Native Americans, and some may have
20, but, on average, you’ll get about eight.) Without disproportionate sampling,
Native Americans would be underrepresented in any national survey in
the United States. When Sugarman et al. (1994) ran the National Maternal and