Russel-Research-Method-in-Anthropology

Sampling Theory 183
and we solve for n:
n 1.96 2 (.38)(.62)/.02 2
n (3.842)(.38)(.62)/.0004 2,263
Generalizing, then, the formula for ‘‘sample size when estimating proportions
in a large population’’ is:
n z 2 (P)(Q)/(confidence interval) 2 Formula 7.5
where z is the area under the normal curve that corresponds to the confidence
limit we choose. When the confidence limit is 95%, then z is 1.96. When the
confidence limit is 99%, then z is 2.58. And so on.
If we start out fresh and have no prior estimate of P, we follow table 7.4 and
set P and Q to .5 each. This maximizes the size of the sample for any given
confidence interval or confidence level. If we want a sample that produces an
estimate of a proportion with a confidence interval of 2 percentage points and
we want to be 95% confident in that estimate, we calculate:
n (sample size) (1.96) 2 (.5)(.5)/(.02) 2 2,401
In time allocation studies, we estimate the proportion of various behaviors
by observing a sample of behaviors. We’ll deal with this in chapter 15, on
methods of direct observation (see especially table 15.2).
Estimating Proportions in Samples for Smaller Populations
This general formula, 7.5, is independent of the size of the population. Florida
has a population of about 17 million. A sample of 400 is .000024 of 17
million; a sample of 2,402 is .00014 of 17 million. Both proportions are
microscopic. A sample of 400 from a population of 1 million gets you the
same confidence level and the same confidence interval as you get with a sample
of 400 from a population of 17 million.
Often, though, we want to take samples from relatively small populations.
The key word here is ‘‘relatively.’’ When formula 7.4 or 7.5 calls for a sample
that turns out to be 5% or more of the total population, we apply the finite
population correction. The formula (from Cochran 1977) is:
n
n
1(n1/N)
Formula 7.6
where n is the sample size calculated from formula 7.5; n (read: n-prime) is
the new value for the sample size; and N is the size of the total population
from which n is being drawn.
Here’s an example. Suppose you are sampling the 540 resident adult men