Russel-Research-Method-in-Anthropology

Sampling Theory 179
Calculating Sample Size for Estimating Means
Nowwearereally close to answering the question about sample size. Suppose
we want to get the standard error down to RM200 instead of RM400. We
need to solve the following equation:
SEM sd 4,000/n 200
n
Solving for n:
n 4,000
200 20 n 202 400
In other words, to reduce the standard error of the mean from RM400 to
RM200, we have to increase the sample size from 100 to 400 people.
Suppose we increase the sample to 400 and we still get a mean of
RM12,600 and a standard deviation of RM4,000. The standard error of the
mean would then be RM200, and we could estimate, with 95% confidence,
that the true mean of the population was between RM12,208 and 12,992. With
just 100 people in the sample, the 95% confidence limits were RM11,816 and
RM13,384. As the standard error goes down, we get narrower—that is, more
precise—confidence limits.
Let’s carry this forward another step. If we wanted to get the standard error
down to RM100 and the 95% confidence interval down to RM200 from
RM400, we would need a sample of 1,600 people. There is a pattern here. To
cut the 95% confidence interval in half, from RM800 to RM400, we had to
quadruple the sample size from 100 to 400. To cut the interval in half again,
to RM200, we’d need to quadruple the sample size again, from 400 to 1,600.
There is another pattern, too. If we want to increase our confidence from
95% to 99% that the true mean of the population is within a particular confidence
interval, we can raise the multiplier in formula 7.2 from roughly 2 standard
deviations to roughly 3. Using the confidence interval of RM400, we
would calculate:
n 3 4,000
400
30 n 30 3 900
We need 900 people, not 400, to be about 99% confident that our sample mean
is within RM400, plus or minus, of the parameter.
Small Samples: The t-Distribution
In anthropology, even doing surveys, we often have no choice about the
matter and have to use small samples.