METHODS OF SELECTING SIMPLE RANDOM SAMPLES 17Two other questions should be considered: Why do we want a simple random
sample, and how can we obtain one?2.2.3 Reasons for Using Simple Random Samples
The main advantage of using a simple random sample is that there are mathemati-
cal methods for these samples that enable the research worker to draw conclusions
concerning the population. For other types of random samples, we can use simi-
lar mathematical methods to reach conclusions, but the formulas are slightly more
complex. For other types of samples, the formulas are more complex and these math-
ematical tools do not apply. This means that when you want to draw conclusions from
your sample to the population you sampled from, there will be no theoretical basis for
your conclusions. This does not necessarily mean that the conclusions are incorrect.
Many researchers try mainly to avoid allowing personal bias to affect their selection
of the sample. In practice, for many medical studies simple random samples are not
used, for a variety of practical reasons.
2.3 METHODS OF SELECTING SIMPLE RANDOM SAMPLES
Next, we describe how to take simple random samples simply by physically drawing
a small sample from a population. Random numbers are discussed and it is shown
how they can be used to obtain a simple random sample.
2.3.1 Selection of a Small Simple Random Sample
Table 2.1 gives a set of 98 blood cholesterol measurements of untreated men aged
40-49. Each horizontal row in Table 2.1 contains 10 measurements except the last
row, which contains eight measurements. For illustrative purposes, these 98 blood
cholesterols may be considered as a population from which we wish to select a simple
random sample of size 5, say. Since the population is quite small, one way of picking
a random sample from it would be to copy each measurement on a small tag. By
mixing the tags well in a large container, we can draw out one tag (without looking
at the writing on the tags in the container), write down the result, and then replace
the tag into the container. If we follow this procedure five times, we obtain a simple
random sample of five measurements.
2.3.2 Tables of Random Numbers
In larger populations, it becomes impracticable to make a tag for each member of the
population and then stir them in a container, so one must attempt to obtain a random
sample in some other way. Sometimes it is possible to obtain a list of the population;
then, we can easily draw a random sample by using a table of random numbers or
from the output of a statistical program.
Table A.l of Appendix A is a table of random digits. These single digits have
been obtained by a process that is equivalent to drawing repeatedly (and immediately