Basic Statistics

APPLICATION OF SAMPLING METHODS IN BIOMEDICAL STUDIES 19

to obtain random digits. Note that each program has its own way of generating the
random numbers and displaying them.

2.3.3 Sampling With and Without Replacement

The first example, in which 5 tags were drawn from a box containing 98 tags marked
with blood cholesterol measurements, illustrates simple random sampling with re-
placement. The tags were removed from the container as they were chosen and were
replaced, so that the same individual could be sampled again. This is called sampling
with replacement since the tag is replaced into the container (the population). For
theoretical purposes, sampling with replacement is usually assumed. In the blood
cholesterol example, if we replace the tag, it is possible for the same tag to be drawn
more than once. If we sample using numbers from a random number table, it is
possible that the same random number will reappear, so we will be sampling with
replacement if we simply take all the random numbers as they appear.
If we do not replace each tag after it is drawn, we are sampling without replacement.
If we wish to sample without replacement from a random number table or from a
statistical program, we will not use a random number if it is a duplicate of one already
drawn.
The reason that sampling with replacement is sometimes discussed, whereas sam-
pling without replacement is actually performed, is that the statistical formulas are
simpler for sampling with replacement. A moment’s consideration should convince
the reader that it makes little difference whether or not we replace when the sample
size is small compared with the size of the population. Small is often taken to mean
that the sample size is < 5 or 10% of the population size. The symbol “<” denotes
“less than.” If the sample size is an appreciable proportion of the population, special
formulas need to be used (see Kalton [1983], Barnett [1994], Kish [1965], or other
textbooks devoted to sampling) for these formulas. Sampling with replacement is not
practical in most studies.

2.4 APPLICATION OF SAMPLING METHODS IN BIOMEDICAL
STUDIES

In Section 2.4.1 we discuss the characteristics of a good sample. How sampling is
usually done for the types of biomedical studies described in Chapter 1 is described
in Sections 2.4.2 to 2.4.5. The reasons for the use and the nonuse of simple random
sampling can be seen from the discussion of sampling plans used in biomedical
studies.

2.4.1 Characteristics of a Good Sampling Plan

What is a good sampling plan? How do we distinguish a good one from a bad one?
Here, we briefly describe the characteristics of a good sampling plan.
The first criterion for a good sample is feasibility. The plan should be feasible in
terms of what is being sampled, how it occurs, what personnel are available to take