Basic Statistics

DEFINITIONS OF TYPES OF SAMPLES 15

When it is feasible to study an entire population, one may learn more about the
population by making a careful study of a small sample than by taking limited mea-
surements on the entire population. In the example of the population of 4000 under-
graduates, the epidemiologist could afford the time and effort necessary to carefully
collect smoking histories and obtain information on type and amount of exercise
that 400 undergraduates do but not on all 4000 undergraduates. Accurate and de-
tailed information on a sample may be more informative than inaccurate or limited
information on the population.

2.2 DEFINITIONS OFTYPES OF SAMPLES

In this section we define simple random samples and two other types of random

samples.

2.2.1 Simple Random Samples

There are many types of samples; here we discuss the simplest kind of sample, called
a simple random sample. A sample is called a simple random sample if it meets two
criteria. First, every observational unit in the population has an equal chance of being
selected. Second, the selection of one unit has no effect on the selection of another
unit (all the units are selected independently). If we wish, for instance, to pick a
simple random sample of 4 cards from a deck of 52 cards, one way is to shuffle the
deck very thoroughly and then pick any 4 cards from the deck without looking at the
faces of the cards. Here, the deck of 52 is the population, and the 4 cards are the
sample.
If we look at the faces of the cards and decide to pick 4 clubs, we are not choosing
a simple random sample from the population, for many possible samples of 4 cards
(e.g., 2 diamonds and 2 hearts) have no chance at all of being selected. Also, if we
make four separate piles of the cards-one all hearts, one all diamonds, one all spades,
and one all clubs-and take 1 card from each pile at random, we still do not have a
simple random sample from the deck of 52 cards. Each card has an equal chance of
being selected, but once one heart is selected we cannot select another heart. Thus,
the selection of one unit has an effect on the selection of another unit.

2.2.2 Other Types of Random Samples

It is possible to have random samples that are not simple random samples. Suppose
that an investigator wishes to sample senior engineering students at a particular col-
lege, and that in this college there are appreciably more male engineering students
than female. If the investigator were to take a simple random sample, it would be
possible that very few female students would be sampled, perhaps too few to draw any
conclusions concerning female students. In cases such as this, a stratijied sampling
is often used. First, the investigator would divide the list of engineering students
into two subpopulations or strata, male and female. Second, separate simple random
samples could be drawn from each stratum. The sample sizes of these samples could