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The Essentials of Biostatistics for Physicians, Nurses, and Clinicians,
First Edition. Michael R. Chernick.
© 2011 John Wiley & Sons, Inc. Published 2011 by John Wiley & Sons, Inc.

CHAPTER 2

2. Sampling from Populations

Populations

One of the key aspects of statistics and statistical inference is to draw

conclusions about a population based on a sample. Our ability to make
good inferences requires an intelligent design and must include some
form of random sampling. Random sampling is needed so that the
sample can be analyzed based on the probability mechanism that gener-
ates the sample. This way, estimates based on the sample data can be
obtained, and inference drawn based on the probability distribution
associated with the sample.
To illustrate, suppose we select fi ve students at random from a math
class of 40 students. We will formally defi ne random sampling later. If
we give a math test to these students based on the material they have
studied in the class, and we average the fi ve scores, we will have a
prediction of what the class average for that test will be. This prediction
will be unbiased (meaning that if we repeatedly took samples of and
averaged them, the average of the averages will approach the class
average).
In practice, we do not repeat the process, but we do draw inference
based on the properties of the sampling procedure. On the other hand,
suppose we selected the fi ve students to be the ones with the highest
class average thus far in the class. In that case, we would not have a