STRESS IS SOMETHINGthat we are all forced to deal with throughout life. It arises in our daily
interactions with those around us, in our interactions with the environment, in the face of an
impending exam, and, for many students, in the realization that they are required to take a
statistics course. Although most of us learn to respond and adapt to stress, the learning
process is often slow and painful. This rather grim preamble may not sound like a great way
to introduce a course on statistics, but it leads to a description of a practical research project,
which in turn illustrates a number of important statistical concepts. I was involved in a very
similar project a number of years ago, so this example is far from hypothetical.
A group of educators has put together a course designed to teach high school students
how to manage stress and the effect of stress management on self-esteem. They need an
outside investigator, however, who can tell them how well the course is working and, in
particular, whether students who take the course have higher self-esteem than do students
who have not taken the course. For the moment we will assume that we are charged with
the task of designing an evaluation of their program. The experiment that we design will
not be complete, but it will illustrate some of the issues involved in designing and analyz-
ing experiments and some of the statistical concepts with which you must be familiar.1.1 Important Terms
Although the program in stress management was designed for high school students, it
clearly would be impossible to apply it to the population of all high school students in the
country. First, there are far too many such students. Moreover, it makes no sense to apply a
program to everyone until we know whether it is a useful program. Instead of dealing with
the entire population of high school students, we will draw a sample of students from that
population and apply the program to them. But we will not draw just any old sample. We
would like to draw a random sample,though I will say shortly that truly random samples
are normally very impractical if not impossible. To draw a random sample, we would fol-
low a particular set of procedures to ensure that each and every element of the population
has an equal chance of being selected. (The common example to illustrate a random sam-
ple is to speak of putting names in a hat and drawing blindly. Although almost no one ever
does exactly that, it is a nice illustration of what we have in mind.) Having drawn our sam-
ple of students, we will randomly assignhalf the subjects to a group that will receive the
stress-management program and half to a group that will not receive the program.
This description has already brought out several concepts that need further elaboration;
namely, a population, a sample, a random sample, and random assignment. A population
is the entire collection of events (students’ scores, people’s incomes, rats’ running speeds,
etc.) in which you are interested. Thus, if you are interested in the self-esteem scores of all
high school students in the United States, then the collection of all high school students’
self-esteem scores would form a population—in this case, a population of many millions
of elements. If, on the other hand, you were interested in the self-esteem scores of high
school seniors only in Fairfax, Vermont (a town of fewer than 4000 inhabitants), the popu-
lation would consist of only about 100 elements.
The point is that a population can be of any size. They could range from a relatively small
set of numbers, which can be collected easily, to a large but finite set of numbers, which
would be impractical to collect in their entirety. In fact they can be an infinite set of numbers,
such as the set of all possible cartoon drawings that students could theoretically produce,
which would be impossible to collect. Unfortunately for us, the populations we are interested
in are usually very large. The practical consequence is that we seldom, if ever, measure entire
populations. Instead, we are forced to draw only a sampleof observations from that popula-
tion and to use that sample to infer something about the characteristics of the population.2 Chapter 1 Basic Concepts
random sample
randomly assign
population
sample