fiasco, the Digest went bankrupt and out of business the following year. If you are wondering why the
Digest was wrong this time with essentially the same techniques used in earlier years, understand that
1936 was the heart of the Depression. In earlier years the lists used to select the sample may have been
more reflective of the voting public, but in 1936 only the well-to-do, Republicans generally, were in the
Digest ’s sample taken from its own subscriber lists, telephone books, etc.
We look more carefully at sources of bias in data collection in Chapter 8 , but the point you need to
remember as you progress through the next couple of chapters is that conclusions based on data are only
meaningful to the extent that the data are representative of the population being studied.
In an experiment or an observational study, the analogous issue to a biased sample in a survey is the
danger of treatment and control groups being somehow systematically different. For example, suppose we
wish to study the effects of exercise on stress reduction. We let 100 volunteers for the study decide if they
want to be in the group that exercises or in the group that doesn’t. There are many reasons why one group
might be systematically different from the other, but the point is that any comparisons between these two
groups is confounded by the fact that the two groups could be different in substantive ways.
Random Variables
We consider random variables in detail in Chapter 9 , but it is important at the beginning to understand the
role they play in statistics. A random variable can be thought of as a numerical outcome of a random
phenomenon or an experiment. As an example of a discrete random variable, we can toss three fair coins,
and let X be the count of heads; we then note that X can take on the values 0, 1, 2, or 3. An example of a
continuous random variable might be the number of centimeters a child grows from age 5 to age 6.
An understanding of random variables is what will allow us to use our knowledge of probability
(Chapter 9 ) in statistical inference. Random variables give rise to probability distributions (a way of
matching outcomes with their probabilities of success), which in turn give rise to our ability to make
probabilistic statements about sampling distributions (distributions of sample statistics such as means
and proportions). This language, in turn, allows us to talk about the probability of a given sample being as
different from expected as it is. This is the basis for inference. All of this will be examined in detail later
in this book, but it’s important to remember that random variables are the foundation for inferential
statistics.
There are a number of definitions in this chapter and many more throughout the book (summarized in
the Glossary). Although you may not be asked specific definitions on the AP Exam, you are expected to
have the working vocabulary needed to understand any statistical situation you might be presented with. In
other words, you need to know and understand the vocabulary presented in the course in order to do your
best on the AP Exam.
Rapid Review
True or False: A study is done in which the data collected are the number of cars a person has owned
in his or her lifetime. This is an example of qualitative data.