Chapter 7
Comparing Two Populations
7.1
Study Suggestions
Only one new formula appears in Chapter 7, the con-
fidence interval for the difference of two proportions.
(It is also stated that the hypothesis test for compar-
ing two proportions reduces to the familiar Fisher’s
test.)
Chapter 7 focuses on four types of studies,
either finite populations or Bernoulli trials matched
with either controlled or observational studies. It is
important to note that a controlled study must have
subjects assigned to treatments by randomization.
A colleague of mine who has taught introductory
statistics several times from early versions of my text
once remarked that Chapter 7 provides perhaps the
best illustration of how my approach to introductory
statistics differs from the standard approach. A text
that follows the standard approach does not empha-
size, and in fact may not even mention, the differ-
ences between these four types of studies because,
after all, the mathematical derivations and formulas
are the same for each study type. The four types of
studies differ greatly, however, in how they are ex-
ecuted, and how they should be interpreted. If, like
me, your teacher wants you to become a critical inter-
preter of the research and conclusions of others, then
these latter issues—execution and interpretation—
need to be emphasized in the course.
If in Chapter 5 you were interested in the infor-
mal ways to check the assumptions of Bernoulli tri-
als, then you may want to take the time to study the
examples in the text that show how the techniques of
Chapter 7 can put the earlier informal examinations
into the familiar framework of hypothesis testing.
The discussion of the limitations of observational
studies is continued in Chapter 9;
see especially
the material on Simpson’s paradox and standardized
rates.
As you continue to work through the text, re-
member that the qualitative differences between con-
trolled and observational studies presented in Chap-
ter 7 for a dichotomous response are equally valid for
a multicategory or numerical result, as presented in
Chapters 11 and 16, respectively.
Chapter 7 introduces the idea of the
practical im-
portance
of results. I find this to be an easy, yet intel-
lectually honest, way to help students to understand
the issue of sample size.
(A reviewer of the first
version of the text opined that I should drop Clyde
Gaines’s Three-Point Basket study from the book be-
cause, “You don’t need to be a statistician to analyze
the data!” Chapter 7 illustrates, however, that some
statistical training can help one realize that for the
goal of estimating a difference, Clyde’s sample size
was much too small.)
7.2
Solutions to Odd-Numbered Ex-
ercises
1.
(b) The values
n
1
=
5,000 and
n
2
=
5,000
are given. It follows that
n
=
10,000, and
a
= ˆ
p
1
n
1
= 0
.
42(
5,000
) =
2,100
.
Similarly,