Chapter 9
Comparing Two Populations: Binomial and
Poisson
9.1
Four Types of Studies
We will focus on the binomial in this chapter. In the last section we extend these ideas to the
Poisson distribution.
When we have a dichotomous response we have focused on BT. The idea of finite population
was introduced in Chapter 2 and presented as a special case of BT. In this section it is convenient
to begin with finite populations.
The four in the title of this section is obtained by multiplying 2 by 2. When we compare two
populations both populations can be trials or both can be finite populations. In addition, as we shall
discuss soon, a study can be
observational
or
experimental
. Combining these two dichotomies,
we get four types of study, for example an observational study on finite populations.
It turns out that the math results are (more or less) identical for the four types of studies, but
the
interpretation
of the math results depends on the type of study.
We begin with an observational study on two finite populations. This example is in Chapter 7
of my textbook; the interested reader can go there for more details.
This was a real study performed over 20 years ago; it was published in 1988. The first finite
population is undergraduate men at at the University of WisconsinMadison and the second popu
lation is undergraduate men at Texas A&M University. Each man’s response is his answer to the
following question:
If a woman is interested in dating you, do you generally prefer for her: to ask you out;
to hint that she wants to go out with you; or to wait for you to act.
The response ‘ask’ is labeled a success and either of the other responses is labeled a failure. The
purpose of the study is to compare the proportion of successes at Wisconsin with the proportion of
successes at Texas A&M.
The two populations obviously fit our definition of finite populations. Why is it called ob
servational? The dichotomy of observational/experimental refers to the
control
available to the
83
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Table 9.1: Responses to the Dating Study.
Observed Frequencies
Row Proportions
Prefer Women to:
Prefer Women to:
Population
Ask
Other
Total
Ask
Other
Total
Wisconsin
60
47
107
0.56
0.44
1.00
Texas A&M
31
69
100
0.31
0.69
1.00
Total
91
116
207
researcher. Suppose that Matt is a member of one of these populations. As a researcher, I have
control over whether I have Matt in my study, but I do
not
have control over the population to
which he belongs. The variable that determines to which population a subject belongs, is often
called a
study factor
. Thus, in the current study, the study factor is school attended and it has
two
levels
: Wisconsin and Texas. This is an observational factor, sometimes called, for obvious
reasons, a classification factor, b/c each subject is classified according to his school.
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 Fall '09
 ProfessorWardrop
 Statistics, Binomial, Poisson Distribution, Dating Study

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