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Chapter 9
Comparing Two Populations: Binomial and
Poisson
9.1
Four Types of Studies
We will focus on the binomial distribution in this chapter. Inthelast(optional)sectionweextend
these ideas to the Poisson distribution.
When we have a dichotomous response we have focused on BT. The idea of Fnite populations
was introduced in Chapter 2 and presented as a special case of BT. In this section it is convenient
to begin with Fnite 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 Fnite populations. In addition, as we shall
discuss soon, a study can be
observational
or
experimental
.Comb
in
ingthe
setwod
icho
tom
ie
s
,
we get four types of study, for example an observational studyonFnitepopulations.
It turns out that the math results are (more or less) identicalforthefourtypesofs
tud
ies
,bu
t
the
interpretation
of the math results depends on the type of study.
We begin with an observational study on two Fnite populations. This was a real study per
formed over 20 years ago; it was published in 1988. The Frst Fnite population is undergraduate
men at at the University of WisconsinMadison and the second population 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 preferforher:toaskyouout;
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 otherresponsesislabe
ledafa
ilure
.The
purpose of the study is to compare the proportion of successesatW
isconsinwiththeproportionof
successes at Texas A&M.
The two populations obviously Ft our deFnition of Fnite populations. Why is it called ob
servational? The dichotomy of observational/experimenta
lreferstothe
control
available to the
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
91
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View Full DocumentTable 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
he belongs. The variable that determines to which populationasubjectbelongs,isoftencalledthe
study factor
.Thus
,inthecu
r
ren
ts
tudy
,thes
tudyfac
to
risschoo
la
t
tended and it has two
levels
:
Wisconsin and Texas A&M. This is an observational factor, sometimes called, for obvious reasons,
aclassi±cationfactor
,becauseeachsubjectisclassi±edaccording to his school.
Table 9.1 presents the data for this
Dating Study
.
Next, we have an example of comparing ±nite populations in an experimental study. Medical
researchers were searching for an improved treatment for persons with
Crohn’s Disease
.T
h
e
y
wanted to compare a new drug therapy,
cyclosporine
,toaninertdrug,calleda
placebo
.
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 Fall '11
 hanlon
 Binomial, Poisson Distribution

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