Chapter 10
One Multicategory Response
10.1
Study Suggestions
In retrospect, I do not like the advice I give in the text
for the visual presentation of an unordered categori
cal response. Insisting, as I do, that the categories be
ordered by frequency of responses can lead to confu
sion when, for example, the most common response
is “None of the above,” or “About the same.” If no
confusion will result, as, for example, in the winning
lottery numbers example, I advocate following my
advice. For situations in which my advice leads to
confusion, the categories may be presented in a nat
ural sequence, but you should remember not to place
any significance on the shape of the bar chart.
The chisquared goodness of fit test is very fa
mous. It was developed by Karl Pearson to provide
a mathematical evaluation of the important work by
Gregor Johann Mendel.
Despite its fame, modern
statisticians are largely indifferent to the test.
The
test’s main problems are twofold. First, one popula
tion inference is inherently less interesting than com
paring two populations. Second, the applicability of
the test is severely restricted by the requirement of
having
k
special values of interest. The goodness of
fit test does, however, provide a good motivation and
framework for the more useful test of Chapter 11.
I use the example of the Wisconsin lottery daily
game on pages 345 and 346 to illustrate one of
my main concerns with the teaching of introductory
statistics: If the only tool students have for analyz
ing one multicategory response is the chisquared
test, then should we be surprised if they apply this
test indiscriminately?
This example in the text il
lustrates the power and flexibility of computer sim
ulation to answer questions that the standard theory
cannot handle.
(Note: I wrote letters to the heads
of the lottery commissions in every state that has a
lottotype game, asking if they perform any statis
tical analyses of the winning numbers to check for
fairness.
Approximately 25 heads wrote back and
said that they did, and all but one of these 25 states
uses the chisquared goodness of fit test, without any
adjustments.)
The computer simulation experiment for the Wis
consin lottery daily game also provides you with the
first example of how to study robustness. This topic
is discussed further in Chapter 15.
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 Fall '09
 ProfessorWardrop
 Statistics, Normal Distribution, Kramer, fit test, chisquared goodness

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