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Statistics 371001, Sp 09
Lecture #182
31 Mar 09
Chapter 10.
Analysis of Categorical Data
1.
ChiSquare Goodness of Fit Test
Hypothesis testing
Categorical data
Multinomial instead of binomial
Nonparametric test, Chisquare,
χ
2
Other questions; estimate proportions or relative frequencies of subjects in response categories of
a distribution vs probability of a success. Eg.,
Number of women dentist compared to number of men dentist.
Which cola is most preferred by Americans, Coke or Pepsi?
Proportion of college students majoring in business today vs 10 yrs ago.
Use sample data to test hypotheses about the shape or proportions of a population distribution.
Chisquare Goodness of Fit Test
♦
Observed frequencies – number of items
from sample
classified in a particular category.
Each subject or observational unit is counted in one and only one category.
Data; relatively simple.
♦
Expected frequencies  number of items in each category
predicted from the null
hypothesis and the sample size, n
.
How well do observed frequencies fit frequencies specified by H
0
??
Expected frequencies can specify H
0
of
No Preference.
Eg.,
Among leading brands of soft drinks, are there preferences?
Coke
Pepsi
Mt. Dew
H
0
:
Expected frequencies can specify H
0
of No Difference from a Known Population.
Eg.,
Same distribution eye color exits in newborns in Wisconsin in 2009
as in 1959?
Lecture 18
page 1
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Brown
Blue
Green
Other
H
0
:
20
10
4
4
Hypothetical Problem:
Volunteers at a teen hotline are assigned based on the assumption that
the primary issue raised by 40% of calls is drugs, for 25% of calls the primary issue is related to
sex, for 25% it’s stress, and for 10% it’s educational issues.
Is the assumption regarding the
distribution of primary topic issue appropriate? 120 calls were randomly selected and categorized
according to the primary issue addressed in the call.
Step 1.
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This note was uploaded on 04/07/2009 for the course STAT 371 taught by Professor Koscik during the Spring '08 term at Wisconsin.
 Spring '08
 KOSCIK
 Statistics, Binomial

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