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Midterm Exam, February 2003, ANSWERS
Categorical Data Analysis for Epidemiologic Studies, CHL5407H
1a.
Adoption of a Pearson chisquare test is reasonable. Only the degrees of freedom
are in question. The Pearson chisquare test should be calculated using two
degrees of freedom since there are no observations, and hence no information, in
the row reserved for subjects with severely impaired lung function. The expected
number of observations in these two cells is zero. How could these cells even be
used to calculate the Pearson chisquare test given by
χ
2
P
=
∑∑
(
O

E
)
2
/E
?
The expected numbers of observations in all other cells are suﬃciently large to
support the use of a Pearson chisquare test with two degrees of freedom.
1b.
Several diﬀerent methods of analysis could be used. Here I will only review one of
these. Several students discussed more than one method. Only the Frst of these
was graded. Students are encouraged to try and answer the question which was
asked.
±isher’s exact test is applicable to analysis of data from an r
×
c contingency table
and so could be used to test for an association between smoking status and lung
function. Adoption of this test would still require omitting the row reserved for
subjects with severely impaired lung function. One advantage of an exact test is
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This note was uploaded on 11/20/2011 for the course STATISTICS ST3241 taught by Professor Manwai's during the Spring '11 term at National University of Singapore.
 Spring '11
 ManWai's
 ChiSquare Test, Degrees Of Freedom

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