Final Exam, December 2000, 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
1. Fisher’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 advan
tage of an exact test is that it is valid regardless of the sample size.
One
disadvantage is that Fisher’s exact test may be overly conservative relative
to Pearson’s chisquare test if the large sample requirements of the latter
procedure are satisfied. If concerned that Fisher’s exact test might not be
applicable to analysis of data from an 3
×
2 contingency table one could col
lapse lung function into two categories.
For example, employees could be
classified as either having normal lung function or as having borderline or
worse than borderline lung function. Now however one is omitting consid
eration for differences in smoking status between employees with borderline
lung function and employees whose lung function is moderately impaired.
The row reserved for subjects with severely impaired lung function must still
be omitted.
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 Spring '11
 ManWai's
 ChiSquare Test, Degrees Of Freedom, Statistical tests, Pearson's chisquare test, lung function, severely impaired lung

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