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Final Exam, December 2001, ANSWERS
Categorical Data Analysis for Epidemiologic Studies, CHL5407H
1a.
No, the Pearson chisquare test is not an appropriate method of analysis to test
for a diﬀerence in the proportion of learning disabled children comparing teachers
to psychologists. The data provided in Table 1 are from a pairmatched study
since each student was assessed twice. The Pearson chisquare test is more ap
propriately used to test for diﬀerences in proportions of two or more independent
samples while McNemar’s chisquare statistic should be used to test for diﬀer
ences in two proportions for paired data. Moreover the expected cell counts in
Table 1 are too small to support approximate statistical inferences constructed
using the Pearson chisquare test.
1b.
From Table 1 we see that teachers were far more likely to classify students as
having a learning disability than were psychologists. For instance, the McNemar’s
odds ratio of being classi±ed as having a learning disability,
ˆ
ψ
MC
=11
/
2=5
.
5
comparing teachers to psychologists. Another way of looking at the data is to
note that 68% percent of teachers (100
×
15
/
22) but only 27% of psychologists
(100
×
6
/
22) classi±ed children as having a learning disability.
Since the same children are classi±ed twice  once by their homeroom teacher and
once by the school psychologist  the proportions are almost certainly correlated.
A method of analysis which takes this correlation into account should be used.
We can use McNemar’s statistic to test
H
0
: the proportion of students classi±ed
as having a learning disability does not diﬀer at the population level between
homeroom teachers and school psychologists vs.
H
A
: the proportion of students
classi±ed as having a learning disability does diﬀer at the population level between
homeroom teachers and school psychologists. This, approximate, one degree of
freedom chisquare test statistic uses only data from the discordant pairs. It is
given by
χ
2
MC
=
(11

2)
2
11 + 2
=6
.
23 (
p<
0
.
05)
.
Therefore, the much greater preference of teachers as compared to psychologists
to classify students as having a learning disability is statistically signi±cant.
This test is likely valid since there are more than 10 discordant pairs. Of course
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 Spring '11
 ManWai's
 ChiSquare Test

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