Chapter 9
Adjusting for a Factor
9.1
Study Suggestions
Simpson’s paradox and standardized rates constitute
a nice completion to the argument, begun in Chap
ter 7, that it is difficult to interpret the findings of an
observational study.
The real importance of Simpson’s paradox rests in
the following realization. The
2
×
2
table of any ob
servational study can be viewed as a ‘collapsed’ ta
ble. The researcher must always remember that there
could exist a meaningful factor for which ‘uncollaps
ing’ the table would result in a reversal of the di
rection of the relationship between the response and
populations.
The main problem my students have with Simp
son’s paradox and standardized rates is in keeping
the roles of the three variables straight.
There is a
response, there is a variable, that defines the pop
ulations to be compared, and there is a factor that
may influence the response.
For example, for the
data on page 295 of the text, the response is the at
titude toward drinking and driving. The populations
consist of female and male drivers.
Finally, it was
conjectured that drinking frequency would influence
response, so the factor was taken to be drinking fre
quency.
Simpson’s paradox can occur, and standardized
rates will yield interesting insight, only if the factor
is strongly related (statistically) to both the popula
tion and the response. For example, if women and
men had the same distribution of drinking frequen
cies then computing the standardized rates would be
a waste of time. (If men and women have the same
weights, the standardized rate would equal the orig
inal rate, since there would be no effect of replacing
the women’s weights with the men’s weights, or vice
versa, since the weights are identical.)
Moreover,
if attitude were not related to drinking frequency,
then the proportion of successes, for either gender,
would be the same in each drinking frequency cate
gory. Thus, the weights used would have no impact,
since we would be computing weighted averages of
identical numbers.
If you use the MantelHaenszel test to analyze data
from an observational study, remember that there
is not necessarily a single correct analysis strategy.
Consider, for example, the study of how attitude to
wards drinking and driving depends on gender that
is analyzed in the text in Chapter 9. If a researcher
simply wants to compare females and males there is
no need to consider using the techniques discussed
in Chapter 9. If, however, the researcher wants to in
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 Fall '09
 ProfessorWardrop
 Statistics, Normal Distribution, researcher, standard normal curve, approximate pvalue, c. Simpson

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