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1.
Suppose we find that among couples that have lived together before they marry
60% end in divorce.
Further, among couples that did not live together before they marry
45% end in divorce.
Identify a variable that subdivides the population into subsets in
which it possible that for every subset of the population couples that have lived together
before marriage will have a lower divorce rate than their counterparts in that subset.
Provide the numbers to make your assertion clear.
Solution.
A possible variable that subdivides the population is income. Let's say that
there are two categories for income : high and low. If we have the following breakdown:
Divorce Rate
High Income
Low Income
Total
Lived Together
70% (80% of all
couples who lived
together)
20% (20% of all
couples who lived
together)
60%
Didn’t live together
80% (30% of all
couples who didn’t
live together)
30% (70 % of all
couples who didn’t
live together)
45%
then we can have a situation where those who lived together before getting married had a
lower divorce rate in both the high and low income groups (70% vs. 80% and 20% vs.
30% respectively), while maintaining that overall, those who live together before getting
married have a higher divorce rate.
2.
Explain the circumstances that can lead to a reversal in a comparison between two
groups.
Solution.
Whenever there is an uneven distribution of any second important
characteristic between the two groups, subdividing the two groups by this second
characteristic can lead to a reversal. The divorce rate was higher in the lived together
group because a disproportionate number of lower income people are in this category.
This is why we must try to have the two groups of interest be similar in all ways
\underline{except} in the variable of interest.
3.
Provide an example to illustrate why we should measure the 'order' or 'time' of a
measurement.
Solution.
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 Spring '08
 ROTHMAN

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