Stat408SolutionsHW022008 - 1 Suppose we find that among...

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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.
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