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Practical Data Analysis: Case Studies in Business Statistics

Solution to Sample Case

Case 8: American History Illustrated

TYPICAL RESULTS AND APPROACHES
This is a classic example of Simpson's paradox: within the individual categories, the renewal rate actually decreased, while in the aggregate, it increased. Our sturdy staff assistant will presumably be mildly embarrassed to have to report back to the boss that no department is contributing to the increase, and yet the increase is there. The challenge is to figure out how to explain this in any coherent way.

This happens because the mix of subscriptions coming due changes from an emphasis on categories with generally low renewal rates (mainly subscription agents) to categories with generally high renewal rates (notably, previously renewed and direct mail). The change in mix overwhelms the deterioration of the individual category renewal rates.

Different ratios correspond to different aspects of the problem. If we care about the external market, we probably want to see how the mix of subscriptions coming due changed. If we wish to evaluate the performance of the managers of the various categories, the within-category renewal rates will help us more.

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