A statistical guide for the ethically perplexed by Lawrence J Hubert; Howard Wainer

By Lawrence J Hubert; Howard Wainer

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Health recommendations such as these pertain to an aggregate populace, possibly subdivided according to various demographic categories. But an individual who seeks some kind of control over breast cancer is not going to give up the only means they have to do so. All women know, at least indirectly, various individuals for whom breast cancer was detected early, and “cured,” even though the given cancer may not have been actually harmful. Similarly, all women know about individuals who died after a cancer had metastasized and before screening located it.

Or perhaps 50%, or 30%? How low must this probability drop before we feel that mammograms may be an unjustifiable drain on resources? 0054, but still very small in magnitude; that is, more than 95% of the positive tests that arise turn out to be incorrect. 1 gives a convenient tree diagram using calculated probabilities to obtain the PPV for mammograms. The values on each branch of the tree should be self-explanatory. The summary figures at the end of each of the four branches are merely the product of the values along its length.

There are several ways of saying this: when some set of observations is the source of an initial suspicion, those same observations should not be used in a calculation that then tests the validity of the suspicion. In Bayesian terms, you should not obtain the posterior probabilities from the same information that gave you the prior probabilities. Alternatively said, it makes no sense 26 A Statistical Guide for the Ethically Perplexed to do formal hypothesis assessment by finding estimated probabilities when the data themselves have suggested the hypothesis in the first place.

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