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| Post hoc theorizing ： ウィキペディア英語版 |
Testing hypotheses suggested by the data
In statistics, hypotheses suggested by the data, if tested using the data set that suggested them, are likely to be accepted even when they are not true. This is because circular reasoning (double dipping) would be involved: something seems true in the limited data set, therefore we hypothesize that it is true in general, therefore we (wrongly) test it on the same limited data set, which seems to confirm that it is true. Generating hypotheses based on data already observed, in the absence of testing them on new data, is referred to as post hoc theorizing (from Latin ''post hoc'', "after this").
The correct procedure is to test any hypothesis on a data set that was not used to generate the hypothesis.
==Example of fallacious acceptance of a hypothesis==
Suppose fifty different researchers, unaware of each other's work, run clinical trials to test whether Vitamin X is efficacious in treating cancer. Forty-nine of them find no significant differences between measurements done on patients who have taken Vitamin X and those who have taken a placebo. The fiftieth study finds a big difference, but the difference is of a size that one would expect to see in about one of every fifty studies even if vitamin X has no effect at all, just due to chance (with patients who were going to get better anyway disproportionately ending up in the Vitamin X group instead of the control group, which can happen since the entire population of cancer patients cannot be included in the study). When all fifty studies are pooled, one would say no effect of Vitamin X was found, because the positive result was not more frequent than chance, i.e. it was not statistically significant. However, it would be reasonable for the investigators running the fiftieth study to consider it likely that they have found an effect, at least until they learn of the other forty-nine studies. Now suppose that the one anomalous study was in Denmark. The data suggest a hypothesis that Vitamin X is more efficacious in Denmark than elsewhere. But Denmark was by chance the one-in-fifty in which an extreme value of the test statistic happened; one expects such extreme cases one time in fifty on average if no effect is present. It would therefore be fallacious to cite the data as serious evidence for this particular hypothesis suggested by the data.
However, if another study is then done in Denmark and again finds a difference between the vitamin and the placebo, then the first study strengthens the case provided by the second study. Or, if a second ''series'' of studies is done on fifty countries, and Denmark stands out in the second study as well, the two series together constitute important evidence even though neither by itself is at all impressive.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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