Real-World Probability Books: Statistics

There are numerous non-technical books on Statistics -- these are some closely connected with probability.

Ziliak, Stephen and McCloskey, Deirdre. The Cult of Statistical Significance. Unversity of Michigan Press, 2008.

Tests of statistical significance are a particular tool which is appropriate in particular situations, basically to prevent you from jumping to conclusions based on too little data. Because this topic lends itself to definite rules which can be mechanically implemented, it has been prominently featured in introductory statistics courses and textbooks for 80 years. But according to the principle "if all you have is a hammer, then everything starts to look like a nail", it has become a ritual requirement for academic papers in fields such as economics, psychology and medicine to include tests of significance. As the book argues at length, this is a misplaced focus; instead of asking "can we be sure beyond reasonable doubt that the size of a certain effect is not zero" one should think about "how can we estimate the size of the effect and its real world significance". A nice touch is the authors' use of the word oomph for "size of effect".

Misplaced emphasis on tests of significance is indeed arguably one of the greatest "wrong turns" in twentieth century science. This point is widely accepted amongst academics who use statistics, but perversely the innate conservatism of authors and academic journals causes them to continue a bad tradition. All this makes a great topic for a book, which in the hands of an inspired author like Steven Jay Gould might have become highly influential. The book under review is perfectly correct in its central logical points, and I hope it does succeed in having influence, but to my taste it's handicapped by several stylistic features.

(1) The overall combative style rapidly becomes grating.

(2) A little history -- how did this state of affairs arise? -- is reasonable, but this book has too much, with a curious emphasis on the personalities of the individuals involved, which is just distracting in a book about errors in statistical logic.

(3) The authors don't seem to have thought carefully about their target audience. For a nonspecialist audience, a lighter "how to lie with statistics" style would surely work better. For an academic audience, a more focused [logical point/example of misuse/what authors should have done] format would surely be more effective.

(4) Their analysis of the number of papers making logical errors (e.g. confusing statistical significance with real-world importance) is wonderfully convincing that this problem hasn't yet gone away. But on the point "is this just an academic game being played badly, or does it have real world consequences" they assert the latter but merely give scattered examples, which are not completely convincing. If people fudge data in the traditional paradigm then surely they would fudge data in any alternate paradigm; if one researcher concludes an important real effect is "statistically insignificant" just because they didn't collect enough data, then won't another researcher be able to collect more data and thereby get the credit for proving it important? Ironically, they demonstrate the real world effect is non-zero but not how large it is ......

Savage, Sam L. The Flaw of Averages: Why we underestimate risk in the face of uncertainty. Wiley, 2009.

See my review.

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