Common Errors in Statistics (and How to Avoid Them), 4th Edition

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For more thorough accounts of decision theory, the interested reader is directed to Berger [1986], Blyth [1970], Cox [1958], DeGroot [1970], and Lehmann [1986]. For an applied perspective, see Clemen [1991], Berry [1995], and Sox, Blatt, Higgins, and Marton [1988].

Over 300 references warning of the misuse of null hypothesis testing can be accessed online at http://www.cnr.colostate.edu/∼anderson/thompson1.html. Alas, the majority of these warnings are ill informed, stressing errors that will not arise if you proceed as we recommend and place the emphasis on the why, not the what, of statistical procedures. Use statistics as a guide to decision making rather than a mandate.

Neyman and Pearson [1933] first formulated the problem of hypothesis testing in terms of two types of error. Extensions and analyses of their approach are given by Lehmann [1986] and Mayo [1996]. Their approach has not gone unchallenged, as seen in Berger [2003], Berger and Berry [1988], Berger and Selke [1987], Berkson [1942], Morrison and Henkel [1970], Savage [1972], Schmidt [1996], Seidenfeld [1979], and Sterne, Smith, and Cox [2001]. Hunter and Schmidt [1997] list and dismiss many of their objections.

Guthery, Lusk, and Peterson [2001] and Rozeboom [1960] are among those who have written about the inadequacy of the null hypothesis.

For more guidelines on formulating meaningful primary hypotheses, see Selike, Bayarri, and Berger [2001]. Clarity in hypothesis formulation is essential; ambiguity ...