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which our objective is to determine the minimum effective dose. Obvi-
ously, if the minimum effective dose is greater than the maximum tolera-
ble dose, or if some dangerous side effects are observed that we didn't
observe in the first set of trials, we'll abandon the drug and go on to some
other research project. But if the signs are favorable, then and only then
will we go to a set of Phase III trials involving a large number of subjects
observed over an extended time period. Then, and only then, will we
hope to get the answers to all our research questions.
Before you begin, list all the consequences of a study and all the actions you
might take. Persist only if you can add to existing knowledge.
TO LEARN MORE
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 et al. [1988].
Over 300 references warning of the misuse of null hypothesis testing
can be accessed online at the URL 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 recom-
mend and place the emphasis on the why, not the what, of statistical pro-
cedures. 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]. For more
work along the lines proposed here, see Selike, Bayarri, and Berger
[2001].
Clarity in hypothesis formulation is essential; ambiguity can only yield
controversy; see, for example, Kaplan [2001].
