The Bactra Review Error and the
Growth of Experimental Knowledge
Yet more formally: The severity of passing S(T, H,
e, d) = P(d(T(~H), H) >
d(e, H)), where H is our hypothesis,
e is our evidence, d( , ) indicates the discrepency between
H and e, and T() stands for the testing procedure,
considered as a random function from the situation (H is true, or it's
false, ~H) to evidence. (I offer this as a gloss on the basis of
"severity criterion 2a" on p. 180, for passing results: "There is a very
high probability that test procedure T would yield a worse fit [than
it does with e], if H were false.")
This is related to, but not the same as, the "power" of the Neyman-Pearson
theory of statistical tests, i.e., the probability of not failing to
reject H if it is false. In a fit of stupidity, I had identified the
two, and thank Prof. Mayo not only for setting me straight, but for not rubbing
it in as much as she justifiably could have.