Answering two criticisms of hypothesis testing

Two generations of methodologists have criticized hypothesis testing by cla iming that most point null hypotheses are false and that hypothesis tests d o not provide the probability that the null hypothesis is true. These criti cisms are answered. (1) The point-null criticism, if correct, undermines on ly the traditional two-tailed rest, not the one-tailed test or the little-k nown directional two-tailed rest. The directional two-tailed test is the on ly hypothesis test that, properly used, provides for deciding the direction of a parameter, that is, deciding whether a parameter is positive or negat ive or whether it falls above or below some interesting nonzero value. The point-null criticism becomes unimportant if we replace traditional one- and two-tailed rests with the directional two-railed rest, a replacement alrea dy recommended for most purposes by previous writers. (2) If one interprets probability as a relative frequency, as most textbooks do, then the concep t of probability cannot meaningfully be attached to the truth of an hypothe sis; hence, it is meaningless to ask for the probability that the null is t rue. (3) Hypothesis tests provide the next best thing, namely, a relative f requency probability that the decision about the statistical hypotheses is correct. Two arguments are offered.