In article <[EMAIL PROTECTED]>, Newsman <[EMAIL PROTECTED]> wrote: >As a layperson who is trying to gain a working knowledge of statistics, >hypothesis testing is something that, for some odd reason, I seem unable >to fully comprehend.
>I understand that the null hypothesis has greater importance than the >alternative hypothesis in the Neyman-Pearson framework. But I really >don't see how the choice of the alternative hypothesis impacts the >ultimate outcome of a particular statistical test. Other than being >entirely arbitrary, how does one choose an alternative hypothesis? It >isn't always as simple as, say, H0: \mu = 0 vs. H1: \mu \neq 0, right? >An example other than the standard ones found in most statistical >textbooks, e.g., whether the mean is or is not equal to a particular >value, would be helpful. There is a good reason for the confusion; until Neyman pointed out clearly that a significance level does not indicate the probability of truth of the hypothesis, which most using statistics had believed for more than a century, the problem could not be seen. This was coupled with the view that the laws of nature could be found exactly, and that one could test whether a formulation was correct. Neyman and Pearson pointed something out, but they did not go far enough; it is not clear that anyone saw the problem at the time. What one has to consider are ALL the consequences of the actions in ALL the states of nature. The real question is not whether the mean is equal to a particular value, but whether it should be treated as such, as this will make it easier to make useful predictions. I suggest you look at discussions of decision theoretic and Bayesian approaches; the problem comes from the user, not the statistician. In any case, if it is YOUR problem, it is YOU who must say what is the alternative. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Deptartment of Statistics, Purdue University [EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558 . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
