In article <IOet7.11245$[EMAIL PROTECTED]>, Magenta <[EMAIL PROTECTED]> wrote:
>"Dennis Roberts" <[EMAIL PROTECTED]> wrote in message >[EMAIL PROTECTED]">news:[EMAIL PROTECTED]... >> let's say that you do a simple (well executed) 2 group study ... >> treatment/control ... and, are interested in the mean difference ... and >> find that a simple t test shows a p value (with mean in favor of >treatment) >> of .009 >> while it generally seems to be held that such a p value would suggest that >> our null model is not likely to be correct (ie, some other alternative >> model might make more sense), does it say ANYthing more than that? >You could use it in conjunction with your sample/group sizes to get an idea >of effect size. For example, if you got that p-value with group sizes of 40 >that could be a very interesting result. However, if each group contained >100,000 subjects it may not be so interesting because the effect size will >be so much smaller. What should be done is to give the likelihood function, which contains the relevant information. One can carry out a simple calculation to show that the idea of a nearly constant p value is WRONG. Feel free to change the model and weights; the results will be somewhat similar, and this one is easy to calculate without using numerical methods. Suppose that one wishes to test that the mean \mu of a distribution is 0. The importance of rejecting the hypothesis if it is true is one; the importance of accepting the hypothesis if it is false, and \mu lies in a set of area A, is A/(2\pi). Let the data be summarized by a normal vector with mean \mu and covariance matrix vI. Then it can be shown that the optimal procedure is to use a p value of v, assuming v < 1. If v >= 1, just reject. -- 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, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399 [EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558 ================================================================= Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =================================================================
