In article <[EMAIL PROTECTED]>, David Jones <[EMAIL PROTECTED]> wrote: >Herman Rubin wrote: >> In article <[EMAIL PROTECTED]>, >> dennis roberts <[EMAIL PROTECTED]> wrote:
>>> actually, p values are rather useless (i am almost prepared to say >>> "useless") since, it would be the RARE case when the null is REALLY >>> exactly true >>> thus, in 99.9999% of the cases ... we KNOW the null is not true so, >>> setting some cutoff for rejection and then actually rejecting the >>> null ... what has this added to our knowledge? >>> and, p values don't speak to the notion of the null being >>> "approximately" true >> I do not see any way to do this other than a decision >> theoretic approach >... but it is covered by the use of a composite null hypothesis, which >is in all the major theoretical books, even if they are little used >practically except for one-sided tests which form a major example. You >could have an interval as the null hypothesis. This is likely to be a poor procedure. The p-value depends on the precise parameter, and thus is not constant over an interval. The maximum is not likely to be what is wanted. The true problem is still a decision problem. >... and it is also covered by the use of confidence intervals, >provided that these are constructed and interpreted via the >"test-inversion" approach: thus you can see immediately the parameter >values that would or would not be accepted by a significance test as >being "true". Confidence intervals, and I include Bayesian intervals, are also not justified as decision procedures. A confidence interval can be a descriptive statistic, but even the Bayesian ones do not provide the information. In all cases, the likelihood function does provide all the information in the data. -- 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/ . =================================================================
