In article <[EMAIL PROTECTED]>, Rich Ulrich <[EMAIL PROTECTED]> wrote: >On 19 Feb 2003 15:57:25 -0500, [EMAIL PROTECTED] (Herman >Rubin) wrote:
>[ snip, previous question ] >> The use of "statistical significance" should be abolished. >> One should use an analysis of risk and const instead. >[ ... ] >I've been looking at this for a week. "const" ? >Herman doesn't value the decision of something >being "statistically significant" the way that most of >us do -- but it is certainly true that some folks over- >value the 5% cutoff as a decision-maker. >Herman is a bit kinder to p-levels; everyone ought to >recognize that p-levels give us the background for >all those decisions -- so, be aware that "the 5%" thing >is a particular, nasty habit, and it is a logical sticking >point for folks, NOT entirely equivalent to p-levels. The p-value is ONE component of risk, and it is usually not even that correctly. That point null hypothesis is almost always false; generally, one should accept if it is close enough to being correct. At this point, the mathematics is likely to be rather difficult, although if close happens to be quite close in comparison with accuracy of estimation, the point null may be a good approximation, but the p-value does not mean what most think it does here. But how should one decide which level for a test? I keep this example on hand, not because I consider it to be that realistic, but because it can be computed in closed form, and that is not at all common, and it gives a correct indication of what to look for. Suppose one is testing whether the mean of a two-dimensional normal distribution with covariance matrix vI, that is, the two coordinates are independent with common variance v. Assume the loss is 1 for a wrong decision, and that the improper prior gives mass 1 to the parameter being 0 and constant density 1/(2pi) on the rest of the space. Do not worry about the infinite integral; it is not important. Then the Bayes procedure is to accept if the observation lies in a circle, with rejection probability v. If one has other loss functions or dimensions, the behavior is similar, with the rejection probability behaving roughly like a power of v, with some logarithms involved. See my paper with Sethuraman in Sankhya 1965. -- 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/ . =================================================================
