In article <[EMAIL PROTECTED]>, Kevin J <[EMAIL PROTECTED]> wrote: >On Mon, 17 Mar 2003 19:27:57 GMT, Jerry Dallal ><[EMAIL PROTECTED]> wrote:
>>Kevin J wrote: >>> I realize there is a distinction between saying this and saying that >>> there is a 95% chance that the population parameter will fall within a >>> _particular_ CI, but I had always thought this distinction very >>> slight. It appears I am wrong. Both of my stats texts do emphasize >>> that there is a distinction, but don't explain what the real world >>> impact of this is. Care to educate me? >>Let X1, X2 be U(theta-1, theta+1), that is uniform on the interval >>(theta-1, theta+1). Then (min(X1,X2), max(X1,X2)) is a 50% CI for >>theta because there is a 25% chance that both X1 and X2 will be less >>than theta and a 25% chance that both will be greater than theta. >>However, if the length of the interval is 1 or more, the interval >>*must* contain theta even though it's a 50% CI. >Awesome, this explains it well. Thanks. >Now I feel a little sheepish, but what _is_ the appropriate use of a >CI? My incorrect assumptions are in my previous post. Is there any for a CI as such? The fundamental principle of decision making should be that one must consider all the consequences of the proposed action in all states of nature. This rules out classical significance testing, as it only considers what happens in one state of nature, which is usually impossible, although few investigators realize this. But for interval estimation, there are two consequences, one of them being the position of the parameter in the interval, and the other being the size of the interval. If size is not a consideration, the entire real line is an excellent 100% confidence interval. -- 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/ . =================================================================
