Hi On 2 Nov 2001, Donald Burrill wrote: > On Fri, 2 Nov 2001, jim clark wrote: > > I would hate to ressurect a debate from sometime in the past > > year, but the chi-squared is a non-directional (commonly referred > > to as two-tailed) test, although it is true that you only > > consider one end (tail) of the distribution. > > Surely this depends on WHICH chi^2 test one is discussing. What you > write is true (if, in my view, misleading) about SOME chi^2 tests, but > not about ALL chi^2 tests.
Don is correct. I (perhaps wrongly) took "standard chi-square," which the original post referred to, as chi-square for a contingency table, the most common use in the psychological literature that I am familiar with. I'm not sure in what sense what I wrote was misleading (unless this IS going to resurrect the earlier debate). > > Just as the upper end of the F distribution contains both tails of > > the t (it is t folded over), > > This is not strictly true; and to the extent that it IS true, it is > true only of the F distribution with 1 and k degrees of freedom, which > can be argued to be a kind of "folded" version of the t distribution > with k degrees of freedom. "Folded over" I consider misleading, because > it suggests that you could see the shape of the distribution by taking a > standard central t distribution and mirroring it about zero. But in fact > the shape of the distribution changes, as well as the "folding": values > less than one are systematically shifted toward zero (and the shift is > greater the further the value is from 1), while values greater than one > are systematically shifted toward infinity (and the shift is greater the > further the value is from 1). Thus the SHAPE of the F distribution (with > 1 and k degrees of freedom) is distinctly different from the shape you'd > get by merely creating a mirror image around zero. My cryptic "both tails" was meant to refer to the probabilities and not to the details of the shape of the distribution, as Don mentioned. And perhaps it was presumptious to not say that this held only when the numerator df was 1, but this is a statistics newsgroup. > > the chi^2 contains both ends of the z (normal) distribution (i.e., z > > is folded over). > > And, correspondingly, this is true only for chi^2 with 1 degree of > freedom, and subject to the same reservations about shape as those > mentioned above with respect to the F distribution. Same comments as above. Best wishes Jim ============================================================================ James M. Clark (204) 786-9757 Department of Psychology (204) 774-4134 Fax University of Winnipeg 4L05D Winnipeg, Manitoba R3B 2E9 [EMAIL PROTECTED] CANADA http://www.uwinnipeg.ca/~clark ============================================================================ ================================================================= Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =================================================================
