```Date: Tue, 30 Jul 1996 16:55:49 +0300 Reply-To: Dvora Zomer Sender: "SAS(r) Discussion" From: Dvora Zomer Subject: Re: Whoops! Re: CHI-SQUARE goodness-of-fit in easy form ?? Comments: To: John Whittington In-Reply-To: <199607291356.OAA03496@wildnet.co.uk> Dear John: You are not perfectly right. In Fisher exact ONE-SIDED test, you have to find ALL the tables that have more extreme value of cases in a certain cell and summarize PROBABILITIES of those tables. Namely for a table ------------------ | a | b | a+b ------------------ | c | d | c+d --------------------- a+c | b+d | n where n=a+b+c+d the P-value is P=((a+b)!*(c+d)!*(a+c)!*(b+d)!/n!)*(SUM(1/(ai!)*(bi!)*(ci!)*(di!)) and SUM is over all tables ai bi ci di The probaility corresponds to Hypergeometric distribution. The distribution arases or from the assumptions that marginals were prefixed before experiment, or from a conditional approach (See Kendall& Stuart v.2). If you are regarding other sampling scheme, you will get different distributions.( See more simple Fleiss Statistical Methods for rates and proportions). Yours Ilya Novikov Ph.D. Senior Statistician fax : 972-3-5348360 Dept. of Clinical Epidemiology voice: 972-3-5303256 The Chaim Sheba Medical Center mail : epid04@post.tau.ac.il Tel Hashomer Israel 52621 On Mon, 29 Jul 1996, John Whittington wrote: > On Thu, 25 Jul 1996, SFBAY0001 wrote: > > >If I am not mistaken, the EXACT test supported in PROC FREQ uses the > >hypergeometric probability distribution, NOT the chi-square distribution. > >It is sometimes referred to as "Fisher's Exact Test for a 2 by 2 table". > > I'm getting slightly confused here. An 'exact' test is surely precisely > what it says - it is a statement of the exact probability of getting a table > 'as extreme as' the one observed, given the marginal totals that one has. > As such, there is no need to refer to any theoretical distribution - one > (the computer!) simply counts up two lists of possibilities and divides one > by the other. Anything less than that may be a good *approximation* to an > 'exact' method, but is not strictly '#exact'. > > .. that's how I see it, anyway. > > John > > ----------------------------------------------------------- > Dr John Whittington, Voice: +44 1296 730225 > Mediscience Services Fax: +44 1296 738893 > Twyford Manor, Twyford, E-mail: johnw@mag-net.co.uk > Buckingham MK18 4EL, UK CompuServe: 100517,3677 > ----------------------------------------------------------- > ```

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