Date:         Tue, 30 Jul 1996 16:55:49 +0300
Reply-To:     Dvora Zomer <epid04@POST.TAU.AC.IL>
Sender:       "SAS(r) Discussion" <SAS-L@UGA.CC.UGA.EDU>
From:         Dvora Zomer <epid04@POST.TAU.AC.IL>
Subject:      Re: Whoops! Re: CHI-SQUARE goodness-of-fit in easy form ??
Comments: To: John Whittington <johnw@MAG-NET.CO.UK>
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 <sfbay0001@aol.com> 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
> -----------------------------------------------------------
>