Elliot Cramer wrote:
>
> In sci.stat.consult Juha Puranen <[EMAIL PROTECTED]> wrote:
> :>
> :> Please clarify what is meant by "the distribution does not
> :> involve [the fixed marginals]". I am not clear on this:
> :> the Fisher test statistic (hypergeometric upper tail probability)
> :> certainly *does* depend on the fixed marginals in this
> :> case -- they appear in every term in that tail sum.
> sorry; didn't say it right
>
> : Usual the assumptions for Fishers exact test are not true.
>
> : What you can fix are the row margins, or column margins or grand total
> These aren't assumptions any more than specific fixed x values are
> assumptions in linear regression
>
> Kendall and Stuart say (under exact test of independence 2x2 table)
>
> We may now demonstrate the remarkable result, first given by Tocher
> (1950) that the exact test based on the Case I probabilities actually
> gives UMPU tests for Cases II and III
>
> The probability statements for case I (fixed marginals) are valid
> conditional on the marginals for every set of marginals and do not
> involve the nuisance parameters for Cases II and III and thus are valid
> unconditionally for all three cases.
>
> This is exactly analagous to the regression model
> y = bx + e
> where you derive the t test for b conditional on the specific x values you
> observe, treating them as fixed. The statistic (a function of the
> x's) has the same t distribution regardless of what x values you observe,
> even if they happen to be sampled from ANY probability distribution
> Thus the regression test for fixed x values is valid for random x values
Hhen N is small this is not true. Here a small example By Survo
TABLE T
7 2
1 4
SIMUMAX=100000
TABTEST T,CUR+1 /
Testing a 2*2 table by simulation: X^2=4.38148 P=0.036331
G^2=4.58269 P=0.032296
Fisher's exact test, Probability statistics
N P Confidence interval (0.95)
100000 0.08949000 0.08772080 lower limit
s.e. 0.00090267 0.09125920 upper limit
TABTEST T,CUR+1 / FIX=RC ----------------------------------- Fisher
exact by simulation
Testing a 2*2 table by simulation: X^2=4.38148 P=0.036331
G^2=4.58269 P=0.032296
Fixed margins, X^2 statistics
N P Confidence interval (0.95)
100000 0.08949000 0.08772080 lower limit
s.e. 0.00090267 0.09125920 upper limit
TABTEST T,CUR+1 / FIX=R ------------------------------------- Row sums
fixed
Testing a 2*2 table by simulation: X^2=4.38148 P=0.036331
G^2=4.58269 P=0.032296
Fixed row margins (horizontal sums), X^2 statistics
N P Confidence interval (0.95)
100000 0.04242000 0.04117083 lower limit
s.e. 0.00063734 0.04366917 upper limit
TABTEST T,CUR+1 / FIX=C -------------------------------------- Col sums
fixed
Testing a 2*2 table by simulation: X^2=4.38148 P=0.036331
G^2=4.58269 P=0.032296
Fixed column margins (vertical sums), X^2 statistics
N P Confidence interval (0.95)
100000 0.04937000 0.04802728 lower limit
s.e. 0.00068507 0.05071272 upper limit
TABTEST T,CUR+1 / FIX=N -------------------------------------- Grand
total fixec
Testing a 2*2 table by simulation: X^2=4.38148 P=0.036331
G^2=4.58269 P=0.032296
No fixed margins, X^2 statistics
N P Confidence interval (0.95)
100000 0.04003000 0.03881502 lower limit
s.e. 0.00061990 0.04124498 upper limit
TABTEST T,CUR+1 / FIX=F(1,1) ------------------------------ n(1,1)= 7
fixed
Testing a 2*2 table by simulation: X^2=4.38148 P=0.036331
G^2=4.58269 P=0.032296
Target value F(1,1)=7, X^2 statistics
N P Confidence interval (0.95)
100000 0.06366000 0.06214679 lower limit
s.e. 0.00077206 0.06517321 upper limit
By simulation there are some differences in P-values
Juha
--
Juha Puranen
Department of Statistics
P.O.Box 54 (Unioninkatu 37), 00014 University of Helsinki, Finland
http://noppa5.pc.helsinki.fi
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