# st: RE: Fisher´s exact test for rxc [2X2] tables: one-tailed or two-tailed[iso-8859-1] ?

 From Allen Buxton To "statalist@hsphsun2.harvard.edu" Subject st: RE: Fisher´s exact test for rxc [2X2] tables: one-tailed or two-tailed[iso-8859-1] ? Date Fri, 1 May 2009 15:46:14 -0700

```Does Stata have both 1-sided Fisher's exact tests available? SAS displays both 'left' and 'right' sided results. As an exception, this issue came up recently where the greater one-sided probability was of interest. For 2X2 tables his can be done with Stata's hypergeometric() function.

Thanks,
-Allen Buxton

Example from table 2.8 exact analysis of a fourfold table, Joseph L. Fleiss 2nd ed. stat. meth. for rates & proportions 1981.

|           b
a |        b1         b2 |     Total
-----------+----------------------+----------
a1 |         2          3 |         5
|     40.00      60.00 |    100.00
|     33.33      60.00 |     45.45
|     18.18      27.27 |     45.45
-----------+----------------------+----------
a2 |         4          2 |         6
|     66.67      33.33 |    100.00
|     66.67      40.00 |     54.55
|     36.36      18.18 |     54.55
-----------+----------------------+----------
Total |         6          5 |        11
|     54.55      45.45 |    100.00
|    100.00     100.00 |    100.00
|     54.55      45.45 |    100.00

Pearson chi2(1) =   0.7822   Pr = 0.376
...omitted output...
Fisher's exact =                 0.567
1-sided Fisher's exact =                 0.392

. di string(`=hypergeometric(11,5,6,2)', "%5.4f") /* Left-sided */
0.3918
. di string(`=1-hypergeometric(11,5,6,1)', "%5.4f") /* Right-sided */
0.9329
. di string(`=hypergeometricp(11,5,6,2)', "%5.4f") /*Table Probability*/
0.3247

Here is SAS on the two one-sided exact tests.
...omitted output...

Fisher's Exact Test
----------------------------------
Cell (1,1) Frequency (F)         2
Left-sided Pr <= F          0.3918
Right-sided Pr >= F         0.9329

Table Probability (P)       0.3247
Two-sided Pr <= P           0.5671

Sample Size = 11

/*begin Stata code*/
clear all
input str2 a str2 b byte w
a1 b1 2
a1 b2 3
a2 b1 4
a2 b2 2
end
ta a b [fw=w],row col cell all exact
/*end Stata code*/

/*begin SAS code*/
data wk00;
length a b \$2.;
input a b w;
datalines;
a1 b1 2
a1 b2 3
a2 b1 4
a2 b2 2
;
run;
proc freq data=wk00;
tables a*b /fisher;
weight w;
run;
/*end SAS code*/

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Tiago V. Pereira
Sent: Friday, May 01, 2009 5:39 AM
To: statalist@hsphsun2.harvard.edu
Subject: st: [iso-8859-1] Fisher´s exact test for rxc tables: one-tailed or two-ta iled[iso-8859-1] ?

Just would like to thank David, Richard  and Steve for their comments on
my last query. The two-sided option seems more plausible, indeed.

Cheers!

Tiago

----------------------------------------------
Dear statalisters,

I was reading some old post regarding exact tests in Stata and have found
the following message:

http://www.stata.com/statalist/archive/2005-06/msg00029.html

The author of this note comments on the possibility of the Fisher´s exact
test for rxc tables available in Stata to be one-tailed. Hence, is it two-
or one-tailed?

All the best,

Tiago

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