On Mon, 24 Dec 2012, yinung at Gmail wrote: > I notice that "xtab" command can do Fisher's exact test. I found that > fisher.test(.) in R (requires vcd package) also produces Fisher's exact > test results. Does anyone know the differences between gretl's and R's > Fisher's exact test? > > I test the following data (which can be downloaded from > http://ibeif.files.wordpress.com/2012/12/fishertea.xls > > obs real guess > 1 1 1 > 2 1 1 > 3 1 1 > 4 1 2 > 5 2 2 > 6 2 2 > 7 2 1 > 8 2 2 > > In gretl, the following script > > <hansl> > open http://ibeif.files.wordpress.com/2012/12/fishertea.xls > xtab real guess > </hansl> > > produces the results: > > Cross-tabulation of real (rows) against guess (columns) > > [ 1][ 2] TOT. > > [ 1] 3 1 4 > [ 2] 1 3 4 > > TOTAL 4 4 8 > > Pearson chi-square test = 2 (1 df, p-value = 0.157299) > Warning: Less than of 80% of cells had expected values of 5 or greater. > > Fisher's Exact Test: > Left: P-value = 0.985714 > Right: P-value = 0.242857 > 2-Tail: P-value = 0.257143 > > However, in gretl with the following R script > > fisher.test(table(real,guess)) > > produces the different results: > > > Fisher's Exact Test for Count Data > > data: table(real, guess) > p-value = 0.4857 > alternative hypothesis: true odds ratio is not equal to 1 > 95 percent confidence interval: > 0.2117329 621.9337505 > sample estimates: > odds ratio > 6.408309
Hmm, there are various ways of computing a 2-sided p-value for this test, and it looks like gretl and R make different choices. You can get a very comprehensive printout at http://www.quantitativeskills.com/sisa/statistics/fisher.htm For this table we see: <output> The total number of cases= 8 The smallest value= 1 The smallest marginal= 4 Use of * (starred) statistics is advised The p for exactly this table= 0.22857 One sided p-values: for p(O>=E): p(O>=E): 0.2428571 * p(O>E): 0.0142857 mid-p: 0.1285714 p(O<=E): 0.9857143 Two sided p-values p(O>=E|O<=E): p= 0.4857143 * (sum of small p's) p= 0.2285714 (left+right-exact) p= 0.2571429 (left+right) p= 0.485714 (double the single sided p) p(O>E|O<E)= 0.02857 (sum of small p's) mid-p 0.2571429 (sum of small p's) </output> So the value gretl is giving for the 2-sided p-value is the one labeled "left+right" above. The one that R gives is the "sum of small p's", which is starred (recommended) on the quantitativeskills page. Perhaps we should reconsider or augment the gretl output. Allin Cottrell
