# [R] test for equal distributions with small numbes of observations

Christoph Lehmann christoph.lehmann at gmx.ch
Tue Aug 19 10:15:52 CEST 2003

```Dear R-pros

I have a problem, for which usually I would apply a chisq.test or a
fisher.test:

40 objects, each given either a "0" or "1", regarding if this object
later on will be remembered by a subject or not.

7 subjects investigated

means: we have a 2x40 matrix, each cell the number of subjects for who
the object i has been given either "0" or "1" e.g.

objects:
1	1	3		39	40
------------------------------------------
"0"	1	2	2	..	7	7
"1"	4	4	5	..	0	0

over all 40 objects, we have 67% of "1" and 33% of "0"

I want to know, if for the 40 objects, the ratio of "0"/"1" differs or
not, i.e. if they have the same distribution.

I cannot use a chisq.test since the expected frequencies are < 5 for the
"0" cells.

Fisher.test seems to run for > 12h on a PIV 1.8GHz...

what do you recommend me to do?

Many thanks

Christoph
--
> recognition
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
[1,]    1    2    2    2    2    3    3    3    3     3     3     3     4     4
[2,]    4    4    5    4    4    3    4    4    4     4     3     4     3     3
[,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
[1,]     4     4     4     4     4     4     5     5     5     5     5     5
[2,]     3     2     3     3     2     3     2     2     2     2     2     2
[,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37] [,38]
[1,]     5     5     5     5     5     6     6     6     6     6     6     6
[2,]     2     2     2     2     2     1     1     1     1     1     1     1
[,39] [,40]
[1,]     7     7
[2,]     0     0

> fisher.test(recognition)

--
Christoph Lehmann <christoph.lehmann at gmx.ch>

```