Perfectly feasible these days to do Fisher's 'exact' test on such a table. I just got p = 0.087 using Stata (tabi 2 1 \ 2 3 \ .... , exact
. Execution took 0.19 seconds).
EDIT after chl's comment below (tried adding as a comment but can't format):
It works in R 2.12.0 for me, though i had to increase the 'workspac'e'workspace' option over its default. (The execution time is slightly quicker than in Stata, but that's of dubious relevance given the time taken to work out the meaning of the error message, which uses 'workspace' to mean something different from R's usual meaning despite the fact that fisher.test is part value of R's core 'stats' package)200000:
> fisher.test(x)
Error in fisher.test(x) : FEXACT error 7.
LDSTP is too small for this problem.
Try increasing the size of the workspace.
> system.time(result<-fisher.test(x, workspace = 400000))
user system elapsed
0.11 0.00 0.11
> result$p.value
[1] 0.0866764
(The execution time is slightly quicker than in Stata, but that's of dubious relevance given the time taken to work out the meaning of the error message, which uses 'workspace' to mean something different from R's usual meaning despite the fact that fisher.test is part of R's core 'stats' package.)