I have count data on different languages from comparable corpora.
It looks something like this, where the counts give the number of clauses with that particular word order attested in each language corpus (constructed example):
SOV SVO VSO 0SV OVS VOS English 3 124 0 0 6 0 Tagalog 2 14 109 0 3 10 Dutch 56 61 4 0 7 0 Hindi 110 1 2 2 6 9
I am interested in the differences between languages, i.e. whether these four languages display different or similar word order patterns. I can use chi-square on the whole table, or for separate columns, but I run into trouble with some cells being 0, or < 5. Fisher's exact test is recommended in those cases, but I haven't been able to do this in R so far. If I try it on the whole table, I get FEXACT errors, complaining either that LDKEY or LDSTP are too big or too small. It does not allow me to take just one column, as it needs a table structure of at least 2x2. It allows me to test two columns at a time, but this does not seem appropriate.
Are these methods even appropriate for count data, or do I need something else entirely? I realise this is not a traditional contingency table.
Is there any implementation of Fisher or something comparable (preferably in R) that can be used on the whole table?
Is there something comparable to Fisher that I could use for a single column? Like I said, chi-squire does not seem appropriate due to low values.
EDIT: I realise that my constructed word order example above has such strong associations between language & word order patterns it doesn't matter too much if chi-squared is used (RE: Nick Cox's answer below).
But what about data distributed like this:
constr1 constr2 constr3 constr4 L1 1 5 20 194 L2 0 4 19 191 L3 1 8 30 180
constr1 constr2 constr3 L1 61 166 0 L2 55 66 2 L3 55 60 2 L4 54 114 4 L5 53 98 5
I guess I really want to know whether there is any alternative to assess the whole table rather than conducting multiple Fisher exact tests (I don't own SAS so Peter's option is not available to me).