# Is a Fisher exact test for count data appropriate with an ordered factor?

I have the following contingency table:

tab = structure(c(35L, 28L, 5L, 11L, 16L, 3L, 8L, 16L, 2L, 5L, 10L,
10L), .Dim = 3:4, .Dimnames = structure(list(question = c("Faculty",
"Graduate student", "Research staff"), value = c("Never", "Rarely",
"Occasionally", "Frequently")), .Names = c("question", "value"
)), class = "table")


Which looks like this:

              value
question           Never Rarely Occasionally Frequently
Faculty             35     11            8          5
Graduate student    28     16           16         10
Research staff       5      3            2         10


I plan to use a Fisher exact test because a Chi-square test results in expected values < 5:

chisq.test(tab)\$expected

value
question               Never    Rarely Occasionally Frequently
Faculty          26.926174 11.879195    10.295302   9.899329
Graduate student 31.946309 14.093960    12.214765  11.744966
Research staff    9.127517  4.026846     3.489933   3.355705


I'm concerned however, because my columns are an ordered factor. Never through Frequently is a spectrum rather than a normal categorical variable.

Is the Fisher exact test or chi-square test appropriate for such a contingency table? Does it matter that my factor is ordered? Is there another test that uses this ordered characteristic better?

• Cannot answer the first part but for comparing ordinal variable across >2 groups, you may consider Kruskal Wallis test. – Penguin_Knight May 17 '16 at 18:33