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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?

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    $\begingroup$ Cannot answer the first part but for comparing ordinal variable across >2 groups, you may consider Kruskal Wallis test. $\endgroup$ – Penguin_Knight May 17 '16 at 18:33
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The chi-square test is appropriate to use with ordinal data but, as you have found, some of your expected frequencies are <5. If your groups are independent and n <30 you can use the Wilcoxon rank-sum test. If the groups are not independent, not normally distributed and n < 30, you can use the Wilcoxon signed ranks test. One tests that the means are equal and the other tests that the medians are equal. Both are appropriate for ordinal data. This is from Basic and Clinical Biostatistics, 4th edition, by Dawson and Trapp, 1994.

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  • $\begingroup$ There are 3 groups. Are you recommending 3 rank-sum tests? $\endgroup$ – gung - Reinstate Monica May 17 '16 at 19:53
  • $\begingroup$ Is there benefit to using a Wilcoxon rank-sum or signed ranks test over the chi-square or Fisher test? $\endgroup$ – CephBirk May 18 '16 at 16:03

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