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I have two ordinal variables, and I'm using the Fisher's Exact Test in lieu of the chi-square test when the expected values for the latter test are lower than 5. My contingency tables are $3\times2$.

I have a couple of concerns:

  • From the Fisher's Exact test, I just expect a $p$-value. Anyway, when I calculate it in SPSS for $3\times2$ tables, I also get a value for the test statistic (like in the Chi-quare test). What does this mean? Should I report it in my results?

  • Would it make sense to report the Chi-square statistic (even if expected values are lower than 5) together with Fisher's Exact Test results? Or would a $p$-value from Fisher's test be enough?

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The test statistic is, as you say, like the chi-square test statistic (or any other). Although not everyone reports it, I think you should. It is the result of running the test; the calculation (on larger than 2x2 tables) is pretty involved but that is what computers are for.

I would not report the chi-square statistic, unless you correct somehow for small sample sizes (e.g. by simulation). I don't know what options SPSS offers, but Fisher's is not the only option.

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  • $\begingroup$ Thanks! Do you also know why SPSS doesn't give me the FI(x) value for 2x2 tables? $\endgroup$ – Forinstance Jan 7 '14 at 15:45
  • $\begingroup$ I have the same problem with R which doesn't provide a value for the statistic (but just the p-value). $\endgroup$ – Forinstance Jan 7 '14 at 15:55
  • $\begingroup$ @Forinstance, why SPSS doesn't give me the FI(x) value for 2x2 tables. I'm not quite sure. I think just because different programs compute it. For 2X2 table, computation is done by the core Crosstabs routine. For greater table, computation is done by Exact tests module. $\endgroup$ – ttnphns Jan 7 '14 at 16:02
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Your SPSS output should note that some cells have an expected frequency of less than 5 (if they do). You can also click on the option to display these expected frequencies in your output. In those cases, use Fisher's exact test, which SPSS should automatically provide. It's not necessary to provide both results, but your methods (or a footnote in the table) should mention that you're using Chi-square "or Fisher's Exact Test as appropriate", i.e., you're using Fisher's if any expected frequencies are less than five.

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