SPSS can’t calculate Exact test for 4x7 table of my data so I did it with Monte Carlo. The output is given below. Considering the rules of Chi-square, I should use Fisher’s $p$-value for the result of my data.

My question is: can I use fisher’s $p$-value with Monte Carlo simulations if I consider the rules? chi square table

  • $\begingroup$ You can use Fisher's $p$-value. However, it seems that your sample has a small frequency in some cases (cells), so you should proceed with care. $\endgroup$ – Ertxiem - reinstate Monica Mar 28 '19 at 10:46
  • $\begingroup$ Can you please clarify which assumptions are you considering? $\endgroup$ – Ertxiem - reinstate Monica Mar 28 '19 at 10:48
  • $\begingroup$ Expected count must be lower than 20% but if this is not ensure,the minimum expected count can be considered that if it is lower than 5 fisher, between 5-25 continuity correction and higher than 25 pearson should be used $\endgroup$ – v.yildirim Mar 28 '19 at 11:08
  • $\begingroup$ Please edit that information into your question. That's not an assumption of chi-square -- that's a version of some rules of thumb that are sometimes used to decide when the chi-squared distribution will be an adequate approximation to the distribution of the chi-squared test statistic (though it looks like some of the original conditions have been lost somewhere along the way). .If you're simulating, you're not using a chi-square approximation, so the chi-square statistic could be used even with low expected frequencies. .... ctd $\endgroup$ – Glen_b Mar 29 '19 at 14:48
  • $\begingroup$ ctd... on the other hand if you're using the Fisher test (simulated or not) it's not clear why you're worried about expected frequencies at all. Power might be a consideration but the distribution of the test statistic would seem to be a nonissue. $\endgroup$ – Glen_b Mar 29 '19 at 14:49

The whole point of the statistics in the SPSS Exact Tests module, which includes the Exact and Monte Carlo results, is that they don't rely on asymptotic approximations, but either directly calculate (exact) or estimate (Monte Carlo) p values instead. So if the rules to which you're referring have to do with when you can use asymptotic approximations, they're irrelevant, and the answer to your question is yes.

Note also that although sometimes you can't get the exact p value calculated using the Exact method due to memory issues, it is possible to get very close to it by extending the coverage level of the confidence intervals for the Monte Carlo method and running a huge number of simulations. If you run enough simulations for many problems you can get a 99.99% interval to have the same lower and upper bounds to 2-3 decimals, which is typically plenty of precision for a p value.

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