confusion in reporting the test results of the Monte Carlo simulation

[smn kr]

Dear Neeraj Sir and respected group members,

Hope you all are doing well. I came across a result that I am a little confused about, and I'm not sure which I should consider. I ran a Fisher's exact test due to violations of chi-square assumptions, but I still did not get the results, so I ran it with a Monte Carlo simulation. where I found that in the Monte Carlo significance (2-sided) column, p = .351 (in Pearson chi-square row), but in the Fisher's exact test row, p = .034. Then, which p-value should I report? As one p-value is not significant, another one is significant. I am attaching the respective result. Please help me with this.

Best Regards

Suman Kumar

PhD research scholar

[Sunil Chawla]

What is the dimension of cross table. 

Since data is sparse, fisher-freeman-halton is more appropriate. However, if you can combine the rows or columns, ie reduce the dimension of table to reduce the cells with less than five cases, it may give comparatively good results. 

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[smn kr]

Dear Chawla Sir,

Thank you for your suggestion, sir, but what I'm asking is: the Monte Carlo significance (2-sided) column shows p = .351 (in the Pearson chi-square row), but in the Fisher's exact test row, p = .034. Then, which p-value should I report? As one p-value is not significant, another one is significant. If any reference for this, please suggest me.

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[Neeraj Kaushik]

Dear Suman

The discrepancy in p-values (Pearson's Chi-Square Monte Carlo $p=.351$ vs. Fisher's Exact Test $p=.034$) is likely explained by the sparse data in your cross-tabulation.

Please look closely at the footnote of your output table, which states that 61 cells have an expected count less than 5. Ideally, this number should be zero for the standard Pearson's Chi-Square test to be reliable. Because the assumption of expected cell frequencies is heavily violated, the Pearson's Chi-Square test value is inaccurate and should not be used.

Therefore, you should report the p-value from Fisher's Exact Test ($p=.034) and base your decision on that result.

Best wishes

Neeraj 

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[smn kr]

Dear Neeraj sir,

Thank you sir for the information clarification. I got the point.

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