Seeking Advice on Statistical Analysis Utilizing Fisher's Exact Test

[Cecilia]

Hello everyone,

I'm reaching out to the jamovi community for advice regarding statistical analysis in a recent study that specifically involved Fisher's exact test.

In our study, we collected data through binary response questions (yes or no). My approach involved initiating the analysis using Fisher's exact test whenever any cell in the contingency table had values below 5, while utilizing the chi-square test when all cells had values above this threshold.

A concern emerged when comparing my methodology to a similar study where they consistently utilized the chi-square value, even when calculated through Fisher's exact test (marked as a red square). However, the jamovi software does not directly calculate Fisher's test (marked as a green square).

My intent is to present the final table to my colleagues, ensuring consistent inclusion of the chi-square test value (marked as a blue square) with its corresponding p-value, while explicitly noting the statistical method utilized, which predominantly involves Fisher's exact test (marked as a purple square).

I would greatly appreciate any guidance or insights from this community regarding this approach and the utilization of Fisher's exact test in statistical analysis. As this project marks my initial foray into significant research, your expertise and advice are invaluable.

Additionally, I was wondering if anyone could shed light on the terminology "χ²(1)/U" (blue square) and in which contexts it would be appropriate to adopt it.

I sincerely thank you for any advice or clarification you can offer on these matters. This is my first significant project, and I feel a bit lost, so I truly value any insights drawn from your expertise and experience.

Thank you very much,
Cecilia

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[Cecilia]

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[MAgojam]

However, the jamovi software does not directly calculate Fisher's test (marked as a green square).

Hey Cecilia,
for the above you could take a look at an old answer of mine here:
viewtopic.php?p=8154#p8154

Apart from your table, could you provide reference links to the works where the other tables are published?

Cheers,
Maurizio
https://www.jamovi.org/about.html

[reason180]

Yes, so regarding "they consistently utilized the chi-square value, even when calculated through Fisher's exact test (marked as a red square). However, the jamovi software does not directly calculate Fisher's test (marked as a green square)." . . .

. . . jamovi does "directly" calculate Fisher's exact test: The exact test outputs a p value. It is not supposed to output a "statistic" the way
chi square test does.

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[Cecilia]

However, the jamovi software does not directly calculate Fisher's test (marked as a green square).

Hey Cecilia,
for the above you could take a look at an old answer of mine here:
viewtopic.php?p=8154#p8154

Apart from your table, could you provide reference links to the works where the other tables are published?

Cheers,
Maurizio
https://www.jamovi.org/about.html

Hi, thank you very much. the article is this https://pubmed.ncbi.nlm.nih.gov/36138695/

[MAgojam]

Hi Cecilia,
So, as you may have read in the post I linked to you, but above all as @reason180 reported to you again (thanks r180, appreciated presence in this Forum) just above, in jamovi you will have the direct calculation of Fisher's exact test with the return of only the p-value.
With a 2x2 contingency table you will have a χ² "statistic" with 1 degree of freedom and the p-value. In the publication you refer to, a non-parametric test for independent data (Mann-Whitney U) was also used which reports a U "statistic" and the relative p-value.
So the row label χ²(1)/U that you find in the tables indicates that the values of that row can be those of a χ² statistic with 1 degree of freedom or a U statistic of a Mann-Whitney U test.
Thus, the table footnote [*] regarding p-values will report which test returned it.

If you look at tables 2 and 3 you will find the correspondences that I have mentioned.

Unfortunately, table 4 (which is the same one you attached in your initial post) has a typo for the label χ²(1)/U, which should have only been χ²(1), since there is no U statistic present , but only a χ² statistic and p-value released by Fisher's exact test.
I don't think anything else is needed other than paying attention when preparing tables for possible publication.

Do with enthusiasm what you like to do.
Maurizio

[decaux]

You could use the likelihood ratio test (LRT), also available under Tests for contingency tables. This will give you both a chi-square and p value.

The LRT is not subject to the restriction that expected values should not be < 5.
Theoretically, it is also the preferred test https://www.preprints.org/manuscript/202311.1495/v1

[MAgojam]

Hi Peter,
Thank for link.

Maurizio