Compare odds in two fisher tests

#1
Dear all,

I performed 3 fisher tests from data implicating in each test the same two sets (A & B) with two different sets in each case (A&B vs C&D, A&B vs E&F, A&B vs G&H; tables below).

Fisher tests for the three sets gave low p values with odds of 6.6, 3.6 and 2.5. I need to know if the odds are significantly different and I though of performing 3 Chi-squared tests between each two matrices (i.e Chi test will give me a pval of 2e-08 between the first two matrices). Is it right from me to consider a Chi test for my purpose ? If not, what is the best test to compare two odds ?

Many thanks for you

Code:
        C	D
A	162	877
B	128	4604

	E	F
A	110	929
B	152	4580

	G	H
A	29	1010
B	53	4679
 

hlsmith

Less is more. Stay pure. Stay poor.
#2
Chi square test should be fine here. The Fisher's exact test is preferred with small samples, which does not appear to be an issue for you.


You are at risk for false discovery if you are comparing the same group to 3 other groups. By chance it could be significantly different. Most people would recommend a correction to your level of significance, making the alpha value smaller. If you do this, you will also want to correct the alpha level in the calculation of your 95% confidence intervals for the odds ratios. The Bonferroni correction is the most popular due to its simplicity.
 
#3
Many thanks for you fast reply.
Just to be sure that I got you well. I used fisher to make the test for each matrix independently and this gave the odds mentioned above. I want now to compare the "rates" between different categories to see if i.e matrix 1 is different from matrix 2 (or in other terms, if the odd obtained in the first matrix differs form the odd in the second one). this is why I though of running a Chi-test where one matrix will be considered as the expected counts and the other as the observed.

Regarding the p.val correction, I imagine that I can use "p.adjust" method in R with one Benferroni or BH ...

thanks again
 

hlsmith

Less is more. Stay pure. Stay poor.
#4
Well your use of the word matrix confuses me a little, but I am presuming you are referencing just running the 3 contingency tables you presented. If you are also trying to compare the results between the three tables, well then you may be looking at running the Cochrane Mantel Hanzel (sp?) test, to compare the odds.


It might help to describe what these variables represent, so we don't lead you the wrong direction. I could also see logistic regression used in this setting.
 
#5
Sorry for the confusion. Yes indeed, these are contingency tables for counts that I have between my different sets.
As an example from the first table, the counts represent number of individuals in set A that fall in category C (162 individuals) and those that fall in category D (877 individuals).
The Fisher test for each contingency table gave me pvalues of P<2.2e-16, P<2.2e-16 and P=2e-04 with the respective odds of 6.6, 3.6 and 2.5.

You are right too, I am trying to compare the results (odds) between the three tables.

Thanks,
 
#7
I would say yes, they are related (maybe indirectly), as the counts are in each case for individuals in A and B that fall in categories C & D, or in categories E & F or in categories G & H.