I've been trying to think of the best way to approach testing for associations of genotypes (i.e. D/D, D/I, I/I) with ethnicity (i.e. African Americans, etc). Specifically, I would like to test whether any one ethnic group has a statistically significant difference in frequency of D/D or D/I genotypes over the other ethnic groups.

                     D/D     D/I     I/I
African American     3       25      160
Hispanic             3       6       57
Non-Hispanic White   0       6       32
Asians               0       1       9
Other                0       0       4

I figure turning to a simple chi-square test for association would work to at least give me a non-directional association, but I know that Chi-square calculations are only valid when all expected values are greater than 1.0 and at least 20% of the expected values are greater than 5. But, these conditions aren't met in this case.

I've tried grouping different ethnicities in an attempt to satisfy these conditions, but to no avail. I'd really appreciate any input on this issue and/or advice on whether there may even be a more appropriate method to answer my question. Novice here.


  • $\begingroup$ Fischer's test using simulation? $\endgroup$
    – SmallChess
    Oct 18 '17 at 15:48

Fisher's test? see http://www.biostathandbook.com/fishers.html for help and you can search other questions on our website.

  • 1
    $\begingroup$ Yeah, I had to do some reading to learn further that a Fisher's test can be for any m x n table with a Monte Carlo (MC) simulation to account for variation and uncertainty. For all the newbies out there like me, I addressed this problem through R in the following manner: > Data<-matrix(c(3,3,0,0,0, 25,6,6,1,0, 160,57,32,4,9), 5,3, dimnames=list(ethnicity=c("African American","Hispanic","Non-Hispanic White","Asian","Other"),genotype=c("D/D","D/I","I/I"))) #create matrix of data > fisher.test(Data, simulate=TRUE, B=1e5) #Fisher's exact test with 1e5 iterations for MC simulation. $\endgroup$
    – Matt
    Oct 18 '17 at 20:32

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