I have three independent group data (Group A, B, and C), which sample size is 128, 100, and 31. Among those, the numbers of sample that showed the type I reaction were 67 for Group A, 40 for Group B, and 18 for Group C, and the numbers of sample that showed the type II reaction were 26 for Group A, 18 for Group B, and 4 for Group C. The sample showed both reactions were independent. I wanted to know the ratio of the sample showed the type I reaction over the type II reaction were significantly different from the expected frequency.

I first calculated its ratio for each group, which is 67/26 = 2.58 for Group A, 40/18 = 2.22 for Group B, and 18/4 = 4.50 for Group C. And the assume the expected frequency would be the total number of the sample showed the type I reaction (67+40+18 = 125) over the total number of the sample showed the type II reaction (26+18+4 = 48) , thus 125/48 = 2.6. And then I was trying to calculate the chi-square but realized the expected frequency was too small less than 5.

I'd very very much appreciate what type of test I can use in this case. Fisher's test doesn't work either because the data is not nominal?

Thanks in advance,

Sam