# Statistical test for differences between proportions, with many zeroes

I have collected data in the form of percentages, ie. what % of the population has Trait A? I measured the frequency three times for each population, giving three replicates. My ultimate goal is to use a statistical test to determine whether the replicates are producing the same results. For example, the first reading of population 1 gave 10.2%, but the second gave 11.5% and the third gave 8.1%, and I want to know if these readings are significantly different from each other. In total, I measured 12 populations, three times each.

Other people online who have dealt with frequency data have used a variety of tests, so I am not sure what is the ideal test for my dataset. Chi-square is often recommended, but I am concerned about using this because some of the populations I measured have expected values under 5. Therefore, I don't think a chi-square test will be best.

Alternative methods that can handle low expected values include fisher's exact test and the Kruskal-Wallis test. Of these two tests, which one is the most appropriate for dealing with this kind of data?

Let's assume, the prevalences are each counted from 1000 individuals, then Fisher's test can easily be computed with absolute numbers, not with percentages. It does not matter, if some numbers are small. Your example in R:

fisher.test(matrix(c(102,115,81,
1000-102,1000-115,1000-81),
nrow=2))


The result being

    Fisher's Exact Test for Count Data

data:  matrix(c(102, 115, 81, 1000 - 102, 1000 - 115, 1000 - 81), nrow = 2)
p-value < 2.2e-16
alternative hypothesis: two.sided


Fisher's test is for count data, which you have. Kruskall-Wallis is made for sample data, measured data.

• What do you mean for count data and sampled data Do you mean there is a fixed N and you have counted them all versus a large N and you have sampled a relatively small number of cases? Jun 22, 2018 at 14:10