I have a specific reference ratio such as 1:2:1 against which I want to compare other ratios. I'd like to know how to rank test ratios like those below in order of how close they are to the reference ratio. How would I calculate this?
Test ratios: 2:1:1, 1:2:2, 1:3:1
One way would be to use a $2\times 3$ table and find its chi-squared statistic.
For example, 1:2:1 vs. 2:1:1 would have rows (1,2,1) and (2,1,1) with ch-sq value $2/3 = 0.67$. By contrast, 1:2:1 vs. 1:3:1 gives $0.09$ (less different).
Just an idea. You would have to judge whether results match your intuition and purpose. At least, it would be easy to find the values for each comparison:
R code for the first:
TBL = rbind(c(1,2,1),c(2,1,1))
chisq.test(TBL)$stat
returns $0.6666667.$
