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I am having problems analysing baseline data for my study population.

My variables are erection dysfunction severity (mild, moderate and severe) and type of erection dysfunction (organic ED and psychogenic ED).

I want to know the percentage of mild, moderate and severe ED in both groups (organic and psychogenic) and whether the difference is significant.

Since the erection severity variable is non-dichotomous I cannot use chi square and Fisher's exact test. Please advise me which test I can use.

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    $\begingroup$ Your assertions (that you cannot use chi-square and Fisher's exact test) are incorrect. However, the ordering suggests other possibilities, depending on the precise alternatives of interest (which are unstated) $\endgroup$ – Glen_b -Reinstate Monica May 6 '18 at 5:03
  • $\begingroup$ Glen_b thanks for the swift reply. I said I cannot use chi square test because the variable ED severity has 3 levels ( mild, moderate and severe), this violates dichotomous rule of chi square. Please correct me if I am wrong on this. $\endgroup$ – demeclocycline SIADH May 6 '18 at 9:09
  • $\begingroup$ I want to know the distribution of ED severity i.e mild, moderate and severe ED in the two groups (organic and psychogenic ED ) and whether the distribution is significant . $\endgroup$ – demeclocycline SIADH May 6 '18 at 9:13
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    $\begingroup$ 1. You can have 20 categories on one and 35 on the other if you want; there's no requirement that chi-square or Fisher exact test be limited to 2x2. If you have a textbook or something that says otherwise it would be incorrect. 2. You can estimate the distribution from the sample proportions; if you have the contingency table you don't really need computers for that (though it's sometimes convenient). ... ctd $\endgroup$ – Glen_b -Reinstate Monica May 6 '18 at 12:03
  • $\begingroup$ ctd... 3. It's not at all clear what you intend by "whether the distribution is significant". What are you trying to find out about the distribution? Without using any statistical terms (like significant), what's the scientific question here? (I can make a guess, but it's best if you identify your own working hypotheses; this will help figure out whether you need something that considers the ordering) $\endgroup$ – Glen_b -Reinstate Monica May 6 '18 at 12:11
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If you're looking for any kind of difference in distribution rather than just a shift up or down, a chi-squared test should be fine. It doesn't matter that the dimension is larger than 2x2.

Similarly a Fisher Exact test may be done on tables larger than 2x2.

If you're specifically interested in a tendency to higher (or lower) categories on the ordered variable, you would want to consider different tests with better power against such alternatives.

Here's examples of a chi=squared and Fisher exact test done on a 2x3 table in R:

> table(ED)
          type
severity   organic psychogenic
  mild          24          15
  moderate      15          15
  severe        10          21

> chisq.test(table(ED))

        Pearson's Chi-squared test

data:  table(ED)
X-squared = 5.9425, df = 2, p-value = 0.05124


> fisher.test(table(ED))

        Fisher's Exact Test for Count Data

data:  table(ED)
p-value = 0.05536
alternative hypothesis: two.sided
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