Suppose we have the following data set:

                Men    Women
Dieting         10      30
Non-dieting     5       60

If I run the Fisher exact test in R then what does alternative = greater (or
less) imply? For example:

mat = matrix(c(10,5,30,60), 2,2)

fisher.test(mat,alternative ="greater")

I get the p-value = 0.01588 and odds ratio = 3.943534. Also, when I flip
the rows of the contingency table like this:

mat = matrix(c(5,10,60,30), 2,2)

fisher.test(mat,alternative ="greater")

then I get the p-value = 0.9967 and odds ratio = 0.2535796. But, when I run
the two contingency table without the alternative argument (i.e.,
fisher.test(mat)) then I get the p-value = 0.02063.

   1. Could you please explain the reason to me?
   2. Also, what is the null hypothesis and alternative hypothesis in the
   above cases?
   3.

   Can I run the fisher test on a contingency table like this:

   mat = matrix(c(5000,10000,69999,39999), 2,2)

Thanks.

PS: I am not a statistician. I am trying to learn statistics so your help
(answers in simple English) would be highly appreciated.

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