As in the title, I have two sets of data that are identical. I performed a paired t-test using R.
The p-value for the difference estimated (which is essentially 0) is NaN.
I wonder if there can be a theoretical p-value for this case.
So I think justifiable p-values for a t-test will actually be what R gave you, while justifiable p-values if you have discrete variables and choose a more appropriate test would generally be 1.
The null hypothesis for a paired t-test is that the mean difference of your two paired samples is equal to zero.
Considering you have identical values for each pair, the difference should always be equal to zero, thus failing to reject the null hypothesis.
This would mean p-value = 1 or NaN (0/0), but this doesn't really imply you should conclude anything.
A p-value of less that 0.05 will suggest the existence of a significantly different mean for each sample.