I made a test with 15 true/false Questions and about 100 people answered these questions.
Now I'm doing the item analysis in R with the package sjPlot and the function sjt.itemanalysis().
Amongst other things this function returns skewness and kurtosis. Does it make sense in my scenario to interprete them? In this case the skewness does not tell me more than the mean/item difficulty, does it?
If you have a binary variable where the values are typically assumed to be independent - like getting a particular question right (1) or wrong (0) - and you look at the average (the proportion of 1's) over a number of observations, you have something completely defined by two numbers (though the information can be expressed several different ways). For example, $p$, the sample proportion of 1's and the total number of values will be sufficient (as would the total number of 1's and the total number of 0's); naturally you can readily convert between pairs of values that carry the information.
Anything calculated from the sample of 0's and 1's can also be calculated directly from the sample proportion, $p$ and the sample size $N$. So a sample skewness or kurtosis is simply a function of $p$ and $N$. Given $N$ as known, and the assumption of independence (so that the order of 0's and 1's is irrelevant, for example), there's no additional information beyond $p$ itself.
That's not to say you can't be interested in knowing skewness or kurtosis, even though they're completely determined by $p$ and $N$.
