What is the concepts of nominal and actual significance level? What is the concepts of nominal and actual significance level?
Although I understood these concepts about five years ago, I totally forgot the notion and cannot find that in Google.
 A: Note: I suspect that there are at least two different meanings of "actual significance level" around, but here's one that makes sense to me:
The nominal significance level is the significance level a test is designed to achieve. This is very often 5% or 1%. Now in many situations the nominal significance level can't be achieved precisely. This can happen because the distribution is discrete and doesn't allow for a precise given rejection probability, and/or because the theory behind the test is asymptotic, i.e., the nominal level is only achieved for $n\to\infty$.
Here's an example. We toss a coin 5 times and we want to test at nominal 5% level whether it's biased in favour of "heads". The probability for five times heads is 1/32<0.05, the probability for four times heads is 5/32>0.05. We can't reject for four heads because then we go beyond the nominal level, therefore we only reject for five heads, leaving us with an actual significance level of 1/32. (In fact Neyman and Pearson had the concept of a randomised test that in case of four heads would reject randomly with a certain probability chosen so that the overall rejection probability is 5% so that nominal and actual significance level are the same, but this is not very appealing.)
