I used Mathematica's function PearsonChiSquareTest to test whether the data were drawn from a normal distribution.
As in the reference, I expected Mathematica to compare the result to a normal distribution, by running:
As I wanted to extract the test statistics from properties, I was "forced" to name the distribution I wanted to compare it to, namely the normal distribution:
What is surprising is that the PValue for the first case is different from the second case where I use the Normal Distribution explicitly. Anyone knows what's the difference here?
data = RandomVariate[NormalDistribution, 10^4]; PearsonChiSquareTest[data] (* ==> 0.3248593157 *) PearsonChiSquareTest[data, NormalDistribution] (* ==> 0.4704917701 *)