Re: [Gretl-users] powerball puzzle
Am 05.12.2016 um 19:19 schrieb Riccardo (Jack) Lucchetti:
On Sun, 4 Dec 2016, Allin Cottrell wrote:
> It seems that under the null the p-value ought to be distributed
> uniformly on (0,1). That appears to the case for the chi-square test,
> but not at all for the two tests that employ the inverse normal
> transformation.
I don't know this lottery and my discrete-valued statistics is probably
lagging, but why would the normal distribution play a role here when you
distribute 605 draws randomly over 69 bins? (Non-negativity / bounded
support being only one of the issues perhaps?)
The way I see it, the series z you're generating in the
"cdftest"
function is not really normally distributed. Rather, is constructed in a
way such that its frequency distribution resembles a Gaussian density,
which wouldn't be guaranteed if data were truly normal. In other words,
your normals are "too good to be true"; hence, your p-values are mostly
very close to 1.
Jack, I know you must mean something else than what you've written --
the data's density "too" Gaussian to be Gaussian??
cheers,
sven