# Normality test with p-value equal to zero [duplicate]

I have an array dataset of about 650.000 points. I want to test if the dataset follow a normal distribution or any other distribution. The first thing I did was to split the data in groups, find the frequency of each one and then create a simple chart. Here is the result:

LogY axis:

Normal axis:

Then, I tried to apply a statistic package in Python for Hypothesis null.

The first one: Link 1 with result (26576.286833062259, 0.0)

The second one: Link 2 with result (1.0, 0.0)

Both of them have p-value equal to zero which means that the data doesn't follow a normal distribution. Do you think that that this is valid or am I doing something wrong?

I tried it also with all the different distributions from this link and here is the results:

anglit (1.0, 0.0)
arcsine (1.0, 0.0)
cauchy (0.97256179317853242, 0.0)
cosine (1.0, 0.0)
expon (0.99998329829920973, 0.0)
gilbrat (0.99251782771674257, 0.0)
gumbel_r (0.99998329843868239, 0.0)
gumbel_l (1.0, 0.0)
halfcauchy (0.94812454120633505, 0.0)
halflogistic (0.99996659715630376, 0.0)
halfnorm (1.0, 0.0)
hypsecant (0.9999893673670458, 0.0)
kstwobign (1.0, 0.0)
laplace (0.99999164914960492, 0.0)
logistic (0.99998329857815205, 0.0)
maxwell (1.0, 0.0)
norm (1.0, 0.0)
rayleigh (1.0, 0.0)
semicircular (1.0, 0.0)
uniform (1.0, 0.0)
wald (0.99981187008374384, 0.0)

• This link may help. Commented Aug 11, 2014 at 10:55
• You have more than half a million points, so you'll reject more or less anything with prejudice at 'conventional levels'. Commented Aug 11, 2014 at 13:31
• If you want to know whether you've run into a software (or a numerical) bug, take subsamples of rather small size and compute the test statistics. p's should shrink to zero as you increase sample size until it's basically zero. Commented Aug 11, 2014 at 13:34
• Then I think that the test is doing what it's meant to. The question that @Zhubarb's comment brings up indirectly is 'what do you want this thing to be Normal for?' If it's to run a linear regression model and interpret coefficients it often won't matter at all. The CLT should have kicked in for most relevant quantities already. Commented Aug 11, 2014 at 13:50
• If you have that many data points, you can use many more bins to think about your distribution. Commented Aug 11, 2014 at 14:05