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fd
Posts:
43
Registered:
7/24/09


Problems with DistributionFitTest
Posted:
Nov 1, 2011 12:29 AM


Dear Group
I'm not a specialist in statistics, but I spoke to one who found this behaviour dubious.
Before using DistributionFitTest I was doing some tests with the normal distribution, like this
data = RandomVariate[NormalDistribution[], 10000];
DistributionFitTest[data]
0.0312946
According to the documentation "A small pvalue suggests that it is unlikely that the data came from dist", and that the test assumes the data is normally distributed
I found this result for the pvalue to be really low, if I rerun the code I often get what I would expect (a number greater than 0.5) but it is not at all rare to obtain p values smaller than 0.05 and even smaller. Through multiple reruns I notice it fluctuates by orders of magnitude.
The statistician I consulted with found this weird since the data was drawn from a a normal distribution and the sample size is big, especially because the Pearson X2 test also fluctuates like this:
H=DistributionFitTest[data, Automatic, "HypothesisTestData"];
H["TestDataTable", All]
Is this a real issue?
Any thougths
Best regards Felipe



