Re: Problems with DistributionFitTest

• To: mathgroup at smc.vnet.net
• Subject: [mg122569] Re: Problems with DistributionFitTest
• From: Ray Koopman <koopman at sfu.ca>
• Date: Tue, 1 Nov 2011 06:58:11 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <j8nuqm\$egv\$1@smc.vnet.net>

```On Oct 31, 10:07 pm, fd <fdi... at gmail.com> wrote:
> 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 p-value 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 p-value to be really low, if I re-run 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 re-runs 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

If the data were generated by the distribution for which you are
testing then, no matter what the sample size is, the p-value is a
sample from a Uniform[0,1] distribution, so 5% of the time it should
be < .05, etc.

```

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