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Re: Determining if samples are normal
From: |
Paul Kienzle |
Subject: |
Re: Determining if samples are normal |
Date: |
Mon, 26 Sep 2005 03:55:52 -0400 |
The Anderson-Darling test is claimed to be pretty good:
http://www.itl.nist.gov/div898/handbook/prc/section2/prc213.htm
http://www.itl.nist.gov/div898/handbook/eda/section3/eda35e.htm
Here's the relevant section from the R manual:
http://www.maths.lth.se/help/R/.R/library/nortest/html/ad.test.html
The Anderson-Darling test is an EDF omnibus test for the composite
hypothesis of normality. The test statistic is
A^2 = -n -frac{1}{n} sum_{i=1}^{n} [2i-1] [ln(p_{(i)}) + ln(1 -
p_{(n-i+1)})],
where p_{(i)} = Phi([x_{(i)} - overline{x}]/s). Here, Phi is the
cumulative distribution function of the standard normal distribution,
and overline{x} and s are mean and standard deviation of the data
values. The p-value is computed from the modified statistic
Z=A^2 (1.0 + 0.75/n +2.25/n^{2})
according to Table 4.9 in Stephens (1986).
Here are the critical values I found elsewhere on the net.
90% 0.631
95% 0.752
97.5% 0.873
99% 1.035
For example, if A^2 > 0.752 you can say that your data set is not
normally distributed with 95% confidence.
This is implemented in octave-forge as 1-p =
anderson_darling_test(x,'normal'). That is, if anderson_darling_test
returns a value of 0.05 then you can say your data set is not normally
distributed with 95% confidence.
- Paul
On Sep 25, 2005, at 1:59 PM, Søren Hauberg wrote:
Hi,
Does anybody know how I can test wether or not some samples are
normaly distributed? I tried graphical methods, such as looking at
histograms and qqplots, but I don't trust my own judgement enough to
use graphical methods.
/Søren
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Re: Determining if samples are normal, Joe Koski, 2005/09/25
Re: Determining if samples are normal,
Paul Kienzle <=
Re: Determining if samples are normal, Henry F. Mollet, 2005/09/27
Re: Determining if samples are normal, Mike Miller, 2005/09/27