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From: Walter Roberson on 27 Jul 2010 14:30
Oleg wrote:
> I have two data tables as a result of two similar experiments. I want to
> check and, if possibly, to compare the chances whether residuals in rows
> have normal distribution with zero mean. The problem is that kstest
> compares with standart normal distribution (fixed mean and SD), and
> lillietest is nonparametric test. Thanks for answers!

Do I gather correctly that the two data tables are to be tested to see if they
are normal distribution with 0 mean, but with possibly two different standard
deviations?

If so, then you might be able to get close by normalizing each of the tables
independently (subtracting mean, dividing by standard deviation afterwards)
and then kstest to see if the distribution is the same.

However, at the moment I do not know how you would use a similar approach to
deal with the possibility that the apparent mean and sd was only a statistical
artifact of a finite sampling of a distribution with a 0 mean and different sd.
From: Peter Perkins on 28 Jul 2010 09:57
On 7/27/2010 2:22 PM, Oleg wrote:
> I have two data tables as a result of two similar experiments. I want to
> check and, if possibly, to compare the chances whether residuals in rows
> have normal distribution with zero mean. The problem is that kstest
> compares with standart normal distribution (fixed mean and SD), and
> lillietest is nonparametric test. Thanks for answers!

Three things:

1) You will not be able to "compute the probability that a set has
normal distribution" unless you adopt a Bayesian analysis, and put a
prior probability on that hypothesis. What you can do with things like
KSTEST is to compute a p-value for that null hypothesis.

2) Lilliefors' test is not non-parametric, at least in the usual sense
of that word. It uses a table of p-values and critical values that has
been computed by simulation, but that's not the same thing. Lilliefors'
test is nothing but the K-S test with the p-values adjusted for the case
when you've estimated the parameters that you are testing against.
Which is to say, it is usually used as a test for "unspecified
normality", as opposed to a test for a specific normal distribution. If
you don't know the std dev of your data, you want LILLIETEST, not KSTEST
(assuming that this kind of GOF test is what you want in the first
place). KSTEST is not appropriate (the p-values will not be correct)
unless you know the mean and std dev in advance.

3) You might want to think about whether you are testing if a particular
set of residuals is normally dist'd, or testing if two sets of residuals
have the same dist'n, or ... .

Hope this helps.

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