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Re: statistical function example
From: |
Dean Allen Provins |
Subject: |
Re: statistical function example |
Date: |
Tue, 6 Sep 2005 13:18:07 -0600 |
User-agent: |
Mutt/1.5.9i |
Matti:
On Thu, Aug 25, 2005 at 09:12:59PM +0000, Matti Picus wrote:
> Dean Allen Provins <provinsd <at> telusplanet.net> writes:
>
> > > On Tue, 23 Aug 2005, Dean Allen Provins wrote:
> > >
> > > >I have been trying to make some sense out of the
> > > >"kolmogorov_smirnov_test"
> > > >function result. Given a sample of 8 data points, for which Swan and
> > > >Sandilands, "Introduction to Geological Data Analysis", give a clear
> > > >answer, I cannot get an answer from the KS test that has any meaning
> > > >for me.
> > > >
> > > >S&S obtain the maximum deviation (about 0.22) and compare that value to
> > > >that which would be exceeded with probability 0.05 (their table indicates
> > > >about 0.46). The second return value from the Octave KS test is much
> > > >larger:
> > > >
> > > > p = 0.053223
> > > > k = 1.3466
> > > >
> > > >I presume the "p" value is the probability of rejecting H0, but what is
> > > >"k"? No such value appears in the one-sided test tables that I located
> > > >on the 'net.
> > > >
> > > >The input data X and the cumulative frquency used (i/n+1) is:
> > > > X CF
> > > > 0.07000 0.11111
> > > > 0.12000 0.22222
> > > > -0.06000 0.33333
> > > > -0.04000 0.44444
> > > > -0.05000 0.55556
> > > > 0.08000 0.66667
> > > > 0.04000 0.77778
> > > > 0.00000 0.88889
> > > >
> > > >Would any readers with some insight care to enlighten me?
> > > >
> > > >
> > > >Thanks,
> > > >
> > > >Dean
> Background : just so we are talking about the same thing...
> The test works like this: given two sampled "cumulative frequencies" F1 and F2
> (btw they are more commonly refereed to as "cumulative distribution
> functions"),
> calculate a value k based on the number of samples in each F1 and F2 and the
> maximum distance between them (maximum distance is defined as follows: plot
> the
> two distributions using the sampled values on the x axis and their associatd
> probablilities on the y axis. Maximum distance is the point at a vertical line
> joining the two plots is maximum length). Then use the value k to look up a
> probability for H0.
>
> You can accept H0 with confidence level p, or alternatively reject it with
> confidence (1-p). A value of 0.05 makes it pretty clear that the two
> distributions are different. There are different methods for calculating p
> from
> k, some authors are a little careless for k values that result in such a clear
> rejection of the null hypothesis since those cases are not interesting to most
> of us.
>
> The call to the octave implementation of the test assumes that you have
> x - a set of raw obesrvations
> i.e. [0, 0.4, -0.1, 0.7, 0.3, 0.4, -0.9]
> dist - a text string that when evaluated using feval('dist_cdf(y)') will yeild
> the CDF of the chosen distribution at the value y
>
> so a call to the function like
> [p,k]=kolmogorov_smirnov_test(x, "uniform", 0, 1)
> would give the probability p that the sample x is drawn from a uniform
> distribution over 0 to 1.
> The value k would be an intermediate value calulated from the length of x and
> the maximum difference between a sampled CDF of x and a uniform distribution,
> used to look up p.
>
> The strength of the test is that the value of k determines directly the
> probablility, with no assumptions about either distribution
>
> Did this help?
> Matti
Thanks for the assistance, and I apologize for not responding sooner.
I have examined the code, and tried to make some sense of it in the light
of the only text (Swan and Sandilands, 1995) that I have that mentions
a KS test.
I think that with your explanation and my code study, I'll be able to
make use of the test with some confidence.
Thanks again,
Dean
--
Dean Provins, P. Geoph.
50.95033N, 114.03791E
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- Re: statistical function example,
Dean Allen Provins <=