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### goodness of fit test?

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>I'm just learning to use the SAS software and am confused about one of
>the readouts. After putting in a set of univariate data and running an
>analysis on it, the goodness of fit for a normal distribution (under
>the K-S method)  reads out a P value that states Psub r > D    >0.150.
>How do I interpret this?   The null should be that the data can be
>modeled by a normal distribution and should be rejected if the Test
>statistic ( D ) ( 0.088 ) exceeds the critical value . Is the P value
>the same thing as the critical value?  So is the read out " >0.150 "
>mean the critical value is 0.150 or that the statistic is less that
>the critical value by 0.150  or what? thanks for any help here. john
Also what is the presumed alpha?  thanks jk
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```road12fg@NETSCAPE.COM wrote back:
>On Wed, 6 Sep 2006 11:19:45 -0700, davidlcassell@MSN.COM (David L
>Cassell) wrote:
>
> >> >I'm just learning to use the SAS software and am confused about one of
> >> >the readouts. After putting in a set of univariate data and running an
> >> >analysis on it, the goodness of fit for a normal distribution (under
> >> >the K-S method)  reads out a P value that states Psub r > D    >0.150.
> >> >How do I interpret this?   The null should be that the data can be
> >> >modeled by a normal distribution and should be rejected if the Test
> >> >statistic ( D ) ( 0.088 ) exceeds the critical value . Is the P value
> >> >the same thing as the critical value?  So is the read out " >0.150 "
> >> >mean the critical value is 0.150 or that the statistic is less that
> >> >the critical value by 0.150  or what? thanks for any help here. john
> >>Also what is the presumed alpha?  thanks jk
> >
> >First off, I do not recommend the K-S test in this situation.  Use the
> >Shapiro-Wilk test instead.  It is more 'reliable'.  None of these tests
> >is perfect, and different sorts of deviaitons from the null-hypothesis
> >distribution can lead to different performance issues with different
>tests.
> >In fact, I wrote a bunch about this in SAS-L just a couple months ago.
> >Obviously, you didn't see that.
> >
> >
> >That said, D is (probably) your test statistic.  I say probably, because
> >you may (or may not) actually want D+ or D-, depending on your
> >chosen alternative hypothesis.  This makes a difference in the p-value
> >too.
> >
> >So you know that your p-value is greater than .15 .  That's all you get
> >here.  (Well, I told you to use a different test, didn't I?)  Your alpha
> >is whatever YOU chose it to be.  If you chose alpha to be .01 or .05
> >or .10, then clearly you didn't reject the null hypothesis.  (That does
> >not mean your distribution is normal, it may just mean that the test
> >didn't find the problems effectively.)
> >
> >
> >And finally, why are you testing that your data are normal?  I see people
> >doing this all the time, and in most of these cases, they are doing the
> >wrong thing.
> >
> >HTH,
> >David

>
>Thanks, this is pretty what I needed. But one question... Does the
>Shapiro -Wilk give a specific P value rather than the "greater than "
>that the K-S  test? thanks jk

K-S only gives that "P > ..." bit under certian circumstances.  Don't
count on that.

Similarly, I canot guarantee that the Shapiro-Wilk statistic will *never*
give you such an output.  It is designed to handle both large and
small n, and it can handle a wide range of p-values.  But there may be
circumstances where someday, somewhere, it will give you such a
message.  Expect that they will be the extreme cases, such as really
minute or really enormous p-values which are so far away from your
cutoff values that you don't need to know an exact number.

Which is basically what happened with your K-S statistic with your data.

HTH,
David
--
David L. Cassell
mathematical statistician
Design Pathways
3115 NW Norwood Pl.
Corvallis OR 97330

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Reply davidlcassell (5578) 9/11/2006 6:06:54 AM

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