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bateman@nsslsun.nssl.uoknor.edu (Monte Bateman) writes:

>I would like to test data for normality.  The books I have
>access to talk about graphing frequencies on "probability paper".

Look up the Kolmogorov-Smirnov (sp?) statistic in a more advanced
statistics text than the ones you have now.  This statistic is
implemented in many of the major commercial stat packages, and is not
hard to compute.  (It is basically a software implementation of using
probability paper.)  Be forewarned, however, that the test is not
very powerful against many alternative distributions, especially the
ones that are "normal-like", so you might need a very large sample to
do a reliable test.

--
T. Scott Thompson              email:  thompson@atlas.socsci.umn.edu
Department of Economics        phone:  (612) 625-0119
University of Minnesota        fax:    (612) 624-0209

In article <1992Sep5.064647.15570@constellation.ecn.uoknor.edu> bateman@nsslsun.nssl.uoknor.edu (Monte Bateman) writes:
>I would like to test data for normality.  The books I have
>access to talk about graphing frequencies on "probability paper".

>First off, I don't have any.

>Second, it seems that there should be software available 
>to do this test.

>Pointers?

>Any/all help appreciated!


There is no shortage of tests for normality.  One problem is that the
behavior of the test statistic, even the size, is generally not computable
except by simulation, even approximately.  The problem is also to get a
reasonably good test against the most likely alternatives.

The Kolmogorov-Smirnov test with the parameters, assuming normality, 
estimated from the data is not difficult to calculate.  There are tables
of the significance levels.
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: (317)494-6054
hrubin@pop.stat.purdue.edu (Internet, bitnet)  
{purdue,pur-ee}!pop.stat!hrubin(UUCP)

In article <thompson.715720959@hermes.socsci.umn.edu>, thompson@atlas.socsci.umn.edu (T. Scott Thompson) writes:
> bateman@nsslsun.nssl.uoknor.edu (Monte Bateman) writes:
> 
>>I would like to test data for normality.  The books I have
>>access to talk about graphing frequencies on "probability paper".
> 
> Look up the Kolmogorov-Smirnov (sp?) statistic in a more advanced
> statistics text than the ones you have now.  

A clarification:  Using the K-S statistic to test for normality, 
calculated after plugging in the sample mean and variance in place of the 
population parameters, is known as
Lilliefors' [Strunk and White be damned!] test.

A Shapiro-Wilk test or a D'Agostino test would probably serve you better.
Lilliefors' test tends to be more sensitive to departures from normality
in the center of the distribution.  (One look at the test statistic will
reveal why.)  THe other tests tend to be more sensitive to departures
from normality in the tails, which is where non-normality is most often a
problem.  

This various tests have been compared most recently in, of all places, 
the Stata Technical Bulletin.  I dislike mentioning articles in a computer 
program's documentation/house organ because they are typically neither peer 
reviewed nor widely circulated, but it's there, so what can I say?
(I have heard rumors that Royston is preparing his contributions for formal 
publication, but they are only second hand rumors.)

RE: Testing for Normality

see the following reference for a good review of the various normality
tests, including comparative power calculations.  This is also a nice
review of the various methods for drawing class intervals in the
chi-squared tests for distributional goodness of fit:

"How to Test Normality and other Distributional Assumptions", SS Shapiro,
American Society for Quality Control - Statistics Division, Volume 3-ASQC
Basic References in Quality Control (1990).

In article <1992Sep5.064647.15570@constellation.ecn.uoknor.edu> bateman@nsslsun.nssl.uoknor.edu (Monte Bateman) writes:
>I would like to test data for normality.  The books I have
>access to talk about graphing frequencies on "probability paper".
>
>First off, I don't have any.
>
>Second, it seems that there should be software available 
>to do this test.
>
>Pointers?
>
>Any/all help appreciated!
>
>
>Monte

I can offer one little pointer, for what its worth.
Box, Hunter, and Hunter, in "Statistics for Experimenters" (I'm guessing
at the title) give the scale factors with which you can create
your own normal probability paper.

Tony

In article <1992Sep5.064647.15570@constellation.ecn.uoknor.edu> bateman@nsslsun.nssl.uoknor.edu (Monte Bateman) writes:
>I would like to test data for normality.  The books I have
>access to talk about graphing frequencies on "probability paper".
>
>First off, I don't have any.

Available at better stationery stores. It's National form 12-083.

>Second, it seems that there should be software available 
>to do this test.

I don't know of any software, but Lillefors's test is relatively simple, and
described in many texts. Kolmogorov's test, which was the basis for Lillefors's,
requires that you _completely_ specify the distribution (including mean and
variance). Lillefors relaxed this requirement.

If you have a spreadsheet with the Gaussian CDF available as a function,
you can program it to perform this test easily. Good luck!

   The reference for D'Agostino's test of normality is:

A Suggestion for Using Powerful and Informative Tests of Normality
  by D'Agostino, Belanger and D'Agostino Jr.
The American Stastician, Nov 1990, Vol 44, No. 4, 316-321

   I found it a good overview of the problem.

						>David<

I AM normal, damn it!                                                 Me too!

In article <Bu5suB.HxM@mentor.cc.purdue.edu> hrubin@pop.stat.purdue.edu (Herman Rubin) writes:
>In article <1992Sep5.064647.15570@constellation.ecn.uoknor.edu> bateman@nsslsun.nssl.uoknor.edu (Monte Bateman) writes:
>>I would like to test data for normality.  The books I have
>>access to talk about graphing frequencies on "probability paper".
>
>>First off, I don't have any.
>
>>Second, it seems that there should be software available 
>>to do this test.
>
>>Pointers?
>
>>Any/all help appreciated!
>
>
>There is no shortage of tests for normality.

Yes, there are many test statistics that can be calculated. The probability
plot, as originally asked for, has the advantage of being GRAPHICAL, so you
actually see your data, and you see HOW it differs from normality.

It is fairly easy to do without the special paper - one way is to :

   1) Order your data from smallest to largest
   2) Determine the expected values of the order statistics from
      a Normal(0,1) population the same size as your sample.
   3) Plot your values against the corresponding order statistics.
   4) Assess normality : if your sample is normal, the data will fall 
      roughly along a straight line.

Step #2 can be done by consulting tables, doing some icky numerical 
integration, or conveniently and approximately if you have access to
an implementation of the inverse of the Normal CDF (call it G(y)).

Just apply the inverse CDF to uniform order statistics :

      r(i) = G((i-1/2)/n)       for i from 1 to n

A slightly better approximation to the normal order statistics is (if
my memory serves me right) :

      r(i) = G((i-3/8)/(n+1/4))  for i from 1 to n

You'll find the inverse normal CDF implemented in surprisingly many
spreadsheets, math librarys, and math&stats packages.

Most statistics packages do perform this plot for you!  
I suggest you find one.


---
Alan Myrvold          3755 Riverside Dr.    
Cognos Incorporated   P.O. Box 9707          alanm@cognos.com
(613) 738-1440 x3317  Ottawa, Ontario       
                      CANADA  K1G 3Z4       

Why not use a traditional chi-square test?

>>>>> "Charles" == Charles Packer <packer@amarna.gsfc.nasa.gov> writes:

Charles> Why not use a traditional chi-square test?

I can think of two possible reasons:

1. It requires an arbitrary partition of the range into panels, *before*
   the sample comes to hand.  (In fact it really does not test normality as
   such, but rather that the grouped sample distribution agrees with a
   similarly grouped normal.)  Arbitrariness always comes at some cost.

2. In seeking to get some power against a very wide class of alternatives
   it manages only to achieve low power against any subclass, including the
   subclass of practically important alternatives.  In this sense it is not
   well focused enough.

[BTW I would be interested in a Bayesian reaction to this question.  It always
seemed to me that tests of fit could be rather an embarrassment to a Bayesian.]
--
___________________________________________________________________________
Bill Venables, Dept. of Statistics, | Email: venables@stats.adelaide.edu.au
Univ. of Adelaide, South Australia. | Tel: +61 8 228 5412  Fax: ...232 5670