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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.


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