Re: st: probability and z-statistic

[Ron�n Conroy <rconroy@rcsi.ie>]

On 5 Noll 2006, at 13:59, Deidra Young wrote:

> I just tried Kit's suggestion.  One variable has two categories and  
> the
> other has three. My test is to determine if there is a difference  
> between
> cases with and without Autism Diagnosis (2) using an ordered severity
> measure with three levels (none, mild or severe).  Using your  
> suggestion, I
> obtained the following result.  Does this look like the p value is
> calculated correctly?
>
> Deidra
>
>
> . tab autism_dx kerr_breath_score, all
>
>                     |  Kerr Score for Disturbed Awake
> Initially Diagnosed |         Breathing Rhythm
>         with Autism |      None       Mild     Severe |     Total
> --------------------+---------------------------------+----------
> No Autism Diagnosis |        75        109         76 |       260
>    Autism Diagnosis |        11         29         15 |        55
> --------------------+---------------------------------+----------
>               Total |        86        138         91 |       315


The test for an ordered association is probably more in line with  
your hypothesis.


. binreg Autism breathscore, rr

Iteration 1:   deviance =  400.4562
Iteration 2:   deviance =  300.4687
Iteration 3:   deviance =  291.5691
Iteration 4:   deviance =  291.3885
Iteration 5:   deviance =  291.3884
Iteration 6:   deviance =  291.3884

Generalized linear models                          No. of obs       
=       315
Optimization     : MQL Fisher scoring              Residual df      
=       313
                   (IRLS EIM)                      Scale parameter  
=         1
Deviance         =  291.3884049                    (1/df) Deviance  
=  .9309534
Pearson          =  314.8318309                    (1/df) Pearson  =   
1.005852

Variance function: V(u) = u*(1-u)                  [Bernoulli]
Link function    : g(u) = ln(u)                    [Log]

                                                   BIC             =  
-1509.167

------------------------------------------------------------------------ 
------
             |                 EIM
      Autism | Risk Ratio   Std. Err.      z    P>|z|     [95% Conf.  
Interval]
------------- 
+----------------------------------------------------------------
breathscore |   1.103058   .1807885     0.60   0.550     .7999973     
1.520926
------------------------------------------------------------------------ 
------

The risk of autism goes up modestly for each 1-unit increase in  
breath score severity, and it's not significant.

You can, of course, just to a trend test

. jonter breath, by(Aut)
Jonckheere-Terpstra Test

       J  = 7498
       J* = 0.57
Prob > J* = 0.28532


or


. nptrend breath, by(Aut)

    Autism     score       obs      sum of ranks
         0         0       260         40732
         1         1        55          9038

          z  =  0.61
  Prob > |z| = 0.544



=========
Ron�n Conroy
Royal College of Surgeons in Ireland
rconroy@rcsi.ie
+353 (0) 1 402 2431
+353 (0) 87 799 97 95
http://www.flickr.com/photos/ronanconroy




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