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Re: st: probability and z-statistic


From   Deidra Young <[email protected]>
To   <[email protected]>
Subject   Re: st: probability and z-statistic
Date   Tue, 05 Dec 2006 21:59:44 +0800

Thanks Kit and Nick,

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

          Pearson chi2(2) =   2.5711   Pr = 0.277
 likelihood-ratio chi2(2) =   2.6204   Pr = 0.270
               Cram�r's V =   0.0903
                    gamma =   0.0759  ASE = 0.116
          Kendall's tau-b =   0.0324  ASE = 0.050

. ret li

scalars:
                 r(N) =  315
                 r(r) =  2
                 r(c) =  3
              r(chi2) =  2.571055140705914
                 r(p) =  .2765046694792958
           r(chi2_lr) =  2.620364965212246
              r(p_lr) =  .2697708234098308
          r(CramersV) =  .0903442295432575
             r(gamma) =  .0758665794637018
           r(ase_gam) =  .1163419665428843
              r(taub) =  .0324087958656579
          r(ase_taub) =  .0497834038046439

. di r(taub) / r(ase_taub)
.65099598

. scalar z=r(taub)/r(ase_taub)

. display "z= " z " with p-value " normden(1-z)
z= .65099598 with p-value .37537099








On 5/12/06 8:22 PM, "Kit Baum" <[email protected]>

> Deidra wants to retrieve the p-value and Kendall tau-b score from a
> tab of two variables.
> 
> 
> . tab anxiety depress,all
> 
>             |             DEPRESS
>     ANXIETY |         1          2          3 |     Total
> -----------+---------------------------------+----------
>           1 |         8          1          0 |         9
>           2 |        14         42          3 |        59
>           3 |         3         21         11 |        35
>           4 |         0          1          3 |         4
> -----------+---------------------------------+----------
>       Total |        25         65         17 |       107
> 
>            Pearson chi2(6) =  46.1892   Pr = 0.000
> likelihood-ratio chi2(6) =  40.9054   Pr = 0.000
>                 Cram�r's V =   0.4646
>                      gamma =   0.7778  ASE = 0.087
>            Kendall's tau-b =   0.4951  ASE = 0.070
> 
> . return list
> 
> scalars:
>                   r(N) =  107
>                   r(r) =  4
>                   r(c) =  3
>                r(chi2) =  46.18917309609633
>                   r(p) =  2.71459405298e-08
>             r(chi2_lr) =  40.90537799483023
>                r(p_lr) =  3.02263811177e-07
>            r(CramersV) =  .4645828854557538
>               r(gamma) =  .7777777777777778
>             r(ase_gam) =  .087050646901156
>                r(taub) =  .4950723482288552
>            r(ase_taub) =  .0704364215558283
> 
> If she wants the p-value of Kendall's tau-b, it can be easily
> calculated (if indeed taub is ~N(0,1)) from what is available in the
> return list:
> 
> . scalar z=r(taub)/r(ase_taub)
> 
> . display "z= " z " with p-value " normden(1-z)
> z= 7.0286414 with p-value 5.114e-09
> 
> 
> 
> Kit Baum, Boston College Economics
> http://ideas.repec.org/e/pba1.html
> An Introduction to Modern Econometrics Using Stata:
> http://www.stata-press.com/books/imeus.html
> 
> 
> 
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