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Re: st: probability and z-statistic


From   Ron�n Conroy <[email protected]>
To   [email protected]
Subject   Re: st: probability and z-statistic
Date   Tue, 5 Dec 2006 13:12:43 +0000

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
[email protected]
+353 (0) 1 402 2431
+353 (0) 87 799 97 95
http://www.flickr.com/photos/ronanconroy




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