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Re: st: difference between -test- and -contrast- in Statat 12


From   Richard Williams <richardwilliams.ndu@gmail.com>
To   statalist@hsphsun2.harvard.edu, "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   Re: st: difference between -test- and -contrast- in Statat 12
Date   Thu, 25 Aug 2011 23:33:40 -0400

At 10:15 PM 8/25/2011, Ricardo Ovaldia wrote:

I am using the new -contrast- command in Stata 12 to test a contrast after ANOVA and I get different p-values than when using -test- although the marginal means are the same.

My guess is that it is because the first statistic is an F statistic with d.f. 1, 63 while the 2nd statistic is chi-square(1). Since N is small the P values don't match exactly. I added [fw=15] to your anova command (to make the sample larger] and the P values were the same to at least 4 decimal places. Try it with larger samples (or just inflate your own sample using fweights) and see if the discrepancies disappear.


I illustrate with the auto data by first making the rep78 variable a 3 level variable and then running an ANOVA follow by -contrast-:

. sysuse auto,clear
. replace rep78=3 if rep78<3
. anova price rep78##foreign
 <output omitted>
. contrast r.foreign@rep78

Contrasts of marginal linear predictions

Margins      : asbalanced

-------------------------------------------------
              |         df           F        P>F
--------------+----------------------------------
foreign@rep78 |
  (1 vs 0) 3  |          1        0.73     0.3965
  (1 vs 0) 4  |          1        0.07     0.7881
  (1 vs 0) 5  |          1        0.80     0.3743
       Joint  |          3        0.53     0.6606
              |
     Residual |         63
-------------------------------------------------

---------------------------------------------------------------
              |   Contrast   Std. Err.     [95% Conf. Interval]
--------------+------------------------------------------------
foreign@rep78 |
  (1 vs 0) 3  |  -1529.739   1792.049     -5110.862    2051.385
  (1 vs 0) 4  |   379.8889   1407.262       -2432.3    3192.078
  (1 vs 0) 5  |   2088.167   2333.681     -2575.322    6751.655
---------------------------------------------------------------

From the above tables the p-value for the test of foreign withing rep78=3 is: p=0.3965

Now using -margin, post- follow by -test- for the same comparison (i.e. foreign withing rep78=3):
. margins ,over(rep78 foreign) post cformat(%5.2f)

Predictive margins                                Number of obs   =         69

Expression   : Linear prediction, predict()
over         : rep78 foreign

-------------------------------------------------------------------------------
              |            Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
--------------+----------------------------------------------------------------
rep78#foreign |
3 0 | 6358.41 490.77 12.96 0.000 5396.51 7320.30 3 1 | 4828.67 1723.54 2.80 0.005 1450.60 8206.74 4 0 | 5881.56 995.08 5.91 0.000 3931.23 7831.89 4 1 | 6261.44 995.08 6.29 0.000 4311.11 8211.77 5 0 | 4204.50 2110.89 1.99 0.046 67.22 8341.78 5 1 | 6292.67 995.08 6.32 0.000 4342.34 8243.00
-------------------------------------------------------------------------------

. test 0.foreign#3.rep78=1.foreign#3.rep78

 ( 1)  3bn.rep78#0bn.foreign - 3bn.rep78#1.foreign = 0

           chi2(  1) =    0.73
         Prob > chi2 =    0.3933

I get a different p-value. Although close in this example, in another case that have the p-values are further apart: (0.0026 vs 0.0089).
Why are these two methods giving different answers?

Thank you,
Ricardo

Ricardo Ovaldia, MS
Statistician
Oklahoma City, OK


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Richard Williams, Notre Dame Dept of Sociology
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