st: Not sure how to interpret -somersd- results

["Jain, Monica (HarvestPlus)" <M.Jain@cgiar.org>]

I am using -somersd- and I am unsure how to interpret the results to test stochastic dominance. I am using Stata 13 for Windows.

I have a two year cross-section data on heights of children 3-5 years. I want to check if the distribution of heights z-score of children in 2006 first order stochastically dominates those in 1996. From previous threads on stochastic dominance, I saw that one could use Somers D statistic for it. I am using the following command where 2006 is year=1, haz is the height z-score:

       somersd year haz, cluster(district)
       
and I get the following result:
Somers' D with variable: year
Transformation: Untransformed
Valid observations: 627
Number of clusters: 4

Symmetric 95% CI
                                   (Std. Err. adjusted for 4 clusters in dist)
------------------------------------------------------------------------------
                  |              Jackknife
        year  |      Coef.          Std. Err.        z       P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       haz06 |    .357832   .0434275     8.24   0.000     .2727157    .4429483
-------------+----------------------------------------------------------------

What I know is that the above result indicates that a randomly selected child in 2006 is 36% more likely to have a higher height z-score than a randomly selected child in 1996, than vice versa. But, what I do not know is how do I state this result in terms of stochastic dominance. Can I say that distribution of height z-scores in 2006 first order stochastically dominates the distribution of height z-scores in 1996? Alternatively, can I make any statement about stochastic dominance from the above result? If yes, what would it be?

Monica Jain



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