st: Why do Stata Cronbach's Alpha values not match SAS?

["Gramig, Benjamin M" <bgramig@purdue.edu>]

I have used the alpha, item- command in Stata to calculate Cronbachs alpha to evaluate scale reliability of a group of Likert scale survey questions and received the following Stata output:

. alpha natural  anthropogenic no_affect_farm warming_will_help invented extreme media policies, item

Test scale = mean(unstandardized items)

                                                                          average
                                     item-test      item-rest      interitem
Item         |  Obs  Sign   correlation   correlation   covariance      alpha
-------------+-----------------------------------------------------------------
natural      |  749    +        0.4101        0.2291        .3454548      0.7859
anthropoge~c |  749    -   0.7044        0.5677         .272278      0.7317
no_affect_~m |  747    +  0.5445        0.3748        .3167923      0.7673
warming_wi~p |  747    + 0.3860        0.2371        .3544383      0.7820
invented     |  742    +       0.7862        0.6657        .2435609      0.7093
extreme      |  747    -       0.6441        0.5121        .2954857      0.7436
media        |  747    +       0.7563        0.6447        .2611056      0.7156
policies     |  746    +       0.6400        0.5080        .2948471      0.7421
-------------+-----------------------------------------------------------------
Test scale   |                                                          .2979834      0.7737
-------------------------------------------------------------------------------

When I attempt to use SAS to calculate the same Alpha reliability  value using the –PROC CORR data alpha- command I get much lower values (pasted below) for items in the scale as well as the overall alpha for the entire scale.  The qualitative results in terms of sign and relative magnitude of alphas calculated when removing individual items from the scale are consistent with Stata, but not the magnitudes. I have read the manuals for both pieces of software and it is not clear to me that there are differences in what is being reported by both software packages.  

Has anyone else encountered this drastic difference?  I assume that there is something systematically different about what is going on in the two packages to calculate the reported values, but I couldn’t determine what this difference was.

It should be noted that I turned to SAS to be able to use polychoric correlations in a PCA with a full set of diagnostics, outputs and rotations available.  This seems necessary for my ordinal data, despite ignoring this in the comparison of alpha calculations shared here. I did explore 
-polychoricpca- in Stata before deciding to use SAS.

Any insights are greatly appreciated,
Ben


******SAS output**************
Cronbach Coefficient Alpha

Variables              Alpha
                                  
    Raw                 0.21871
Standardized        0.230030


                       Cronbach Coefficient Alpha with Deleted Variable

                           Raw Variables                Standardized Variables

Deleted             Correlation                         Correlation
Variable             with Total         Alpha        with Total          Alpha  Label
 natural                0.272378      0.069753      0.270229       0.082498  natural
anthropogenic       -.422341      0.495123      -.400057       0.472209  anthropogenic
no_affect_farm     0.239609      0.085832      0.239147       0.104634  no_affect_farm
warming_will_help0.165372      0.154351      0.160833       0.158495  warming_will_help
invented               0.271282      0.038784      0.283484       0.072925  invented
extreme                -.340953      0.424482      -.339788       0.443982  extreme
media                  0.389877      -.032350      0.373906       0.005444  media
policies               0.355568      0.016073      0.335595       0.034502  policies

------------------
Benjamin M. Gramig
Assistant Professor
Dept. of Agricultural Economics
Purdue University
bgramig@purdue.edu
http://web.ics.purdue.edu/~bgramig/
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