Re: asymptotic standard error of lambda

[John Darrington]

I did a quick (ish) calculation on paper and the first ASE came out to be 
0.0394 
which is not too far from what your reference says,  so perhaps there is an 
error in 
our implementation.

From where is NaN coming?  Presumamble it must be as a result of taking the 
square root
of a negative number.  This should give us a hint of the problem.

J'

On Sun, May 04, 2014 at 09:59:15PM -0700, Ben Pfaff wrote:
     The CROSSTABS command can compute Goodman and Kruskal's lambda.  It also
     calculates the standard error of lambda according to the formula for
     ASE0 given here:
     
http://pic.dhe.ibm.com/infocenter/spssstat/v22r0m0/index.jsp?topic=%2Fcom.ibm.spss.statistics.algorithms%2Falg_crosstabs_measures.htm
     
     This page gives an example of the SPSS calculation:
     http://www.csupomona.edu/~jlkorey/POWERMUTT/Topics/contingency_tables.html
     
     Here is PSPP syntax that should reproduce the given on that page:
     
     SET FORMAT F8.3.
     
     * From 
http://www.csupomona.edu/~jlkorey/POWERMUTT/Topics/contingency_tables.html.
     DATA LIST LIST NOTABLE/x y w.
     WEIGHT BY w.
     BEGIN DATA.
     1 1 424
     1 2 213
     1 3 59
     3 1 55
     3 2 188
     3 3 357
     END DATA.
     
     Directional measures.
     
#========================================#=====#===========#========#=========#
     #Category      Statistic       Type      #Value|Asymp. Std.| Approx.|  
Approx.#
     #                                        #     |      Error|       T|     
Sig.#
     
#----------------------------------------#-----+-----------+--------+---------#
     #Nominal by    Lambda          Symmetric # .423|       .021|  15.281|      
   #
     #Nominal                                 #     |           |        |      
   #
     #                              x         # .497|        NaN|  15.986|      
   #
     #                              Dependent #     |           |        |      
   #
     #                              y         # .370|        NaN|  16.339|      
   #
     #                              Dependent #     |           |        |      
   #
     #             
---------------------------#-----+-----------+--------+---------#
     #              Goodman and     x         # .382|           |        |      
   #
     #              Kruskal tau     Dependent #     |           |        |      
   #
     #                              y         # .198|           |        |      
   #
     #                              Dependent #     |           |        |      
   #
     
#========================================#=====#===========#========#=========#
     
     However, the asymmetrics ASEs given above are wrong.  The first NaN
     should be .024 and the second one should be .020 according to that
     example webpage.
     
     Worse, the ASEs given above don't match those calculated by other
     software.  For example, if you enter the data above into
     http://vassarstats.net/newcs.html, you get the same lambda values .497
     and .370 (well, to one extra digit), but ASEs .034 and .028,
     respectively.
     
     Can anyone explain how to calculate the asymptotic standard error of
     lambda in a way that matches the SPSS results?
     
     _______________________________________________
     pspp-dev mailing list
     address@hidden
     https://lists.gnu.org/mailman/listinfo/pspp-dev

-- 
PGP Public key ID: 1024D/2DE827B3 
fingerprint = 8797 A26D 0854 2EAB 0285  A290 8A67 719C 2DE8 27B3
See http://sks-keyservers.net or any PGP keyserver for public key.

signature.asc
Description: Digital signature