CROSSTABS: Fixed the reporting of the standard error of Cohen's Kappa

The Standard error assuming the null hypothesis was being reported
when the standard error NOT assuming the null hypothesis ought to
have been.

Thanks to Joanne Ingram <joanne.ingram@ed.ac.uk> for reporting this
problem, and to Douglas Bonett <dgbonett@ucsc.edu> for explaining
how to fix it.

diff --git a/src/language/stats/crosstabs.q b/src/language/stats/crosstabs.q
index 6e6cb20d9750b2c517c1d886a107f639db394c4e..ab73f96ad5bea6b37bb481b488b39fdf33c79202 100644 (file)
--- a/src/language/stats/crosstabs.q
+++ b/src/language/stats/crosstabs.q
@@ -2600,6 +2600,7 @@ calc_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
   /* Cohen's kappa. */
   if (proc->statistics & (1u << CRS_ST_KAPPA) && pt->ns_rows == pt->ns_cols)
     {
+      double ase_under_h0;
       double sum_fii, sum_rici, sum_fiiri_ci, sum_fijri_ci2, sum_riciri_ci;
       int i, j;
 
@@ -2628,24 +2629,23 @@ calc_symmetric (struct crosstabs_proc *proc, struct pivot_table *pt,
 
       v[8] = (pt->total * sum_fii - sum_rici) / (pow2 (pt->total) - sum_rici);
 
-      ase[8] = sqrt ((pow2 (pt->total) * sum_rici
-                     + sum_rici * sum_rici
-                     - pt->total * sum_riciri_ci)
-                    / (pt->total * (pow2 (pt->total) - sum_rici) * (pow2 (pt->total) - sum_rici)));
-#if 0
-      t[8] = v[8] / sqrt (pt->total * (((sum_fii * (pt->total - sum_fii))
+      ase_under_h0 = sqrt ((pow2 (pt->total) * sum_rici
+                           + sum_rici * sum_rici
+                           - pt->total * sum_riciri_ci)
+                          / (pt->total * (pow2 (pt->total) - sum_rici) * (pow2 (pt->total) - sum_rici)));
+      
+      ase[8] = sqrt (pt->total * (((sum_fii * (pt->total - sum_fii))
                                / pow2 (pow2 (pt->total) - sum_rici))
                               + ((2. * (pt->total - sum_fii)
                                   * (2. * sum_fii * sum_rici
                                      - pt->total * sum_fiiri_ci))
-                                 / cube (pow2 (pt->total) - sum_rici))
+                                 / pow3 (pow2 (pt->total) - sum_rici))
                               + (pow2 (pt->total - sum_fii)
                                  * (pt->total * sum_fijri_ci2 - 4.
                                     * sum_rici * sum_rici)
                                  / pow4 (pow2 (pt->total) - sum_rici))));
-#else
-      t[8] = v[8] / ase[8];
-#endif
+
+      t[8] = v[8] / ase_under_h0;
     }
 
   return 1;

diff --git a/tests/language/stats/crosstabs.at b/tests/language/stats/crosstabs.at
index d2e9e8ff179baa72a653b5287792d53a8d834668..559a13355ff970323782a52e692c643ebf905454 100644 (file)
--- a/tests/language/stats/crosstabs.at
+++ b/tests/language/stats/crosstabs.at
@@ -1442,6 +1442,51 @@ Ordinal by Ordinal,Somers' d,Symmetric,.209,,3.338,.001
 ])
 AT_CLEANUP
 
+AT_SETUP([CROSSTABS Cohens Kappa])
+
+dnl Example from Wood J. M. 
+dnl "Understanding and Computing Cohen's Kappa: A Tutorial"
+dnl WebPsychEmpiricist. Oct 3 2007
+AT_DATA([kappa.sps], [dnl
+SET FORMAT=F8.3.
+
+data list notable list /p1 * p2 * w *.
+begin data.
+0 0 18
+1 0 1
+0 1 1
+end data.
+
+weight by w.
+
+crosstabs /table = p1 by p2
+       statistics = kappa
+       .
+])
+
+AT_CHECK([pspp -O format=csv kappa.sps], [0], [dnl
+Table: Summary.
+,Cases,,,,,
+,Valid,,Missing,,Total,
+,N,Percent,N,Percent,N,Percent
+p1 * p2,20.000,100.0%,.000,0.0%,20.000,100.0%
+
+Table: p1 * p2 [[count]].
+,p2,,
+p1,.000,1.000,Total
+.000,18.000,1.000,19.000
+1.000,1.000,.000,1.000
+Total,19.000,1.000,20.000
+
+Table: Symmetric measures.
+Category,Statistic,Value,Asymp. Std. Error,Approx. T,Approx. Sig.
+Measure of Agreement,Kappa,-.053,.037,-.235,
+N of Valid Cases,,20.000,,,
+])
+
+AT_CLEANUP
+
+
 AT_SETUP([CROSSTABS many statistics])
 AT_DATA([crosstabs.sps], [dnl
 SET FORMAT=F8.4.