From: John Darrington <john@darrington.wattle.id.au>
Date: Fri, 26 Jun 2015 09:59:07 +0000 (+0200)
Subject: CROSSTABS: Fixed the reporting of the standard error of Cohen's Kappa
X-Git-Url: https://pintos-os.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=3fe5cc7ed8d6fd1951f016a794415a00ea4059a2;hp=0ba4c8816d6c9b2b59becab264b8ed3738fc1984;p=pspp

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 6e6cb20d97..ab73f96ad5 100644
--- 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 d2e9e8ff17..559a13355f 100644
--- 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.