CROSSTABS: Drop buggy ASE for asymmetric lambda; fix T for symmetric lambda.

I really can't figure out how SPSS calculates the ASE for asymmetric
lambda, despite hours of effort.

diff --git a/doc/statistics.texi b/doc/statistics.texi
index afa3b1aef2bb0b31953dd999b8148665cfec79b6..2e29b047ef56b797f5074d839e8b628fe471eae8 100644 (file)
--- a/doc/statistics.texi
+++ b/doc/statistics.texi
@@ -599,13 +599,13 @@ some statistics are calculated only in integer mode.
 @subcmd{STATISTICS} subcommand is not given, no statistics are calculated.
 
 @strong{Please note:} Currently the implementation of @cmd{CROSSTABS} has the
-followings bugs:
+following bugs:
 
 @itemize @bullet
 @item
 Significance of symmetric and directional measures is not calculated.
 @item
-Asymmetric ASEs and T values for lambda are wrong.
+Asymptotic standard error is not calculated for asymmetric lambda.
 @item
 ASE of Goodman and Kruskal's tau is not calculated.
 @item

diff --git a/src/language/stats/crosstabs.q b/src/language/stats/crosstabs.q
index e8f6aa5833f8ba150f65baf6a666867c735a5d44..21947ee45785426476716947b4581cc65ec3fac6 100644 (file)
--- a/src/language/stats/crosstabs.q
+++ b/src/language/stats/crosstabs.q
@@ -17,7 +17,7 @@
 /* FIXME:
 
    - How to calculate significance of symmetric and directional measures?
-   - Asymmetric ASEs and T values for lambda are wrong.
+   - How to calculate ASE for asymmetric lambda?
    - ASE of Goodman and Kruskal's tau is not calculated.
    - ASE of symmetric somers' d is wrong.
    - Approx. T of uncertainty coefficient is wrong.
@@ -2800,22 +2800,8 @@ calc_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
       v[1] = (sum_fmj - rm) / (pt->total - rm);
       v[2] = (sum_fim - cm) / (pt->total - cm);
 
-      /* ASE1 for Y given PT. */
-      {
-       double accum;
-
-       for (accum = 0., i = 0; i < pt->n_rows; i++)
-         for (j = 0; j < pt->n_cols; j++)
-           {
-             const int deltaj = j == cm_index;
-             accum += (pt->mat[j + i * pt->n_cols]
-                       * pow2 ((j == fim_index[i])
-                              - deltaj
-                              + v[0] * deltaj));
-           }
-
-       ase[2] = sqrt (accum - pt->total * v[0]) / (pt->total - cm);
-      }
+      /* XXX We don't have a working formula for ASE1. */
+      ase[2] = SYSMIS;
 
       /* ASE0 for Y given PT. */
       {
@@ -2828,22 +2814,8 @@ calc_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
        t[2] = v[2] / (sqrt (accum - pow2 (sum_fim - cm) / pt->total) / (pt->total - cm));
       }
 
-      /* ASE1 for PT given Y. */
-      {
-       double accum;
-
-       for (accum = 0., i = 0; i < pt->n_rows; i++)
-         for (j = 0; j < pt->n_cols; j++)
-           {
-             const int deltaj = i == rm_index;
-             accum += (pt->mat[j + i * pt->n_cols]
-                       * pow2 ((i == fmj_index[j])
-                              - deltaj
-                              + v[0] * deltaj));
-           }
-
-       ase[1] = sqrt (accum - pt->total * v[0]) / (pt->total - rm);
-      }
+      /* XXX We don't have a working formula for ASE1. */
+      ase[1] = SYSMIS;
 
       /* ASE0 for PT given Y. */
       {
@@ -2871,7 +2843,7 @@ calc_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
                         * pow2 (temp0 + (v[0] - 1.) * temp1));
            }
        ase[0] = sqrt (accum1 - 4. * pt->total * v[0] * v[0]) / (2. * pt->total - rm - cm);
-       t[0] = v[0] / (sqrt (accum0 - pow2 ((sum_fim + sum_fmj - cm - rm) / pt->total))
+       t[0] = v[0] / (sqrt (accum0 - pow2 (sum_fim + sum_fmj - cm - rm) / pt->total)
                       / (2. * pt->total - rm - cm));
       }
 

diff --git a/tests/language/stats/crosstabs.at b/tests/language/stats/crosstabs.at
index ec2d313add8e922eefe7cafb8998725ab0f247f8..ce95d75e9f4f3f07c4175f0d5bb4b3b701f9333a 100644 (file)
--- a/tests/language/stats/crosstabs.at
+++ b/tests/language/stats/crosstabs.at
@@ -376,9 +376,9 @@ z,Category,Statistic,Value,Asymp. Std. Error,Approx. T,Approx. Sig.
 
 Table: Directional measures.
 z,Category,Statistic,Type,Value,Asymp. Std. Error,Approx. T,Approx. Sig.
-1,Nominal by Nominal,Lambda,Symmetric,.40,.28,1.02,
-,,,x Dependent,.25,NaN,1.12,
-,,,y Dependent,1.00,NaN,1.12,
+1,Nominal by Nominal,Lambda,Symmetric,.40,.28,1.12,
+,,,x Dependent,.25,,1.12,
+,,,y Dependent,1.00,,1.12,
 ,,Goodman and Kruskal tau,x Dependent,.25,,,
 ,,,y Dependent,1.00,,,
 ,,Uncertainty Coefficient,Symmetric,.47,.18,1.51,
@@ -389,9 +389,9 @@ z,Category,Statistic,Type,Value,Asymp. Std. Error,Approx. T,Approx. Sig.
 ,,,y Dependent,.00,.20,.00,
 ,Nominal by Interval,Eta,x Dependent,.04,,,
 ,,,y Dependent,1.00,,,
-2,Nominal by Nominal,Lambda,Symmetric,.50,.25,1.51,
-,,,x Dependent,.33,NaN,1.15,
-,,,y Dependent,1.00,NaN,1.15,
+2,Nominal by Nominal,Lambda,Symmetric,.50,.25,2.00,
+,,,x Dependent,.33,,1.15,
+,,,y Dependent,1.00,,1.15,
 ,,Goodman and Kruskal tau,x Dependent,.33,,,
 ,,,y Dependent,1.00,,,
 ,,Uncertainty Coefficient,Symmetric,.58,.17,1.56,
@@ -964,3 +964,104 @@ Interval by Interval,Pearson's R,.992,.004,22.638,
 N of Valid Cases,,10,,,
 ])
 AT_CLEANUP
+
+AT_SETUP([CROSSTABS Goodman and Kruskal's lambda])
+AT_DATA([lambda.sps], [dnl
+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.
+
+CROSSTABS x BY y/CELLS=NONE/STATISTICS=LAMBDA.
+
+* From http://vassarstats.net.
+DATA LIST LIST NOTABLE/x y w.
+WEIGHT BY w.
+BEGIN DATA.
+1 1 19
+1 2 26
+1 3 8
+2 1 21
+2 2 13
+2 3 5
+3 1 6
+3 2 12
+3 3 27
+END DATA.
+
+CROSSTABS x BY y/CELLS=NONE/STATISTICS=LAMBDA.
+
+* From Goodman, L.A., Kruskal, W.H. (1954) "Measures of association for
+  cross classifications". Part I. Journal of the American Statistical
+  Association, 49, 732-764.
+DATA LIST LIST NOTABLE/x y w.
+WEIGHT BY w.
+BEGIN DATA.
+1 1 1768
+1 2 807
+1 3 189
+1 4 47
+2 1 946
+2 2 1387
+2 3 746
+2 4 53
+3 1 115
+3 2 438
+3 3 288
+3 4 16
+END DATA.
+CROSSTABS x BY y/CELLS=NONE/STATISTICS=LAMBDA.
+])
+AT_CHECK([pspp -O format=csv lambda.sps], [0], [dnl
+Table: Summary.
+,Cases,,,,,
+,Valid,,Missing,,Total,
+,N,Percent,N,Percent,N,Percent
+x * y,1296.000,100.0%,.000,0.0%,1296.000,100.0%
+
+Table: Directional measures.
+Category,Statistic,Type,Value,Asymp. Std. Error,Approx. T,Approx. Sig.
+Nominal by Nominal,Lambda,Symmetric,.423,.021,16.875,
+,,x Dependent,.497,,15.986,
+,,y Dependent,.370,,16.339,
+,Goodman and Kruskal tau,x Dependent,.382,,,
+,,y Dependent,.198,,,
+
+Table: Summary.
+,Cases,,,,,
+,Valid,,Missing,,Total,
+,N,Percent,N,Percent,N,Percent
+x * y,137.000,100.0%,.000,0.0%,137.000,100.0%
+
+Table: Directional measures.
+Category,Statistic,Type,Value,Asymp. Std. Error,Approx. T,Approx. Sig.
+Nominal by Nominal,Lambda,Symmetric,.259,.081,2.902,
+,,x Dependent,.250,,2.479,
+,,y Dependent,.267,,2.766,
+,Goodman and Kruskal tau,x Dependent,.129,,,
+,,y Dependent,.123,,,
+
+Table: Summary.
+,Cases,,,,,
+,Valid,,Missing,,Total,
+,N,Percent,N,Percent,N,Percent
+x * y,6800.000,100.0%,.000,0.0%,6800.000,100.0%
+
+Table: Directional measures.
+Category,Statistic,Type,Value,Asymp. Std. Error,Approx. T,Approx. Sig.
+Nominal by Nominal,Lambda,Symmetric,.208,.010,18.793,
+,,x Dependent,.224,,16.076,
+,,y Dependent,.192,,14.438,
+,Goodman and Kruskal tau,x Dependent,.089,,,
+,,y Dependent,.081,,,
+])
+AT_CLEANUP