CROSSTABS: Calculate significance for lambda and Somers' d.

John Darrington pointed out that lambda just uses normal significance.
Somers' d appears to do so also (based on only a few examples though).

diff --git a/doc/statistics.texi b/doc/statistics.texi
index 82d853568f6df985434f45c135dbedfaed3129b7..47478f5f69b06407ec93015952cd7ff60639893d 100644 (file)
--- a/doc/statistics.texi
+++ b/doc/statistics.texi
@@ -603,7 +603,7 @@ following bugs:
 
 @itemize @bullet
 @item
-Significance of symmetric and directional measures is not calculated.
+Significance of some symmetric and directional measures is not calculated.
 @item
 Asymptotic standard error is not calculated for
 Goodman and Kruskal's tau or symmetric Somers' d.

diff --git a/src/language/stats/crosstabs.q b/src/language/stats/crosstabs.q
index be22e62600c0bb72c21fbba98204196f00e6963d..aa7e2457ee24ae9d41d40bd989da985b2c822fe3 100644 (file)
--- a/src/language/stats/crosstabs.q
+++ b/src/language/stats/crosstabs.q
@@ -16,7 +16,7 @@
 
 /* FIXME:
 
-   - How to calculate significance of symmetric and directional measures?
+   - How to calculate significance of some symmetric and directional measures?
    - How to calculate ASE for symmetric Somers ' d?
    - How to calculate ASE for Goodman and Kruskal's tau?
    - How to calculate approx. T of symmetric uncertainty coefficient?
@@ -1974,7 +1974,7 @@ display_risk (struct pivot_table *pt, struct tab_table *risk)
 
 static int calc_directional (struct crosstabs_proc *, struct pivot_table *,
                              double[N_DIRECTIONAL], double[N_DIRECTIONAL],
-                            double[N_DIRECTIONAL]);
+                            double[N_DIRECTIONAL], double[N_DIRECTIONAL]);
 
 /* Display directional measures. */
 static void
@@ -2041,10 +2041,11 @@ display_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
   double direct_v[N_DIRECTIONAL];
   double direct_ase[N_DIRECTIONAL];
   double direct_t[N_DIRECTIONAL];
+  double sig[N_DIRECTIONAL];
 
   int i;
 
-  if (!calc_directional (proc, pt, direct_v, direct_ase, direct_t))
+  if (!calc_directional (proc, pt, direct_v, direct_ase, direct_t, sig))
     return;
 
   tab_offset (direct, pt->n_consts + pt->n_vars - 2, -1);
@@ -2086,7 +2087,7 @@ display_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
        tab_double (direct, 4, 0, TAB_RIGHT, direct_ase[i], NULL, RC_OTHER);
       if (direct_t[i] != SYSMIS)
        tab_double (direct, 5, 0, TAB_RIGHT, direct_t[i], NULL, RC_OTHER);
-      /*tab_double (direct, 6, 0, TAB_RIGHT, normal_sig (direct_v[i]), NULL, RC_PVALUE);*/
+      tab_double (direct, 6, 0, TAB_RIGHT, sig[i], NULL, RC_PVALUE);
       tab_next_row (direct);
     }
 
@@ -2720,13 +2721,13 @@ calc_risk (struct pivot_table *pt,
 static int
 calc_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
                   double v[N_DIRECTIONAL], double ase[N_DIRECTIONAL],
-                 double t[N_DIRECTIONAL])
+                 double t[N_DIRECTIONAL], double sig[N_DIRECTIONAL])
 {
   {
     int i;
 
     for (i = 0; i < N_DIRECTIONAL; i++)
-      v[i] = ase[i] = t[i] = SYSMIS;
+      v[i] = ase[i] = t[i] = sig[i] = SYSMIS;
   }
 
   /* Lambda. */
@@ -2864,11 +2865,15 @@ calc_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
                       / (2. * pt->total - rm - cm));
       }
 
+      for (i = 0; i < 3; i++)
+        sig[i] = 2 * gsl_cdf_ugaussian_Q (t[i]);
+
       free (fim);
       free (fim_index);
       free (fmj);
       free (fmj_index);
 
+      /* Tau. */
       {
        double sum_fij2_ri, sum_fij2_ci;
        double sum_ri2, sum_cj2;
@@ -2967,6 +2972,7 @@ calc_directional (struct crosstabs_proc *proc, struct pivot_table *pt,
               v[8 + i] = somers_d_v[i];
               ase[8 + i] = somers_d_ase[i];
               t[8 + i] = somers_d_t[i];
+              sig[8 + i] = 2 * gsl_cdf_ugaussian_Q (fabs (somers_d_t[i]));
             }
         }
     }

diff --git a/tests/language/stats/crosstabs.at b/tests/language/stats/crosstabs.at
index ad34a60f6288ebbf60a58cdadeae698a2f28fbd8..1191215333c6997361a7f68ccd349b928756f5f1 100644 (file)
--- a/tests/language/stats/crosstabs.at
+++ b/tests/language/stats/crosstabs.at
@@ -376,32 +376,32 @@ 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,.28,1.12,
-,,,x Dependent,.25,.22,1.12,
-,,,y Dependent,1.00,.00,1.12,
-,,Goodman and Kruskal tau,x Dependent,.25,,,
-,,,y Dependent,1.00,,,
-,,Uncertainty Coefficient,Symmetric,.47,.18,,
-,,,x Dependent,.31,.15,2.02,
-,,,y Dependent,1.00,.00,2.02,
-,Ordinal by Ordinal,Somers' d,Symmetric,.00,,.00,
-,,,x Dependent,.00,.50,.00,
-,,,y Dependent,.00,.20,.00,
-,Nominal by Interval,Eta,x Dependent,.04,,,
-,,,y Dependent,1.00,,,
-2,Nominal by Nominal,Lambda,Symmetric,.50,.25,2.00,
-,,,x Dependent,.33,.27,1.15,
-,,,y Dependent,1.00,.00,1.15,
-,,Goodman and Kruskal tau,x Dependent,.33,,,
-,,,y Dependent,1.00,,,
-,,Uncertainty Coefficient,Symmetric,.58,.17,,
-,,,x Dependent,.41,.17,2.36,
-,,,y Dependent,1.00,.00,2.36,
-,Ordinal by Ordinal,Somers' d,Symmetric,-.67,,-1.73,
-,,,x Dependent,-1.00,.00,-1.73,
-,,,y Dependent,-.50,.29,-1.73,
-,Nominal by Interval,Eta,x Dependent,.73,,,
-,,,y Dependent,1.00,,,
+1,Nominal by Nominal,Lambda,Symmetric,.40,.28,1.12,.264
+,,,x Dependent,.25,.22,1.12,.264
+,,,y Dependent,1.00,.00,1.12,.264
+,,Goodman and Kruskal tau,x Dependent,.25,,,.   @&t@
+,,,y Dependent,1.00,,,.   @&t@
+,,Uncertainty Coefficient,Symmetric,.47,.18,,.   @&t@
+,,,x Dependent,.31,.15,2.02,.   @&t@
+,,,y Dependent,1.00,.00,2.02,.   @&t@
+,Ordinal by Ordinal,Somers' d,Symmetric,.00,,.00,1.000
+,,,x Dependent,.00,.50,.00,1.000
+,,,y Dependent,.00,.20,.00,1.000
+,Nominal by Interval,Eta,x Dependent,.04,,,.   @&t@
+,,,y Dependent,1.00,,,.   @&t@
+2,Nominal by Nominal,Lambda,Symmetric,.50,.25,2.00,.046
+,,,x Dependent,.33,.27,1.15,.248
+,,,y Dependent,1.00,.00,1.15,.248
+,,Goodman and Kruskal tau,x Dependent,.33,,,.   @&t@
+,,,y Dependent,1.00,,,.   @&t@
+,,Uncertainty Coefficient,Symmetric,.58,.17,,.   @&t@
+,,,x Dependent,.41,.17,2.36,.   @&t@
+,,,y Dependent,1.00,.00,2.36,.   @&t@
+,Ordinal by Ordinal,Somers' d,Symmetric,-.67,,-1.73,.083
+,,,x Dependent,-1.00,.00,-1.73,.083
+,,,y Dependent,-.50,.29,-1.73,.083
+,Nominal by Interval,Eta,x Dependent,.73,,,.   @&t@
+,,,y Dependent,1.00,,,.   @&t@
 ]])
 AT_CLEANUP
 
@@ -1030,11 +1030,11 @@ 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,.024,15.986,
-,,y Dependent,.370,.020,16.339,
-,Goodman and Kruskal tau,x Dependent,.382,,,
-,,y Dependent,.198,,,
+Nominal by Nominal,Lambda,Symmetric,.423,.021,16.875,.000
+,,x Dependent,.497,.024,15.986,.000
+,,y Dependent,.370,.020,16.339,.000
+,Goodman and Kruskal tau,x Dependent,.382,,,.   @&t@
+,,y Dependent,.198,,,.   @&t@
 
 Table: Summary.
 ,Cases,,,,,
@@ -1044,11 +1044,11 @@ 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,.089,2.479,
-,,y Dependent,.267,.085,2.766,
-,Goodman and Kruskal tau,x Dependent,.129,,,
-,,y Dependent,.123,,,
+Nominal by Nominal,Lambda,Symmetric,.259,.081,2.902,.004
+,,x Dependent,.250,.089,2.479,.013
+,,y Dependent,.267,.085,2.766,.006
+,Goodman and Kruskal tau,x Dependent,.129,,,.   @&t@
+,,y Dependent,.123,,,.   @&t@
 
 Table: Summary.
 ,Cases,,,,,
@@ -1058,11 +1058,11 @@ 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,.013,16.076,
-,,y Dependent,.192,.012,14.438,
-,Goodman and Kruskal tau,x Dependent,.089,,,
-,,y Dependent,.081,,,
+Nominal by Nominal,Lambda,Symmetric,.208,.010,18.793,.000
+,,x Dependent,.224,.013,16.076,.000
+,,y Dependent,.192,.012,14.438,.000
+,Goodman and Kruskal tau,x Dependent,.089,,,.   @&t@
+,,y Dependent,.081,,,.   @&t@
 ])
 AT_CLEANUP
 
@@ -1116,9 +1116,9 @@ x * y,1.000000,100.0%,.000000,0.0%,1.000000,100.0%
 
 Table: Directional measures.
 Category,Statistic,Type,Value,Asymp. Std. Error,Approx. T,Approx. Sig.
-Ordinal by Ordinal,Somers' d,Symmetric,-.084,,-.149,
-,,x Dependent,-.045,.300,-.149,
-,,y Dependent,-.684,2.378,-.149,
+Ordinal by Ordinal,Somers' d,Symmetric,-.084,,-.149,.882
+,,x Dependent,-.045,.300,-.149,.882
+,,y Dependent,-.684,2.378,-.149,.882
 
 Table: Summary.
 ,Cases,,,,,
@@ -1135,9 +1135,9 @@ N of Valid Cases,,687.000,,,
 
 Table: Directional measures.
 Category,Statistic,Type,Value,Asymp. Std. Error,Approx. T,Approx. Sig.
-Ordinal by Ordinal,Somers' d,Symmetric,.371,,10.669,
-,,x Dependent,.351,.032,10.669,
-,,y Dependent,.394,.035,10.669,
+Ordinal by Ordinal,Somers' d,Symmetric,.371,,10.669,.000
+,,x Dependent,.351,.032,10.669,.000
+,,y Dependent,.394,.035,10.669,.000
 ])
 
 AT_DATA([ordinal.sps], [dnl
@@ -1263,9 +1263,9 @@ N of Valid Cases,,150.000,,,
 
 Table: Directional measures.
 Category,Statistic,Type,Value,Asymp. Std. Error,Approx. T,Approx. Sig.
-Ordinal by Ordinal,Somers' d,Symmetric,1.000,,24.841,
-,,x Dependent,1.000,.000,24.841,
-,,y Dependent,1.000,.000,24.841,
+Ordinal by Ordinal,Somers' d,Symmetric,1.000,,24.841,.000
+,,x Dependent,1.000,.000,24.841,.000
+,,y Dependent,1.000,.000,24.841,.000
 
 Table: Summary.
 ,Cases,,,,,
@@ -1281,9 +1281,9 @@ N of Valid Cases,,150.000,,,
 
 Table: Directional measures.
 Category,Statistic,Type,Value,Asymp. Std. Error,Approx. T,Approx. Sig.
-Ordinal by Ordinal,Somers' d,Symmetric,1.000,,24.841,
-,,x Dependent,1.000,.000,24.841,
-,,y Dependent,1.000,.000,24.841,
+Ordinal by Ordinal,Somers' d,Symmetric,1.000,,24.841,.000
+,,x Dependent,1.000,.000,24.841,.000
+,,y Dependent,1.000,.000,24.841,.000
 
 Table: Summary.
 ,Cases,,,,,
@@ -1299,9 +1299,9 @@ N of Valid Cases,,150.000,,,
 
 Table: Directional measures.
 Category,Statistic,Type,Value,Asymp. Std. Error,Approx. T,Approx. Sig.
-Ordinal by Ordinal,Somers' d,Symmetric,-1.000,,-24.841,
-,,x Dependent,-1.000,.000,-24.841,
-,,y Dependent,-1.000,.000,-24.841,
+Ordinal by Ordinal,Somers' d,Symmetric,-1.000,,-24.841,.000
+,,x Dependent,-1.000,.000,-24.841,.000
+,,y Dependent,-1.000,.000,-24.841,.000
 
 Table: Summary.
 ,Cases,,,,,
@@ -1317,9 +1317,9 @@ N of Valid Cases,,150.000,,,
 
 Table: Directional measures.
 Category,Statistic,Type,Value,Asymp. Std. Error,Approx. T,Approx. Sig.
-Ordinal by Ordinal,Somers' d,Symmetric,.971,,24.841,
-,,x Dependent,.944,.013,24.841,
-,,y Dependent,1.000,.000,24.841,
+Ordinal by Ordinal,Somers' d,Symmetric,.971,,24.841,.000
+,,x Dependent,.944,.013,24.841,.000
+,,y Dependent,1.000,.000,24.841,.000
 
 Table: Summary.
 ,Cases,,,,,
@@ -1335,9 +1335,9 @@ N of Valid Cases,,150.000,,,
 
 Table: Directional measures.
 Category,Statistic,Type,Value,Asymp. Std. Error,Approx. T,Approx. Sig.
-Ordinal by Ordinal,Somers' d,Symmetric,.035,,1.009,
-,,x Dependent,.805,.032,1.009,
-,,y Dependent,.018,.017,1.009,
+Ordinal by Ordinal,Somers' d,Symmetric,.035,,1.009,.313
+,,x Dependent,.805,.032,1.009,.313
+,,y Dependent,.018,.017,1.009,.313
 
 Table: Summary.
 ,Cases,,,,,
@@ -1353,9 +1353,9 @@ N of Valid Cases,,148.000,,,
 
 Table: Directional measures.
 Category,Statistic,Type,Value,Asymp. Std. Error,Approx. T,Approx. Sig.
-Ordinal by Ordinal,Somers' d,Symmetric,-.206,,-2.641,
-,,x Dependent,-.182,.069,-2.641,
-,,y Dependent,-.237,.089,-2.641,
+Ordinal by Ordinal,Somers' d,Symmetric,-.206,,-2.641,.008
+,,x Dependent,-.182,.069,-2.641,.008
+,,y Dependent,-.237,.089,-2.641,.008
 
 Table: Summary.
 ,Cases,,,,,
@@ -1372,14 +1372,14 @@ N of Valid Cases,,148.000,,,
 
 Table: Directional measures.
 Category,Statistic,Type,Value,Asymp. Std. Error,Approx. T,Approx. Sig.
-Nominal by Nominal,Lambda,Symmetric,.338,.059,4.743,
-,,x Dependent,.640,.085,4.875,
-,,y Dependent,.174,.050,3.248,
-,Goodman and Kruskal tau,x Dependent,.534,,,
-,,y Dependent,.167,,,
-Ordinal by Ordinal,Somers' d,Symmetric,-.074,,-1.022,
-,,x Dependent,-.060,.059,-1.022,
-,,y Dependent,-.096,.094,-1.022,
+Nominal by Nominal,Lambda,Symmetric,.338,.059,4.743,.000
+,,x Dependent,.640,.085,4.875,.000
+,,y Dependent,.174,.050,3.248,.001
+,Goodman and Kruskal tau,x Dependent,.534,,,.   @&t@
+,,y Dependent,.167,,,.   @&t@
+Ordinal by Ordinal,Somers' d,Symmetric,-.074,,-1.022,.307
+,,x Dependent,-.060,.059,-1.022,.307
+,,y Dependent,-.096,.094,-1.022,.307
 
 Table: Summary.
 ,Cases,,,,,
@@ -1396,14 +1396,14 @@ N of Valid Cases,,212.000,,,
 
 Table: Directional measures.
 Category,Statistic,Type,Value,Asymp. Std. Error,Approx. T,Approx. Sig.
-Nominal by Nominal,Lambda,Symmetric,.102,.067,1.473,
-,,x Dependent,.027,.087,.302,
-,,y Dependent,.165,.065,2.349,
-,Goodman and Kruskal tau,x Dependent,.051,,,
-,,y Dependent,.068,,,
-Ordinal by Ordinal,Somers' d,Symmetric,.209,,3.338,
-,,x Dependent,.202,.060,3.338,
-,,y Dependent,.217,.064,3.338,
+Nominal by Nominal,Lambda,Symmetric,.102,.067,1.473,.141
+,,x Dependent,.027,.087,.302,.763
+,,y Dependent,.165,.065,2.349,.019
+,Goodman and Kruskal tau,x Dependent,.051,,,.   @&t@
+,,y Dependent,.068,,,.   @&t@
+Ordinal by Ordinal,Somers' d,Symmetric,.209,,3.338,.001
+,,x Dependent,.202,.060,3.338,.001
+,,y Dependent,.217,.064,3.338,.001
 ])
 AT_CLEANUP
 
@@ -1451,17 +1451,17 @@ N of Valid Cases,,66.0000,,,
 
 Table: Directional measures.
 Category,Statistic,Type,Value,Asymp. Std. Error,Approx. T,Approx. Sig.
-Nominal by Nominal,Lambda,Symmetric,.0455,.1629,.2723,
-,,x Dependent,.0000,.0000,NaN,
-,,y Dependent,.0500,.1791,.2723,
-,Goodman and Kruskal tau,x Dependent,.1054,,,
-,,y Dependent,.0434,,,
-,Uncertainty Coefficient,Symmetric,.0780,.0474,,
-,,x Dependent,.2217,.1062,1.5373,
-,,y Dependent,.0473,.0306,1.5373,
-Ordinal by Ordinal,Somers' d,Symmetric,.1960,,1.9920,
-,,x Dependent,.1152,.0572,1.9920,
-,,y Dependent,.6573,.1417,1.9920,
+Nominal by Nominal,Lambda,Symmetric,.0455,.1629,.2723,.785
+,,x Dependent,.0000,.0000,NaN,NaN
+,,y Dependent,.0500,.1791,.2723,.785
+,Goodman and Kruskal tau,x Dependent,.1054,,,.   @&t@
+,,y Dependent,.0434,,,.   @&t@
+,Uncertainty Coefficient,Symmetric,.0780,.0474,,.   @&t@
+,,x Dependent,.2217,.1062,1.5373,.   @&t@
+,,y Dependent,.0473,.0306,1.5373,.   @&t@
+Ordinal by Ordinal,Somers' d,Symmetric,.1960,,1.9920,.046
+,,x Dependent,.1152,.0572,1.9920,.046
+,,y Dependent,.6573,.1417,1.9920,.046
 ])
 AT_CLEANUP
 
@@ -1491,13 +1491,13 @@ x * y,987.000,100.0%,.000,0.0%,987.000,100.0%
 
 Table: Directional measures.
 Category,Statistic,Type,Value,Asymp. Std. Error,Approx. T,Approx. Sig.
-Nominal by Nominal,Lambda,Symmetric,.000,.000,NaN,
-,,x Dependent,.000,.000,NaN,
-,,y Dependent,.000,.000,NaN,
-,Goodman and Kruskal tau,x Dependent,.076,,,
-,,y Dependent,.108,,,
-,Uncertainty Coefficient,Symmetric,.105,.012,,
-,,x Dependent,.073,.009,7.890,
-,,y Dependent,.184,.019,7.890,
+Nominal by Nominal,Lambda,Symmetric,.000,.000,NaN,NaN
+,,x Dependent,.000,.000,NaN,NaN
+,,y Dependent,.000,.000,NaN,NaN
+,Goodman and Kruskal tau,x Dependent,.076,,,.   @&t@
+,,y Dependent,.108,,,.   @&t@
+,Uncertainty Coefficient,Symmetric,.105,.012,,.   @&t@
+,,x Dependent,.073,.009,7.890,.   @&t@
+,,y Dependent,.184,.019,7.890,.   @&t@
 ])
 AT_CLEANUP