Calculation supplied by Douglas Bonett <dgbonett@ucsc.edu>:
http://lists.gnu.org/archive/html/pspp-dev/2014-05/msg00007.html
@item
Significance of symmetric and directional measures is not calculated.
@item
@item
Significance of symmetric and directional measures is not calculated.
@item
-Asymptotic standard error is not calculated for asymmetric lambda,
-Goodman and Kruskal's tau, or symmetric Somers' d.
+Asymptotic standard error is not calculated for
+Goodman and Kruskal's tau or symmetric Somers' d.
@item
Approximate T is not calculated for symmetric uncertainty coefficient.
@end itemize
@item
Approximate T is not calculated for symmetric uncertainty coefficient.
@end itemize
/* FIXME:
- How to calculate significance of symmetric and directional measures?
/* FIXME:
- How to calculate significance of symmetric and directional measures?
- - How to calculate ASE for asymmetric lambda?
- 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?
- 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?
v[1] = (sum_fmj - rm) / (pt->total - rm);
v[2] = (sum_fim - cm) / (pt->total - cm);
v[1] = (sum_fmj - rm) / (pt->total - rm);
v[2] = (sum_fim - cm) / (pt->total - cm);
- /* XXX We don't have a working formula for ASE1. */
- ase[2] = SYSMIS;
+ /* ASE1 for Y given PT. */
+ {
+ double accum;
+
+ accum = 0.;
+ for (i = 0; i < pt->n_rows; i++)
+ if (cm_index == fim_index[i])
+ accum += fim[i];
+ ase[2] = sqrt ((pt->total - sum_fim) * (sum_fim + cm - 2. * accum)
+ / pow3 (pt->total - cm));
+ }
/* ASE0 for Y given PT. */
{
/* ASE0 for Y given PT. */
{
t[2] = v[2] / (sqrt (accum - pow2 (sum_fim - cm) / pt->total) / (pt->total - cm));
}
t[2] = v[2] / (sqrt (accum - pow2 (sum_fim - cm) / pt->total) / (pt->total - cm));
}
- /* XXX We don't have a working formula for ASE1. */
- ase[1] = SYSMIS;
+ /* ASE1 for PT given Y. */
+ {
+ double accum;
+
+ accum = 0.;
+ for (j = 0; j < pt->n_cols; j++)
+ if (rm_index == fmj_index[j])
+ accum += fmj[j];
+ ase[1] = sqrt ((pt->total - sum_fmj) * (sum_fmj + rm - 2. * accum)
+ / pow3 (pt->total - rm));
+ }
/* ASE0 for PT given Y. */
{
/* ASE0 for PT given Y. */
{
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,
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,,1.12,
-,,,y Dependent,1.00,,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,,
,,Goodman and Kruskal tau,x Dependent,.25,,,
,,,y Dependent,1.00,,,
,,Uncertainty Coefficient,Symmetric,.47,.18,,
,Nominal by Interval,Eta,x Dependent,.04,,,
,,,y Dependent,1.00,,,
2,Nominal by Nominal,Lambda,Symmetric,.50,.25,2.00,
,Nominal by Interval,Eta,x Dependent,.04,,,
,,,y Dependent,1.00,,,
2,Nominal by Nominal,Lambda,Symmetric,.50,.25,2.00,
-,,,x Dependent,.33,,1.15,
-,,,y Dependent,1.00,,1.15,
+,,,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,,
,,Goodman and Kruskal tau,x Dependent,.33,,,
,,,y Dependent,1.00,,,
,,Uncertainty Coefficient,Symmetric,.58,.17,,
Table: Directional measures.
Category,Statistic,Type,Value,Asymp. Std. Error,Approx. T,Approx. Sig.
Nominal by Nominal,Lambda,Symmetric,.423,.021,16.875,
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,
+,,x Dependent,.497,.024,15.986,
+,,y Dependent,.370,.020,16.339,
,Goodman and Kruskal tau,x Dependent,.382,,,
,,y Dependent,.198,,,
,Goodman and Kruskal tau,x Dependent,.382,,,
,,y Dependent,.198,,,
Table: Directional measures.
Category,Statistic,Type,Value,Asymp. Std. Error,Approx. T,Approx. Sig.
Nominal by Nominal,Lambda,Symmetric,.259,.081,2.902,
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,
+,,x Dependent,.250,.089,2.479,
+,,y Dependent,.267,.085,2.766,
,Goodman and Kruskal tau,x Dependent,.129,,,
,,y Dependent,.123,,,
,Goodman and Kruskal tau,x Dependent,.129,,,
,,y Dependent,.123,,,
Table: Directional measures.
Category,Statistic,Type,Value,Asymp. Std. Error,Approx. T,Approx. Sig.
Nominal by Nominal,Lambda,Symmetric,.208,.010,18.793,
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,
+,,x Dependent,.224,.013,16.076,
+,,y Dependent,.192,.012,14.438,
,Goodman and Kruskal tau,x Dependent,.089,,,
,,y Dependent,.081,,,
])
,Goodman and Kruskal tau,x Dependent,.089,,,
,,y Dependent,.081,,,
])
Table: Directional measures.
Category,Statistic,Type,Value,Asymp. Std. Error,Approx. T,Approx. Sig.
Nominal by Nominal,Lambda,Symmetric,.338,.059,4.743,
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,,4.875,
-,,y Dependent,.174,,3.248,
+,,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,
,Goodman and Kruskal tau,x Dependent,.534,,,
,,y Dependent,.167,,,
Ordinal by Ordinal,Somers' d,Symmetric,-.074,,-1.022,
Table: Directional measures.
Category,Statistic,Type,Value,Asymp. Std. Error,Approx. T,Approx. Sig.
Nominal by Nominal,Lambda,Symmetric,.102,.067,1.473,
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,,.302,
-,,y Dependent,.165,,2.349,
+,,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,
,Goodman and Kruskal tau,x Dependent,.051,,,
,,y Dependent,.068,,,
Ordinal by Ordinal,Somers' d,Symmetric,.209,,3.338,
Table: Directional measures.
Category,Statistic,Type,Value,Asymp. Std. Error,Approx. T,Approx. Sig.
Nominal by Nominal,Lambda,Symmetric,.0455,.1629,.2723,
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,,NaN,
-,,y Dependent,.0500,,.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,,
,Goodman and Kruskal tau,x Dependent,.1054,,,
,,y Dependent,.0434,,,
,Uncertainty Coefficient,Symmetric,.0780,.0474,,
Table: Directional measures.
Category,Statistic,Type,Value,Asymp. Std. Error,Approx. T,Approx. Sig.
Nominal by Nominal,Lambda,Symmetric,.000,.000,NaN,
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,,NaN,
-,,y Dependent,.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,,
,Goodman and Kruskal tau,x Dependent,.076,,,
,,y Dependent,.108,,,
,Uncertainty Coefficient,Symmetric,.105,.012,,