Somers’ D

BESH Stat starting version 0.21 offers the computation of the Somers’ d statistics which is a non-parametric measure of the strength and direction of association that exists between an ordinal dependent variable and an ordinal independent variable in contingency table. It is an asymmetric modification of the Kendall’s tau-b (already available in the BESH Stat). Somers’ d is available by selecting the BESH Stat main menu on the Excel Add-ins tab > Contingency table analysis > RxC table and then by checking the Ordinal association checkbox on the Options tab.

Note that BESH Stat is always treating columns as a dependent variable when computing Somers’ d statistic, therefore unlike the other measures (Goodman-Kruskal gamma, Kendall’s tau-b and tau-c) swapping of the table rows/columns change the results.

Example: Consider the crosstabulation data of the customer satisfaction and hotel room cleanliness (see Sommers’ d results on this data as computed by SPSS).

Somers’ d can be calculated only when both variables are ordered. It’s value is always in range -1 ≤ d ≤ 1. For the computational algorithm (formulas BESH Stat use to compute test statistic and standard errors) see BESH Stats help file (present in the BESH Stat zip package on the download page) or check for example SAS documentation because BESH Stat use the procedure.

Somers’ d results provided by the BESH Stat (see rows highlighted in abler color below) match the SPSS output:

Somers’ d value of ~0.603 indicates that the increased hotel room cleanliness (use in analysis as an independent variable) is associated with increased customer satisfaction (dependent variable). The resulted p-value of 0 is < 0.05 and therefore the computed Somers’ d is statistically significant (i.e. significantly different from zero).