Somers D

src.meliora.core.somersd(array_1, array_2, alternative='two-sided')[source]

Calculates Somers’ D, an asymmetric measure of ordinal association. This is a wrapper around scipy.stats.somersd function. Somers’ \(D\) is a measure of the correspondence between two rankings. It considers the difference between the number of concordant and discordant pairs in two rankings and is normalized such that values close to 1 indicate strong agreement and values close to -1 indicate strong disagreement. :param x: 1D array of rankings, treated as the (row) independent variable.

Alternatively, a 2D contingency table.

Parameters

  • y (array_like, optional) – If x is a 1D array of rankings, y is a 1D array of rankings of the same length, treated as the (column) dependent variable. If x is 2D, y is ignored.

  • alternative ({'two-sided', 'less', 'greater'}, optional) – Defines the alternative hypothesis. Default is ‘two-sided’. The following options are available: * ‘two-sided’: the rank correlation is nonzero * ‘less’: the rank correlation is negative (less than zero) * ‘greater’: the rank correlation is positive (greater than zero)

Returns

res –

A SomersDResult object with the following fields:
correlationfloat

The Somers’ \(D\) statistic.

pvaluefloat

The p-value for a hypothesis test whose null hypothesis is an absence of association, \(D=0\). See notes for more information.

table2D array

The contingency table formed from rankings x and y (or the provided contingency table, if x is a 2D array)

Return type

SomersDResult

References

[1] Robert H. Somers, “A New Asymmetric Measure of Association for

Ordinal Variables”, American Sociological Review, Vol. 27, No. 6, pp. 799–811, 1962.

[2] Morton B. Brown and Jacqueline K. Benedetti, “Sampling Behavior of

Tests for Correlation in Two-Way Contingency Tables”, Journal of the American Statistical Association Vol. 72, No. 358, pp. 309–315, 1977.

[3] SAS Institute, Inc., “The FREQ Procedure (Book Excerpt)”,

SAS/STAT 9.2 User’s Guide, Second Edition, SAS Publishing, 2009.

[4] Laerd Statistics, “Somers’ d using SPSS Statistics”, *SPSS

Statistics Tutorials and Statistical Guides*, https://statistics.laerd.com/spss-tutorials/somers-d-using-spss-statistics.php, Accessed July 31, 2020.

Examples

>>> table = [[27, 25, 14, 7, 0], [7, 14, 18, 35, 12], [1, 3, 2, 7, 17]]
>>> res = somersd(table)
>>> res.statistic
0.6032766111513396
>>> res.pvalue
1.0007091191074533e-27