Selecting Statistics
Statistical Test
Somers' d
Statistical Measure
if N>10 refer critical ratio of S to unit normal table;
if N<=10 refer d to table of critical values of S;
also • Median test; • Mann-Whitney U test; • Kolmogorov-Smirnov two sample; • runs test
Notes
Somers, R. H. A new asymmetric measure of association for ordinal variables. American Sociological Review 27 (1962): 799-811.Critical ratio of S: Kendall, M. G. Rank Correlation Methods. Fourth edition. London: Griffin, 1970. p. 52
Standard error of S assuming ties: Kendall, M. G. Rank Correlation Methods. Fourth edition. London: Griffin, 1970. p. 55
Table of Critical Values of S assuming ties: Harshbarger, T. R. Introductory Statistics: A Decision Map. New York: Macmillan, 1971. p. 535
Median test: Siegel, S. Nonparametric Methods for the Behavioral Sciences. New York: McGraw-Hill, 1956. p. 111
Mann-Whitney U: Siegel, S. Nonparametric Methods for the Behavioral Sciences. New York: McGraw-Hill, 1956. p. 116
Kolmogorov-Smirnov: Siegel, S. Nonparametric Methods for the Behavioral Sciences. New York: McGraw-Hill, 1956. p. 127
runs test: Siegel, S. Nonparametric Methods for the Behavioral Sciences. New York: McGraw-Hill, 1956. p. 136
Somers' d and Critical Ratio of S:
SPSS: CROSSTABS
SAS: FREQ
Median test:
SPSS: NPAR
SAS: NPAR1WAY, MRANK
Mann-Whitney U:
SPSS: NPAR
SAS: NPAR1WAY, MRANK
Kolmogorov -Smirnov:
SPSS: NPAR
Runs test: