Statistics Toolbox™

ranksum - Wilcoxon rank sum test

Syntax

p = ranksum(x,y)
[p,h] = ranksum(x,y)
[p,h] = ranksum(x,y,'alpha',alpha)
[p,h] = ranksum(...,'method',method)
[p,h,stats] = ranksum(...)

Description

p = ranksum(x,y) performs a two-sided rank sum test of the null hypothesis that data in the vectors x and y are independent samples from identical continuous distributions with equal medians, against the alternative that they do not have equal medians. x and y can have different lengths. The p-value of the test is returned in p. The test is equivalent to a Mann-Whitney U-test.

[p,h] = ranksum(x,y) returns the result of the test in h. h = 1 indicates a rejection of the null hypothesis at the 5% significance level. h = 0 indicates a failure to reject the null hypothesis at the 5% significance level.

[p,h] = ranksum(x,y,'alpha',alpha) performs the test at the (100*alpha)% significance level. The default, when unspecified, is alpha = 0.05.

[p,h] = ranksum(...,'method',method) computes the p-value using either an exact algorithm, when method is 'exact', or a normal approximation, when method is 'approximate'. The default, when unspecified, is the exact method for small samples and the approximate method for large samples.

[p,h,stats] = ranksum(...) returns the structure stats with the following fields:

• ranksum — Value of the rank sum test statistic

• zval — Value of the z-statistic (computed only for large samples)

Example

Test the hypothesis of equal medians for two independent unequal-sized samples. The sampling distributions are identical except for a shift of 0.25.

x = unifrnd(0,1,10,1);
y = unifrnd(0.25,1.25,15,1);
[p,h] = ranksum(x,y)
p =
  0.0375
h =
   1

The test rejects the null hypothesis of equal medians at the default 5% significance level.

References

[1] Gibbons, J. D., Nonparametric Statistical Inference, 2nd edition, M. Dekker, 1985.

[2] Hollander, M., and D. A. Wolfe, Nonparametric Statistical Methods, Wiley, 1973.

See Also

kruskalwallis, signrank, signtest, ttest2

range

raylcdf