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Mann-Whitney U Test

Nonparametric hypothesis test comparing two independent samples.

Usage

var mannWhitneyU = require( '@stdlib/stats/mannwhitneyu' );

mannWhitneyU( x, y[, options] )

Given two independent samples x and y, the function computes the Mann–Whitney U rank-sum test to assess whether the distributions differ.

var out = mannWhitneyU( [ 7, 8, 9 ], [ 1, 2, 3 ] );
/* returns
    {
        'U': 0,
        'pValue': 0.025,
        'rejected': true
    }
*/

out = mannWhitneyU( [ 10, 11, 10, 12 ], [ 9, 11, 10, 10 ] );
/* returns
    {
        'U': 4.5,
        'pValue': 0.312,
        'rejected': false
    }
*/

The function accepts the following options:

  • alpha: number in the interval [0,1] giving the significance level of the hypothesis test. Default: 0.05.
  • alternative: Either two-sided, less or greater. Indicates the direction of the hypothesis test. 'greater' tests whether values in x tend to be larger than those in y, 'less' tests whether values in x tend to be smaller than those in y, and 'two-sided' tests for any difference in distributions.

By default, the hypothesis test is carried out at a significance level of 0.05. To choose a different significance level, set the alpha option.

var out = mannWhitneyU( [ 7, 8, 9 ], [ 1, 2, 3 ], {
    'alpha': 0.05,
    'alternative': 'greater'
});
/* returns
    {
        'U': 0,
        'pValue': 0.025,
        'rejected': true
    }
*/

By default, a two-sided test is performed. To perform either of the one-sided tests, set the alternative option to less or greater.

var out = mannWhitneyU( [ 5, 6, 7, 8 ], [ 1, 2, 3, 4 ], {
    'alternative': 'greater',
    'alpha': 0.05
});
/* returns
    {
        'U': 0,
        'pValue': 0.0104,
        'rejected': true
    }
*/

out = mannWhitneyU( [ 5, 6, 7, 8 ], [ 1, 2, 3, 4 ], {
    'alternative': 'less',
    'alpha': 0.05
});
/* returns
    {
        'U': 0,
        'pValue': 0.9896,
        'rejected': false
    }
*/

Examples

var mannWhitneyU = require( '@stdlib/stats/mannwhitneyu' );

var x = [ 12, 15, 14, 10, 13 ];
var y = [ 7, 9, 6, 8, 7 ];

var out = mannWhitneyU( x, y );
/* returns
    {
       'U': 0,
       'pValue': 0.009,
       'rejected': true
    }
*/

out = mannWhitneyU( [ 5, 6, 7, 8 ], [ 1, 2, 3, 4 ] );
/* returns
    {
        'U': 0,
        'pValue': 0.0208,
        'rejected': true
    }
*/

out = mannWhitneyU( [ 5, 6, 7, 8 ], [ 1, 2, 3, 4 ], {
    'alternative': 'greater'
});
/* returns
    {
        'U': 0,
        'pValue': 0.0104,
        'rejected': true
    }
*/

out = mannWhitneyU( [ 1, 2, 2, 3 ], [ 2, 3, 4, 5 ], {
    'alternative': 'greater',
    'alpha': 0.05
});
/* returns
    {
        'U': 2.5,
        'pValue': 0.057,
        'rejected': false
    }
*/