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* @license Apache-2.0
*
* Copyright (c) 2018 The Stdlib Authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
'use strict';
// MODULES //
var isCollection = require( '@stdlib/assert/is-collection' );
var isPlainObject = require( '@stdlib/assert/is-plain-object' );
var setReadOnly = require( '@stdlib/utils/define-read-only-property' );
var countBy = require( '@stdlib/utils/count-by' );
var objectKeys = require( '@stdlib/utils/keys' );
var rank = require( '@stdlib/stats/ranks' );
var pow = require( '@stdlib/math/base/special/pow' );
var chisqCDF = require( '@stdlib/stats/base/dists/chisquare/cdf' );
var identity = require( '@stdlib/utils/identity-function' );
var incrspace = require( '@stdlib/array/base/incrspace' );
var format = require( '@stdlib/string/format' );
var validate = require( './validate.js' );
var print = require( './print.js' ); // eslint-disable-line stdlib/no-redeclare
// MAIN //
/**
* Computes the Kruskal-Wallis test for equality of medians.
*
* @param {...NumberArray} arguments - either two or more number arrays or a single numeric array if an array of group indicators is supplied as an option
* @param {Options} [options] - function options
* @param {number} [options.alpha=0.05] - significance level
* @param {Array} [options.groups] - array of group indicators
* @throws {Error} must provide at least two array-like arguments if `groups` is not set
* @throws {TypeError} must provide array-like arguments
* @throws {TypeError} options must be an object
* @throws {TypeError} must provide valid options
* @throws {RangeError} alpha option has to be a number in the interval `[0,1]`
* @returns {Object} test results
*
* @example
* // Data from Hollander & Wolfe (1973), p. 116:
* var x = [ 2.9, 3.0, 2.5, 2.6, 3.2 ];
* var y = [ 3.8, 2.7, 4.0, 2.4 ];
* var z = [ 2.8, 3.4, 3.7, 2.2, 2.0 ];
*
* var out = kruskal( x, y, z );
* // returns {...}
*/
function kruskal() {
var groupsIndicators;
var groupRankSums;
var tieSumTerm;
var ngroups;
var options;
var levels;
var alpha;
var param;
var ranks;
var vals;
var opts;
var pval;
var stat;
var ties;
var arg;
var err;
var key;
var out;
var i;
var j;
var n;
var N;
var x;
var v;
ngroups = arguments.length;
opts = {};
if ( isPlainObject( arguments[ ngroups - 1 ] ) ) {
options = arguments[ ngroups - 1 ];
ngroups -= 1;
err = validate( opts, options );
if ( err ) {
throw err;
}
}
groupRankSums = {};
n = {};
if ( opts.groups ) {
x = arguments[ 0 ];
if ( x.length !== opts.groups.length ) {
throw new RangeError( format( 'invalid arguments. First argument and `%s` must be arrays having the same length.', 'opts.groups' ) );
}
n = countBy( opts.groups, identity );
levels = objectKeys( n );
ngroups = levels.length;
for ( i = 0; i < ngroups; i++ ) {
key = levels[ i ];
groupRankSums[ key ] = 0;
}
if ( ngroups < 2 ) {
throw new Error( format( 'invalid option. `%s` option must be an array containing at least two unique elements. Option: `%s`.', 'groups', levels ) );
}
groupsIndicators = opts.groups;
} else {
x = [];
groupsIndicators = [];
if ( ngroups < 2 ) {
throw new Error( format( 'invalid invocation. Incorrect number of arguments. Must provide at least two array-like arguments. Value: `%s`.', arg ) );
}
for ( i = 0; i < ngroups; i++ ) {
arg = arguments[ i ];
if ( !isCollection( arg ) ) {
throw new TypeError( format( 'invalid argument. Must provide array-like arguments. Value: `%s`.', arg ) );
}
if ( arg.length === 0 ) {
throw new Error( format( 'invalid argument. Supplied arrays cannot be empty. Value: `%s`.', arg ) );
} else {
n[ i ] = arg.length;
}
groupRankSums[ i ] = 0;
for ( j = 0; j < n[ i ]; j++ ) {
groupsIndicators.push( i );
x.push( arg[ j ] );
}
}
levels = incrspace( 0, ngroups, 1 );
}
if ( opts.alpha === void 0 ) {
alpha = 0.05;
} else {
alpha = opts.alpha;
}
if ( alpha < 0.0 || alpha > 1.0 ) {
throw new RangeError( format( 'invalid option. `%s` must be a number on the interval: [0, 1]. Value: `%f`.', 'alpha', alpha ) );
}
N = x.length;
ranks = rank( x );
// Calculate # ties for each value & rank sums per group:
ties = {};
for ( i = 0; i < N; i++ ) {
groupRankSums[ groupsIndicators[ i ] ] += ranks[ i ];
if ( x[ i ] in ties ) {
ties[ x[ i ] ] += 1;
} else {
ties[ x[ i ] ] = 1;
}
}
// Calculate test statistic using short-cut formula:
stat = 0.0;
for ( i = 0; i < ngroups; i++ ) {
key = levels[ i ];
stat += pow( groupRankSums[ key ], 2.0 ) / n[ key ];
}
stat = ( ( 12.0 / ( N * (N+1) ) ) * stat ) - ( 3.0 * (N+1) );
// Correction for ties:
tieSumTerm = 0;
vals = objectKeys( ties );
for ( i = 0; i < vals.length; i++ ) {
v = ties[ vals[ i ] ];
tieSumTerm += pow( v, 3.0 ) - v;
}
stat /= 1.0 - ( ( tieSumTerm ) / ( pow( N, 3 ) - N ) );
param = ngroups - 1;
pval = 1.0 - chisqCDF( stat, param );
out = {};
setReadOnly( out, 'rejected', pval <= alpha );
setReadOnly( out, 'alpha', alpha );
setReadOnly( out, 'df', param );
setReadOnly( out, 'pValue', pval );
setReadOnly( out, 'statistic', stat );
setReadOnly( out, 'method', 'Kruskal-Wallis Test' );
setReadOnly( out, 'print', print );
return out;
}
// EXPORTS //
module.exports = kruskal;
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