time-to-botec

main.js (5635B)

---

 /**
 * @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( './../../ranks' );
 var pow = require( '@stdlib/math/base/special/pow' );
 var chisqCDF = require( './../../base/dists/chisquare/cdf' );
 var identity = require( '@stdlib/utils/identity-function' );
 var incrspace = require( '@stdlib/array/incrspace' );
 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 has to be simple 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( 'invalid arguments. First argument and `opts.groups` must be arrays of the same length.' );
 		}
 		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( 'invalid number of groups. `groups` array must contain at least two unique elements. Value: `' + levels + '`.' );
 		}
 		groupsIndicators = opts.groups;
 	} else {
 		x = [];
 		groupsIndicators = [];
 		if ( ngroups < 2 ) {
 			throw new Error( 'invalid number of input arguments. Must provide at least two array-like arguments. Value: `' + arg + '`.' );
 		}
 		for ( i = 0; i < ngroups; i++ ) {
 			arg = arguments[ i ];
 			if ( !isCollection( arg ) ) {
 				throw new TypeError( 'invalid argument. Must provide array-like arguments. Value: `' + arg + '`.' );
 			}
 			if ( arg.length === 0 ) {
 				throw new Error( 'invalid argument. Supplied arrays cannot be empty. Value: `' + 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( 'invalid option. `alpha` must be a number in the range 0 to 1. Value: `' + 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;