312 lines
8.3 KiB
JavaScript
312 lines
8.3 KiB
JavaScript
/* eslint-disable max-statements, max-lines-per-function */
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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2020 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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// MODULES //
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var isNumberArray = require( '@stdlib/assert/is-number-array' ).primitives;
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var isTypedArrayLike = require( '@stdlib/assert/is-typed-array-like' );
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var setReadOnly = require( '@stdlib/utils/define-read-only-property' );
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var isObject = require( '@stdlib/assert/is-plain-object' );
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var ranks = require( './../../ranks' );
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var normalCDF = require( './../../base/dists/normal/cdf' ).factory;
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var signrankCDF = require( './../../base/dists/signrank/cdf' );
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var tabulate = require( '@stdlib/utils/tabulate' );
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var signum = require( '@stdlib/math/base/special/signum' );
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var sqrt = require( '@stdlib/math/base/special/sqrt' );
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var abs = require( '@stdlib/math/base/special/abs' );
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var Float64Array = require( '@stdlib/array/float64' );
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var validate = require( './validate.js' );
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var unique = require( './unique.js' );
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var print = require( './print.js' ); // eslint-disable-line stdlib/no-redeclare
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// VARIABLES //
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var pnorm = normalCDF( 0.0, 1.0 );
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// MAIN //
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/**
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* Computes a Wilcoxon signed rank test.
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*
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* @param {NumericArray} x - data array
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* @param {NumericArray} [y] - optional paired data array
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* @param {Options} [options] - function options
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* @param {number} [options.alpha=0.05] - significance level
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* @param {string} [options.alternative='two-sided'] - alternative hypothesis (`two-sided`, `less`, or `greater`)
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* @param {string} [options.zeroMethod='wilcox'] - method governing how zero-differences are handled (`pratt`, `wilcox`, or `zsplit`)
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* @param {boolean} [options.correction=true] - continuity correction adjusting the Wilcoxon rank statistic by 0.5 towards the mean
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* @param {boolean} [options.exact=false] - whether to force using the exact distribution instead of a normal approximation when there are more than fifty data points
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* @param {number} [options.mu=0] - location parameter under H0
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* @throws {TypeError} `x` must be a numeric array
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* @throws {TypeError} `y` must be a numeric array
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* @throws {TypeError} options has to be simple object
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* @throws {TypeError} `alpha` option has to be a number primitive
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* @throws {RangeError} `alpha` option has to be a number in the interval `[0,1]`
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* @throws {TypeError} `alternative` option has to be a string primitive
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* @throws {Error} `alternative` option must be `two-sided`, `less`, or `greater`
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* @throws {TypeError} `zeroMethod` option has to be a string primitive
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* @throws {Error} `zeroMethod` option must be `pratt`, `wilcox`, or `zsplit`
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* @throws {TypeError} `correction` option has to be a boolean primitive
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* @throws {TypeError} `exact` option has to be a boolean primitive
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* @throws {TypeError} `mu` option has to be a number primitive
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* @returns {Object} test result object
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*
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* @example
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* var x = [ 6, 8, 14, 16, 23, 24, 28, 29, 41, -48, 49, 56, 60, -67, 75 ];
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* var out = wilcoxon( x, {
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* 'mu': 2
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* });
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*
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* @example
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* var x = [ 6, 8, 14, 16, 23, 24, 28, 29, 41, -48, 49, 56, 60, -67, 75 ];
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* var out = wilcoxon( x, {
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* 'alternative': 'greater'
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* });
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*/
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function wilcoxon() {
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var correction;
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var zeroMethod;
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var options;
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var hasTies;
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var counts;
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var repsum;
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var rplus;
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var nzero;
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var rzero;
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var alpha;
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var pval;
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var opts;
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var stat;
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var alt;
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var err;
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var len;
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var tmp;
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var out;
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var ad;
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var mu;
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var mn;
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var se;
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var d;
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var i;
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var r;
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var T;
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var v;
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var x;
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var y;
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x = arguments[ 0 ];
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if ( !isTypedArrayLike( x ) && !isNumberArray( x ) ) {
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throw new TypeError( 'invalid argument. First argument must be a numeric array. Value: `' + x + '`.' );
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}
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len = x.length;
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if ( arguments.length > 1 ) {
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if ( isObject( arguments[ 1 ] ) ) {
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options = arguments[ 1 ];
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} else {
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y = arguments[ 1 ];
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if ( !isTypedArrayLike( y ) && !isNumberArray( y ) ) {
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throw new TypeError( 'invalid argument. `y` argument must be a numeric array. Value: `' + y + '`.' );
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}
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if ( len !== y.length ) {
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throw new Error( 'invalid arguments. The first and second arguments must have the same length.' );
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}
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if ( arguments.length > 2 ) {
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options = arguments[ 2 ];
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}
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}
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}
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opts = {};
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if ( options ) {
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err = validate( opts, options );
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if ( err ) {
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throw err;
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}
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}
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mu = opts.mu || 0.0;
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if ( opts.correction === void 0 ) {
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correction = true;
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} else {
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correction = opts.correction;
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}
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if ( opts.alpha === void 0 ) {
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alpha = 0.05;
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} else {
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alpha = opts.alpha;
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}
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if ( len < 2 ) {
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throw new Error( 'invalid argument. First argument must contain at least two elements. Value: `' + x + '`' );
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}
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alt = opts.alternative || 'two-sided';
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zeroMethod = opts.zeroMethod || 'wilcox';
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if ( zeroMethod === 'wilcox' ) {
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// Only keep all non-zero differences:
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d = [];
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if ( y ) {
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for ( i = 0; i < len; i++ ) {
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v = ( x[ i ] - y[ i ] ) - mu;
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if ( v !== 0 ) {
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d.push( v );
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}
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}
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} else {
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for ( i = 0; i < len; i++ ) {
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if ( x[ i ] !== 0 ) {
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d.push( x[ i ] - mu );
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}
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}
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}
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nzero = x.length - d.length;
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} else {
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d = new Float64Array( len );
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nzero = 0;
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if ( y ) {
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for ( i = 0; i < len; i++ ) {
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d[ i ] = ( x[ i ] - y[ i ] ) - mu;
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if ( d[ i ] === 0 ) {
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nzero += 1;
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}
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}
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} else {
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for ( i = 0; i < len; i++ ) {
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d[ i ] = x[ i ] - mu;
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if ( d[ i ] === 0 ) {
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nzero += 1;
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}
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}
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}
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}
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if ( nzero === len ) {
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throw new Error( '`x` or `x - y` cannot be zero for all elements.' );
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}
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// Update length after potentially discarding zero values:
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len = d.length;
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ad = new Float64Array( len );
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for ( i = 0; i < len; i++ ) {
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ad[ i ] = abs( d[ i ] );
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}
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r = ranks( ad );
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rplus = 0;
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rzero = 0;
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for ( i = 0; i < len; i++ ) {
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if ( d[ i ] > 0 ) {
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rplus += r[ i ];
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}
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else if ( d[ i ] === 0 ) {
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rzero += r[ i ];
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}
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}
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hasTies = unique( r ).length !== r.length;
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if ( zeroMethod === 'zsplit' ) {
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rplus += rzero / 2.0;
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}
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T = rplus;
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mn = len * ( len + 1.0 ) * 0.25;
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se = len * ( len + 1.0 ) * ( ( 2.0 * len ) + 1.0 );
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if ( zeroMethod === 'pratt' ) {
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tmp = [];
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for ( i = 0; i < len; i++ ) {
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if ( d[ i ] !== 0 ) {
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tmp.push( r[ i ] );
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}
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}
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r = tmp;
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mn -= nzero * ( nzero + 1.0 ) * 0.25;
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se -= nzero * ( nzero + 1.0 ) * ( ( 2.0 * nzero ) + 1.0 );
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}
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counts = tabulate( r );
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repsum = 0;
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for ( i = 0; i < counts.length; i++ ) {
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if ( counts[ i ][ 1 ] > 1 ) {
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v = counts[ i ][ 1 ];
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repsum += v * ( (v*v) - 1 );
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}
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}
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if ( repsum > 0 ) {
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// Correction for repeated values:
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se -= 0.5 * repsum;
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}
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se = sqrt( se / 24.0 );
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if (
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( len > 50 && !opts.exact ) ||
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nzero > 0 ||
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hasTies
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) {
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d = 0.0;
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if ( correction ) {
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switch ( alt ) {
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case 'two-sided':
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d = 0.5 * signum( T - mn );
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break;
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case 'less':
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d = -0.5;
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break;
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default:
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d = 0.5;
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break;
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}
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}
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// Compute test statistic and p-value using normal approximation:
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stat = ( T - mn - d ) / se;
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if ( alt === 'two-sided' ) {
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pval = 2.0 * ( 1.0 - pnorm( abs( stat ) ) );
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} else if ( alt === 'greater' ) {
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pval = 1.0 - pnorm( stat );
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} else {
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pval = pnorm( stat );
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}
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} else {
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// Compute test statistic and p-value using exact critical values:
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stat = T;
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if ( alt === 'two-sided' ) {
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if ( stat > ( len * ( len+1 ) / 4 ) ) {
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pval = 2.0 * ( 1 - signrankCDF( stat - 1, len ) );
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} else {
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pval = 2.0 * signrankCDF( stat, len );
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}
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} else if ( alt === 'greater' ) {
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pval = 1.0 - signrankCDF( stat - 1, len );
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} else {
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pval = signrankCDF( stat, len );
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}
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}
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out = {};
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setReadOnly( out, 'rejected', pval <= alpha );
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setReadOnly( out, 'alpha', alpha );
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setReadOnly( out, 'pValue', pval );
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setReadOnly( out, 'statistic', T );
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setReadOnly( out, 'nullValue', mu );
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setReadOnly( out, 'alternative', alt );
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setReadOnly( out, 'method', ( ( y ) ? 'Paired' : 'One-Sample' ) + ' Wilcoxon signed rank test' );
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setReadOnly( out, 'print', print );
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return out;
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}
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// EXPORTS //
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module.exports = wilcoxon;
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