time-to-botec

main.js (5804B)

---

 /**
 * @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 isNumberArray = require( '@stdlib/assert/is-number-array' ).primitives;
 var isTypedArrayLike = require( '@stdlib/assert/is-typed-array-like' );
 var setReadOnly = require( '@stdlib/utils/define-read-only-property' );
 var tCDF = require( './../../base/dists/t/cdf' );
 var tQuantile = require( './../../base/dists/t/quantile' );
 var sqrt = require( '@stdlib/math/base/special/sqrt' );
 var abs = require( '@stdlib/math/base/special/abs' );
 var pow = require( '@stdlib/math/base/special/pow' );
 var mean = require( './../../base/mean' );
 var variance = require( './../../base/variance' );
 var NINF = require( '@stdlib/constants/float64/ninf' );
 var PINF = require( '@stdlib/constants/float64/pinf' );
 var validate = require( './validate.js' );
 var print = require( './print.js' ); // eslint-disable-line stdlib/no-redeclare
 
 
 // MAIN //
 
 /**
 * Computes a two-sample Student's t test.
 *
 * @param {NumericArray} x - first data array
 * @param {NumericArray} y - second data array
 * @param {Options} [options] - function options
 * @param {number} [options.alpha=0.05] - significance level
 * @param {string} [options.alternative='two-sided'] - alternative hypothesis (`two-sided`, `less` or `greater`)
 * @param {number} [options.difference=0] - difference in means under H0
 * @param {string} [options.variance='unequal'] - whether variances are `equal` or `unequal` under H0
 * @throws {TypeError} x argument has to be a typed array or array of numbers
 * @throws {TypeError} y argument has to be a typed array or array of numbers
 * @throws {TypeError} options has to be simple object
 * @throws {TypeError} alpha option has to be a number primitive
 * @throws {RangeError} alpha option has to be a number in the interval `[0,1]`
 * @throws {TypeError} alternative option has to be a string primitive
 * @throws {Error} alternative option must be `two-sided`, `less` or `greater`
 * @throws {TypeError} difference option has to be a number primitive
 * @throws {TypeError} variance option has to be a string primitive
 * @throws {Error} variance option must be `equal` or `unequal`
 * @returns {Object} test result object
 */
 function ttest2( x, y, options ) {
 	var stderr;
 	var alpha;
 	var xmean;
 	var ymean;
 	var vars;
 	var cint;
 	var diff;
 	var opts;
 	var pval;
 	var xvar;
 	var yvar;
 	var stat;
 	var sdx;
 	var sdy;
 	var alt;
 	var err;
 	var out;
 	var nx;
 	var ny;
 	var df;
 	var v;
 
 	if ( !isTypedArrayLike( x ) && !isNumberArray( x ) ) {
 		throw new TypeError( 'invalid argument. First argument `x` must be a numeric array. Value: `' + x + '`.' );
 	}
 	if ( !isTypedArrayLike( y ) && !isNumberArray( y ) ) {
 		throw new TypeError( 'invalid argument. Second argument `y` must be a numeric array. Value: `' + y + '`.' );
 	}
 	opts = {};
 	if ( options ) {
 		err = validate( opts, options );
 		if ( err ) {
 			throw err;
 		}
 	}
 	diff = opts.difference || 0.0;
 	if ( opts.alpha === void 0 ) {
 		alpha = 0.05;
 	} else {
 		alpha = opts.alpha;
 	}
 	if ( alpha < 0.0 || alpha > 1.0 ) {
 		throw new RangeError( 'invalid argument. Option `alpha` must be a number in the range 0 to 1. Value: `' + alpha + '`.' );
 	}
 	nx = x.length;
 	ny = y.length;
 
 	xvar = variance( nx, 1, x, 1 );
 	yvar = variance( ny, 1, y, 1 );
 
 	vars = opts.variance || 'unequal';
 	if ( vars === 'equal' ) {
 		df = nx + ny - 2;
 		v = ((nx-1) * xvar) + ((ny-1) * yvar);
 		v /= df;
 		stderr = sqrt( v * ((1/nx) + (1/ny)) );
 	}
 	else if ( vars === 'unequal' ) {
 		sdx = sqrt( xvar/nx );
 		sdy = sqrt( yvar/ny );
 		stderr = sqrt( (sdx*sdx) + (sdy*sdy) );
 		v = pow( sdx, 4 ) / ( nx - 1 );
 		v += pow( sdy, 4 ) / ( ny - 1 );
 		df = pow( stderr, 4 ) / v;
 	}
 	else {
 		throw new Error( 'Invalid option. `variance` must be either `equal` or `unequal`. Value: `' + vars + '`' );
 	}
 
 	xmean = mean( nx, x, 1 );
 	ymean = mean( ny, y, 1 );
 	stat = ( xmean - ymean - diff ) / stderr;
 
 	alt = opts.alternative || 'two-sided';
 	switch ( alt ) {
 	case 'two-sided':
 		pval = 2.0 * tCDF( -abs(stat), df );
 		cint = [
 			stat - tQuantile( 1.0-(alpha/2.0), df ),
 			stat + tQuantile( 1.0-(alpha/2.0), df )
 		];
 		cint[ 0 ] = diff + (cint[ 0 ] * stderr);
 		cint[ 1 ] = diff + (cint[ 1 ] * stderr);
 		break;
 	case 'greater':
 		pval = 1.0 - tCDF( stat, df );
 		cint = [ stat - tQuantile( 1.0-alpha, df ), PINF ];
 		cint[ 0 ] = diff + (cint[ 0 ] * stderr);
 		break;
 	case 'less':
 		pval = tCDF( stat, df );
 		cint = [ NINF, stat + tQuantile( 1.0-alpha, df ) ];
 		cint[ 1 ] = diff + (cint[ 1 ] * stderr);
 		break;
 	default:
 		throw new Error( 'Invalid option. `alternative` must be either `two-sided`, `less` or `greater`. Value: `' + alt + '`' );
 	}
 	out = {};
 	setReadOnly( out, 'rejected', pval <= alpha );
 	setReadOnly( out, 'alpha', alpha );
 	setReadOnly( out, 'pValue', pval );
 	setReadOnly( out, 'statistic', stat );
 	setReadOnly( out, 'ci', cint );
 	setReadOnly( out, 'alternative', alt );
 	setReadOnly( out, 'df', df );
 	setReadOnly( out, 'method', ( vars === 'equal' ) ? 'Two-sample t-test' : 'Welch two-sample t-test' );
 	setReadOnly( out, 'nullValue', diff );
 	setReadOnly( out, 'xmean', xmean );
 	setReadOnly( out, 'ymean', ymean );
 	setReadOnly( out, 'print', print );
 	return out;
 }
 
 
 // EXPORTS //
 
 module.exports = ttest2;