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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 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 fCDF = require( '@stdlib/stats/base/dists/f/cdf' );
var fQuantile = require( '@stdlib/stats/base/dists/f/quantile' );
var variance = require( '@stdlib/stats/strided/variance' );
var format = require( '@stdlib/string/format' );
var min = require( '@stdlib/math/base/special/min' );
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 F-test for equal variances.
*
* @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 {PositiveNumber} [options.ratio=1] - ratio of population variances 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 must be an object
* @throws {TypeError} alpha option has to be a number
* @throws {RangeError} alpha option has to be a number in the interval `[0,1]`
* @throws {TypeError} alternative option has to be a string
* @throws {Error} alternative option must be `two-sided`, `less` or `greater`
* @throws {TypeError} ratio option has to be a number
* @returns {Object} test result object
*
* @example
* var x = [ 610, 610, 550, 590, 565, 570 ];
* var y = [ 560, 550, 580, 550, 560, 590, 550, 590 ];
*
* var out = vartest( x, y );
*/
function vartest( x, y, options ) {
var estimate;
var alpha;
var ratio;
var beta;
var cint;
var opts;
var pval;
var stat;
var xvar;
var yvar;
var alt;
var err;
var out;
var dfX;
var dfY;
if ( !isTypedArrayLike( x ) && !isNumberArray( x ) ) {
throw new TypeError( format( 'invalid argument. First argument must be a numeric array. Value: `%s`.', x ) );
}
if ( !isTypedArrayLike( y ) && !isNumberArray( y ) ) {
throw new TypeError( format( 'invalid argument. Second argument must be a numeric array. Value: `%s`.', y ) );
}
opts = {};
if ( options ) {
err = validate( opts, options );
if ( err ) {
throw err;
}
}
ratio = opts.ratio || 1.0;
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` option must be a number on the interval: [0, 1]. Option: `%f`.', 'alpha', alpha ) );
}
dfX = x.length - 1;
dfY = y.length - 1;
xvar = variance( x.length, 1, x, 1 );
yvar = variance( y.length, 1, y, 1 );
estimate = xvar / yvar;
stat = estimate / ratio;
pval = fCDF( stat, dfX, dfY );
alt = opts.alternative || 'two-sided';
switch ( alt ) {
case 'two-sided':
pval = 2.0 * min( pval, 1.0 - pval );
beta = alpha / 2.0;
cint = [
estimate / fQuantile( 1.0 - beta, dfX, dfY ),
estimate / fQuantile( beta, dfX, dfY )
];
break;
case 'greater':
pval = 1.0 - pval;
cint = [
estimate / fQuantile( 1.0 - alpha, dfX, dfY ),
PINF
];
break;
case 'less':
cint = [
0.0,
estimate / fQuantile( alpha, dfX, dfY )
];
break;
default:
throw new Error( format( 'invalid option. `%s` option must be one of the following: "%s". Option: `%s`.', 'alternative', [ 'two-sided', 'less', 'greater' ].join( '", "' ), 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, 'xvar', xvar );
setReadOnly( out, 'yvar', yvar );
setReadOnly( out, 'dfX', dfX );
setReadOnly( out, 'dfY', dfY );
setReadOnly( out, 'method', 'F test for comparing two variances' );
setReadOnly( out, 'nullValue', ratio );
setReadOnly( out, 'print', print );
return out;
}
// EXPORTS //
module.exports = vartest;
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