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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 quantileFactory = require( '@stdlib/stats/base/dists/normal/quantile' ).factory;
var cdfFactory = require( '@stdlib/stats/base/dists/normal/cdf' ).factory;
var format = require( '@stdlib/string/format' );
var atanh = require( '@stdlib/math/base/special/atanh' );
var tanh = require( '@stdlib/math/base/special/tanh' );
var tCDF = require( '@stdlib/stats/base/dists/t/cdf' );
var sqrt = require( '@stdlib/math/base/special/sqrt' );
var min = require( '@stdlib/math/base/special/min' );
var print = require( './print.js' ); // eslint-disable-line stdlib/no-redeclare
var pcorr = require( './pcorr.js' );
var validate = require( './validate.js' );
// VARIABLES //
var normQuantile = quantileFactory( 0.0, 1.0 );
var normCDF = cdfFactory( 0.0, 1.0 );
// MAIN //
/**
* Computes a Pearson product-moment correlation test between paired samples.
*
* @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.rho=0.0] - correlation under H0
* @throws {TypeError} first argument has to be a typed array or array of numbers
* @throws {TypeError} second argument has to be a typed array or array of numbers
* @throws {RangeError} first and second arguments must have the same length
* @throws {Error} first and second arguments must be arrays having the same length
* @throws {Error} first and second arguments must contain at least four elements
* @throws {TypeError} options must be an object
* @throws {TypeError} must provide valid options
* @returns {Object} test result object
*
* @example
* var x = [ 2, 4, 3, 1, 2, 3 ];
* var y = [ 3, 2, 4, 1, 2, 4 ];
* var out = pcorrTest( x, y );
*/
function pcorrTest( x, y, options ) {
var method;
var alpha;
var cint;
var opts;
var pval;
var stat;
var alt;
var err;
var out;
var rho;
var val;
var df;
var se;
var n;
var r;
var z;
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 ) );
}
n = x.length;
if ( n !== y.length ) {
throw new RangeError( 'invalid arguments. First and second arguments must be arrays having the same length.' );
}
opts = {};
if ( options ) {
err = validate( opts, options );
if ( err ) {
throw err;
}
}
if ( opts.alpha === void 0 ) {
alpha = 0.05;
} else {
alpha = opts.alpha;
}
if ( n < 4 ) {
throw new Error( 'invalid arguments. Not enough observations. First and second arguments must contain at least four observations.' );
}
if ( opts.rho === void 0 ) {
rho = 0.0;
} else {
rho = opts.rho;
}
if ( opts.alternative === void 0 ) {
alt = 'two-sided';
} else {
alt = opts.alternative;
}
r = pcorr( x, y );
z = atanh( r );
se = 1.0 / sqrt( n - 3 );
if ( rho === 0.0 ) {
// Use t-test for H0: rho = 0.0 vs H1: rho != 0.0...
method = 't-test for Pearson correlation coefficient';
df = n - 2;
stat = sqrt( df ) * r / sqrt( 1.0 - (r*r) );
switch ( alt ) {
case 'greater':
pval = 1.0 - tCDF( stat, df );
break;
case 'less':
pval = tCDF( stat, df );
break;
case 'two-sided':
default:
pval = 2.0 * min( tCDF( stat, df), 1.0 - tCDF( stat, df ) );
break;
}
} else {
// Use large-sample normality to calculate p-value based on Fisher's z transform...
method = 'Fisher\'s z transform test for Pearson correlation coefficient';
stat = ( z - atanh( rho ) ) * sqrt( n - 3 );
switch ( alt ) {
case 'greater':
pval = normCDF( -stat );
break;
case 'less':
pval = 1.0 - normCDF( -stat );
break;
case 'two-sided':
default:
pval = 2.0 * min( normCDF( -stat ), 1.0 - normCDF( -stat ) );
break;
}
}
switch ( alt ) {
case 'greater':
cint = [ tanh( z - ( se*normQuantile( 1.0 - alpha ) ) ), 1.0 ];
break;
case 'less':
cint = [ -1.0, tanh( z + ( se*normQuantile( 1.0 - alpha ) ) ) ];
break;
case 'two-sided':
default:
val = se * normQuantile( 1.0 - ( alpha/2.0 ) );
cint = [ tanh( z - val ), tanh( z + val ) ];
break;
}
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, 'method', method );
setReadOnly( out, 'nullValue', rho );
setReadOnly( out, 'pcorr', r );
setReadOnly( out, 'print', print );
return out;
}
// EXPORTS //
module.exports = pcorrTest;
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