141 lines
4.1 KiB
JavaScript
141 lines
4.1 KiB
JavaScript
/**
|
|
* @license Apache-2.0
|
|
*
|
|
* Copyright (c) 2020 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 setReadOnly = require( '@stdlib/utils/define-read-only-property' );
|
|
var isNonNegativeIntegerArray = require( '@stdlib/assert/is-nonnegative-integer-array' );
|
|
var isMatrixLike = require( '@stdlib/assert/is-matrix-like' );
|
|
var isArrayArray = require( '@stdlib/assert/is-array-array' );
|
|
var array = require( '@stdlib/ndarray/array' );
|
|
var incrmin = require( './../../incr/min' );
|
|
var gsum = require( '@stdlib/blas/ext/base/gsum' );
|
|
var min = require( '@stdlib/math/base/special/min' );
|
|
var copy = require( '@stdlib/utils/copy' );
|
|
var chisqCDF = require( './../../base/dists/chisquare/cdf' );
|
|
var prettyPrint = require( './print.js' );
|
|
var defaults = require( './defaults.json' );
|
|
var sumByDimension = require( './sum.js' );
|
|
var outer = require( './outer.js' );
|
|
var absdiff = require( './absdiff.js' );
|
|
var validate = require( './validate.js' );
|
|
|
|
|
|
// MAIN //
|
|
|
|
/**
|
|
* Performs a chi-square independence test.
|
|
*
|
|
* @param {(ndarray|ArrayArray)} x - two-way table of cell counts
|
|
* @param {Options} [options] - function options
|
|
* @param {number} [options.alpha=0.05] - significance level
|
|
* @param {boolean} [options.correct=true] - boolean indicating whether to use Yates' continuity correction when provided a 2x2 contingency table
|
|
* @throws {TypeError} first argument must be an array of arrays or ndarray-like object with dimension two
|
|
* @returns {Object} test results
|
|
*
|
|
* @example
|
|
*
|
|
* @example
|
|
* var x = [ [ 20, 30 ], [ 30, 20 ] ];
|
|
* var out = chi2test( x );
|
|
* // returns { 'rejected': false, 'alpha': 0.05, 'pValue': ~0.072, ... }
|
|
*/
|
|
function chi2test( x, options ) {
|
|
var absDiff;
|
|
var colSums;
|
|
var rowSums;
|
|
var minAbs;
|
|
var yates;
|
|
var means;
|
|
var param;
|
|
var nrow;
|
|
var ncol;
|
|
var opts;
|
|
var pval;
|
|
var stat;
|
|
var err;
|
|
var out;
|
|
var N;
|
|
var i;
|
|
|
|
if ( isArrayArray( x ) ) {
|
|
x = array( x );
|
|
}
|
|
if ( !isMatrixLike( x ) ) {
|
|
throw new TypeError( 'invalid argument. First argument `x` must be an array of arrays or ndarray-like object with dimension two. Value: `' + x + '`.' );
|
|
}
|
|
if ( !isNonNegativeIntegerArray( x.data ) ) {
|
|
throw new TypeError( 'invalid argument. First argument `x` must contain nonnegative integers. Value: `' + x + '`.' );
|
|
}
|
|
opts = copy( defaults );
|
|
if ( arguments.length > 1 ) {
|
|
err = validate( opts, options );
|
|
if ( err ) {
|
|
throw err;
|
|
}
|
|
}
|
|
N = gsum( x.length, x.data, 1 );
|
|
nrow = x.shape[ 0 ];
|
|
ncol = x.shape[ 1 ];
|
|
|
|
colSums = sumByDimension( x, 1 );
|
|
rowSums = sumByDimension( x, 2 );
|
|
means = outer( rowSums, colSums );
|
|
for ( i = 0; i < means.length; i++ ) {
|
|
means.data[ i ] /= N;
|
|
}
|
|
absDiff = absdiff( x, means );
|
|
|
|
if ( opts.correct && nrow === 2 && ncol === 2 ) {
|
|
// Apply Yates' continuity correction:
|
|
minAbs = incrmin();
|
|
for ( i = 0; i < absDiff.length; i++ ) {
|
|
minAbs( absDiff[ i ] );
|
|
}
|
|
yates = min( 0.5, minAbs() );
|
|
for ( i = 0; i < absDiff.length; i++ ) {
|
|
absDiff[ i ] -= yates;
|
|
}
|
|
}
|
|
for ( i = 0; i < absDiff.length; i++ ) {
|
|
absDiff[ i ] *= absDiff[ i ];
|
|
absDiff[ i ] /= means.data[ i ];
|
|
}
|
|
stat = gsum( absDiff.length, absDiff, 1 );
|
|
param = ( nrow - 1 ) * ( ncol - 1 );
|
|
pval = 1 - chisqCDF( stat, param );
|
|
|
|
out = {};
|
|
setReadOnly( out, 'rejected', pval <= opts.alpha );
|
|
setReadOnly( out, 'alpha', opts.alpha );
|
|
setReadOnly( out, 'pValue', pval );
|
|
setReadOnly( out, 'df', param );
|
|
setReadOnly( out, 'expected', means );
|
|
setReadOnly( out, 'statistic', stat );
|
|
setReadOnly( out, 'method', 'Chi-square independence test' );
|
|
setReadOnly( out, 'print', prettyPrint( out ) );
|
|
return out;
|
|
}
|
|
|
|
|
|
// EXPORTS //
|
|
|
|
module.exports = chi2test;
|