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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 isCollection = require( '@stdlib/assert/is-collection' );
var isPlainObject = require( '@stdlib/assert/is-plain-object' );
var objectKeys = require( '@stdlib/utils/keys' );
var qnorm = require( '@stdlib/stats/base/dists/normal/quantile' );
var chisqCDF = require( '@stdlib/stats/base/dists/chisquare/cdf' );
var group = require( '@stdlib/utils/group' );
var ranks = require( '@stdlib/stats/ranks' );
var abs = require( '@stdlib/math/strided/special/abs' );
var pow = require( '@stdlib/math/base/special/pow' );
var indexOf = require( '@stdlib/utils/index-of' );
var format = require( '@stdlib/string/format' );
var filled = require( '@stdlib/array/base/filled' );
var Float64Array = require( '@stdlib/array/float64' );
var median = require( './median.js' );
var validate = require( './validate.js' );
var Results = require( './results.js' );
// MAIN //
/**
* Computes the Fligner-Killeen test for equal variances.
*
* @param {...NumericArray} arguments - either two or more number arrays or a single numeric array if an array of group indicators is supplied as an option
* @param {Options} [options] - function options
* @param {number} [options.alpha=0.05] - significance level
* @param {Array} [options.groups] - array of group indicators
* @throws {TypeError} must provide array-like arguments
* @throws {RangeError} alpha option has to be a number in the interval `[0,1]`
* @throws {Error} must provide at least two array-like arguments if `groups` is not set
* @throws {TypeError} options must be an object
* @throws {TypeError} must provide valid options
* @returns {Object} test results
*
* @example
* // Data from Hollander & Wolfe (1973), p. 116:
* var x = [ 2.9, 3.0, 2.5, 2.6, 3.2 ];
* var y = [ 3.8, 2.7, 4.0, 2.4 ];
* var z = [ 2.8, 3.4, 3.7, 2.2, 2.0 ];
*
* var out = fligner( x, y, z );
* // returns {...}
*/
function fligner() {
var variance;
var options;
var ngroups;
var levels;
var groups;
var scores;
var table;
var alpha;
var delta;
var args;
var mean;
var opts;
var pval;
var sums;
var xabs;
var stat;
var err;
var loc;
var df;
var M2;
var a;
var n;
var x;
var i;
var j;
args = [];
ngroups = arguments.length;
opts = {};
if ( isPlainObject( arguments[ ngroups - 1 ] ) ) {
options = arguments[ ngroups - 1 ];
ngroups -= 1;
err = validate( opts, options );
if ( err ) {
throw err;
}
}
if ( opts.groups ) {
groups = opts.groups;
table = group( arguments[ 0 ], groups );
levels = objectKeys( table );
ngroups = levels.length;
if ( ngroups < 2 ) {
throw new Error( format( 'invalid option. `%s` option must be an array containing at least two unique elements. Option: `%s`.', 'groups', levels ) );
}
for ( i = 0; i < ngroups; i++ ) {
args.push( table[ levels[ i ] ] );
}
} else {
groups = [];
for ( i = 0; i < ngroups; i++ ) {
args.push( arguments[ i ] );
groups = groups.concat( filled( i, arguments[ i ].length ) );
}
}
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 ) );
}
x = [];
for ( i = 0; i < ngroups; i++ ) {
if ( !isCollection( args[ i ] ) ) {
throw new TypeError( format( 'invalid argument. Must provide array-like arguments. Value: `%s`.', args[ i ] ) );
}
if ( args[ i ].length === 0 ) {
throw new Error( format( 'invalid argument. Supplied arrays cannot be empty. Value: `%s`.', args[ i ] ) );
}
loc = median( args[ i ] );
for ( j = 0; j < args[ i ].length; j++ ) {
args[ i ][ j ] -= loc;
}
x = x.concat( args[ i ] );
}
n = x.length;
xabs = new Float64Array( n );
abs( n, 'float64', x, 1, 'float64', xabs, 1 );
scores = ranks( xabs );
a = new Float64Array( n );
mean = 0.0;
M2 = 0.0;
sums = filled( 0.0, ngroups );
for ( i = 0; i < n; i++ ) {
a[ i ] = qnorm( ( 1.0 + ( scores[ i ]/(n+1) ) ) / 2.0, 0.0, 1.0 );
sums[ ( levels ) ? indexOf( levels, groups[i] ) : groups[i] ] += a[ i ];
delta = a[ i ] - mean;
mean += delta / ( i+1 );
M2 += delta * ( a[ i ] - mean );
}
variance = M2 / ( n - 1 );
stat = 0.0;
for ( i = 0; i < ngroups; i++ ) {
stat += pow( sums[ i ], 2 ) / args[ i ].length;
}
stat = ( stat - ( n * pow( mean, 2 ) ) ) / variance;
df = ngroups - 1;
pval = 1.0 - chisqCDF( stat, df );
return new Results( pval, opts.alpha, stat, df );
}
// EXPORTS //
module.exports = fligner;
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