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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 isArray = require( '@stdlib/assert/is-array' );
var setReadOnly = require( '@stdlib/utils/define-read-only-property' );
var hasOwnProp = require( '@stdlib/assert/has-own-property' );
var format = require( '@stdlib/string/format' );
var cdf = require( '@stdlib/stats/base/dists/f/cdf' );
var defaults = require( './defaults.js' );
var validate = require( './validate.js' );
var unique = require( './unique.js' );
var meanTable = require( './mean_table.js' );
var mean = require( './mean.js' );
var prettyPrint = require( './print.js' );
// MAIN //
/**
* Perform a one-way analysis of variance (ANOVA).
*
* @param {NumericArray} x - measured values
* @param {Array} factor - array of treatments
* @param {Options} [options] - function options
* @param {number} [options.alpha=0.05] - significance level
* @throws {TypeError} options argument must be an object
* @throws {TypeError} must provide valid options
* @throws {TypeError} first argument must be a numeric array
* @throws {TypeError} second argument must be an array
* @throws {RangeError} `factor` must contain at least two unique elements
* @throws {RangeError} length of `x` must be greater than or equal to two
* @throws {RangeError} `x` and `factor` must have the same length
* @returns {Object} test results
*/
function anova1( x, factor, options ) {
var meanSumSqTreat; // Mean sum of squares
var meanSumSqError;
var ssTreatment;
var sumSqTotal;
var sumSqError;
var treatment; // Index variable
var grandMean;
var nGroups;
var fScore;
var treats;
var means;
var numDf;
var denDf;
var nobs;
var pVal;
var opts;
var err;
var out;
var sq;
var i;
if ( !isTypedArrayLike( x ) && !isNumberArray( x ) ) {
throw new TypeError( format( 'invalid argument. First argument must be a numeric array. Value: `%s`.', x ) );
}
opts = defaults();
if ( arguments.length > 2 ) {
err = validate( opts, options );
if ( err ) {
throw err;
}
}
nobs = x.length;
if ( nobs <= 1 ) {
throw new RangeError( format( 'invalid argument. First argument must contain at least two elements. Value: `%s`.', x ) );
}
if ( !isArray( factor ) ) {
throw new TypeError( format( 'invalid argument. Second argument must be an array. Value: `%s`.', treats ) );
}
treats = unique( factor );
nGroups = treats.length;
if ( nGroups <= 1 ) {
throw new RangeError( format( 'invalid argument. Second argument must contain at least two unique elements. Value: `%s`.', treats ) );
}
if ( nobs !== factor.length ) {
throw new RangeError( 'invalid arguments. First and second arguments must be arrays having the same length.' );
}
sumSqTotal = 0.0;
ssTreatment = 0.0;
means = meanTable( x, factor, treats );
grandMean = mean( x );
// Now get total ss:
for ( i = 0; i < nobs; i++ ) {
sq = ( x[i] - grandMean ) * ( x[i] - grandMean );
sumSqTotal += sq;
}
sq = 0.0;
for ( treatment in means ) {
if ( hasOwnProp( means, treatment ) ) {
// Already have sq defined
sq = ( means[treatment].mean - grandMean ) *
( means[treatment].mean - grandMean );
ssTreatment += means[treatment].sampleSize * sq;
}
}
numDf = nGroups - 1;
denDf = nobs - nGroups;
sumSqError = sumSqTotal - ssTreatment;
meanSumSqTreat = ssTreatment / numDf;
meanSumSqError = sumSqError / denDf;
fScore = meanSumSqTreat / meanSumSqError;
pVal = 1.0 - cdf( fScore, numDf, denDf );
out = {};
treatment = {};
setReadOnly( treatment, 'df', numDf );
setReadOnly( treatment, 'ss', ssTreatment );
setReadOnly( treatment, 'ms', meanSumSqTreat );
setReadOnly( out, 'treatment', treatment );
err = {};
setReadOnly( err, 'df', denDf );
setReadOnly( err, 'ss', sumSqError );
setReadOnly( err, 'ms', meanSumSqError );
setReadOnly( out, 'error', err );
setReadOnly( out, 'statistic', fScore );
setReadOnly( out, 'pValue', pVal );
setReadOnly( out, 'means', means );
setReadOnly( out, 'method', 'One-Way ANOVA' );
setReadOnly( out, 'alpha', opts.alpha );
setReadOnly( out, 'rejected', pVal <= opts.alpha );
setReadOnly( out, 'print', prettyPrint( out ) );
return out;
}
// EXPORTS //
module.exports = anova1;
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