Press n or j to go to the next uncovered block, b, p or k for the previous block.
| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 | 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x | /**
* @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 isPositiveNumber = require( '@stdlib/assert/is-positive-number' ).isPrimitive;
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 cdfFactory = require( '@stdlib/stats/base/dists/normal/cdf' ).factory;
var quantileFactory = require( '@stdlib/stats/base/dists/normal/quantile' ).factory;
var format = require( '@stdlib/string/format' );
var sqrt = require( '@stdlib/math/base/special/sqrt' );
var abs = require( '@stdlib/math/base/special/abs' );
var mean = require( '@stdlib/stats/strided/mean' );
var NINF = require( '@stdlib/constants/float64/ninf' );
var PINF = require( '@stdlib/constants/float64/pinf' );
var validate = require( './validate.js' );
var print = require( './print.js' ); // eslint-disable-line stdlib/no-redeclare
// VARIABLES //
var normalCDF = cdfFactory( 0.0, 1.0 );
var normalQuantile = quantileFactory( 0.0, 1.0 );
// MAIN //
/**
* Computes a one-sample z-test.
*
* @param {NumericArray} x - data array
* @param {PositiveNumber} sigma - known standard deviation
* @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.mu=0] - mean under H0
* @throws {TypeError} x argument has to be a typed array or array of numbers
* @throws {TypeError} sigma argument has to be a positive number
* @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} mu option has to be a number
* @throws {TypeError} sigma option has to be a positive number
* @returns {Object} test result object
*
* @example
* var arr = [ 4, 4, 6, 6, 5 ];
* var out = ztest( arr, 1.0, {
* 'mu': 5
* });
*
* @example
* var arr = [ 4, 4, 6, 6, 5 ];
* var out = ztest( arr, 1.0, {
* 'alternative': 'greater'
* });
*/
function ztest( x, sigma, options ) {
var stderr;
var alpha;
var xmean;
var cint;
var pval;
var opts;
var stat;
var alt;
var err;
var out;
var len;
var mu;
if ( !isTypedArrayLike( x ) && !isNumberArray( x ) ) {
throw new TypeError( format( 'invalid argument. First argument must be a numeric array. Value: `%s`.', x ) );
}
if ( !isPositiveNumber( sigma ) ) {
throw new TypeError( format( 'invalid argument. Second argument must be a positive number. Value: `%s`.', sigma ) );
}
len = x.length;
opts = {};
if ( options ) {
err = validate( opts, options );
if ( err ) {
throw err;
}
}
mu = opts.mu || 0.0;
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 ) );
}
if ( len < 2 ) {
throw new Error( format( 'invalid argument. First argument must contain at least two elements. Value: `%s`.', x ) );
}
stderr = sqrt( sigma*sigma / len );
xmean = mean( len, x, 1 );
stat = ( xmean - mu ) / stderr;
alt = opts.alternative || 'two-sided';
switch ( alt ) {
case 'two-sided':
pval = 2.0 * normalCDF( -abs(stat) );
cint = [
stat - normalQuantile( 1.0-(alpha/2.0) ),
stat + normalQuantile( 1.0-(alpha/2.0) )
];
cint[ 0 ] = mu + (cint[ 0 ] * stderr);
cint[ 1 ] = mu + (cint[ 1 ] * stderr);
break;
case 'greater':
pval = 1.0 - normalCDF( stat );
cint = [ stat - normalQuantile( 1.0-alpha ), PINF ];
cint[ 0 ] = mu + (cint[ 0 ] * stderr);
break;
case 'less':
pval = normalCDF( stat );
cint = [ NINF, stat + normalQuantile( 1.0-alpha ) ];
cint[ 1 ] = mu + (cint[ 1 ] * stderr);
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, 'nullValue', mu );
setReadOnly( out, 'sd', stderr );
setReadOnly( out, 'method', 'One-sample z-test' );
setReadOnly( out, 'print', print );
return out;
}
// EXPORTS //
module.exports = ztest;
|