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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 | 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 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 isObject = require( '@stdlib/assert/is-plain-object' );
var tCDF = require( '@stdlib/stats/base/dists/t/cdf' );
var tQuantile = require( '@stdlib/stats/base/dists/t/quantile' );
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 variance = require( '@stdlib/stats/strided/variance' );
var gcopy = require( '@stdlib/blas/base/gcopy' );
var NINF = require( '@stdlib/constants/float64/ninf' );
var PINF = require( '@stdlib/constants/float64/pinf' );
var Float64Array = require( '@stdlib/array/float64' );
var validate = require( './validate.js' );
var print = require( './print.js' ); // eslint-disable-line stdlib/no-redeclare
// MAIN //
/**
* Computes a one-sample or paired Student's t test.
*
* @param {NumericArray} x - input array
* @param {NumericArray} [y] - optional paired 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.mu=0.0] - mean under `H0`
* @throws {TypeError} first argument must be a numeric array
* @throws {Error} first argument must contain at least two elements
* @throws {Error} paired array must have the same length as the first argument
* @throws {TypeError} second argument must be either a numeric array or an options object
* @throws {TypeError} `alpha` option must be number
* @throws {RangeError} `alpha` option must be reside along the interval `[0,1]`
* @throws {TypeError} `alternative` option must be a recognized option value (`two-sided`, `less`, or `greater`)
* @throws {TypeError} `mu` option must be a number
* @returns {Object} test results
*
* @example
* var x = [ 4.0, 4.0, 6.0, 6.0, 5.0 ];
* var opts = {
* 'mu': 5.0
* };
* var out = ttest( x, opts );
* // returns {...}
*
* @example
* var x = [ 4.0, 4.0, 6.0, 6.0, 5.0 ];
* var opts = {
* 'alternative': 'greater'
* };
* var out = ttest( x, opts );
* // returns {...}
*/
function ttest( x ) {
var stderr;
var xmean;
var cint;
var pval;
var opts;
var stat;
var err;
var len;
var out;
var df;
var tq;
var y;
var i;
if ( !isTypedArrayLike( x ) && !isNumberArray( x ) ) {
throw new TypeError( format( 'invalid argument. First argument must be a numeric array. Value: `%s`.', x ) );
}
len = x.length;
if ( len < 2 ) {
throw new Error( format( 'invalid argument. First argument must contain at least two elements. Value: `%s`.', x ) );
}
opts = {
'mu': 0.0,
'alpha': 0.05,
'alternative': 'two-sided'
};
if ( arguments.length === 2 ) {
if ( isObject( arguments[ 1 ] ) ) {
err = validate( opts, arguments[ 1 ] );
if ( err ) {
throw err;
}
} else {
y = arguments[ 1 ];
if ( !isTypedArrayLike( y ) && !isNumberArray( y ) ) {
throw new TypeError( format( 'invalid argument. Second argument must be either a numeric array or an options object. Value: `%s`.', y ) );
}
}
} else if ( arguments.length > 2 ) {
y = arguments[ 1 ];
if ( !isTypedArrayLike( y ) && !isNumberArray( y ) ) {
throw new TypeError( format( 'invalid argument. Second argument must be a numeric array. Value: `%s`.', y ) );
}
err = validate( opts, arguments[ 2 ] );
if ( err ) {
throw err;
}
}
if ( y ) {
if ( y.length !== len ) {
throw new Error( 'invalid arguments. First and second arguments must have the same length.' );
}
x = gcopy( len, x, 1, new Float64Array( len ), 1 );
for ( i = 0; i < len; i++ ) {
x[ i ] -= y[ i ];
}
}
stderr = sqrt( variance( len, 1, x, 1 ) / len ); // TODO: replace with base/sem
xmean = mean( len, x, 1 ); // TODO: ideally, we would get both the sem and the mean from the same function and without needing to traverse 3-4 times
stat = ( xmean-opts.mu ) / stderr;
df = len - 1;
if ( opts.alternative === 'two-sided' ) {
pval = 2.0 * tCDF( -abs(stat), df );
tq = tQuantile( 1.0-(opts.alpha/2.0), df );
cint = [
opts.mu + ( (stat-tq)*stderr ),
opts.mu + ( (stat+tq)*stderr )
];
} else if ( opts.alternative === 'greater' ) {
pval = 1.0 - tCDF( stat, df );
tq = tQuantile( 1.0-opts.alpha, df );
cint = [
opts.mu + ( (stat-tq)*stderr ),
PINF
];
} else { // opts.alternative === 'less'
pval = tCDF( stat, df );
tq = tQuantile( 1.0-opts.alpha, df );
cint = [
NINF,
opts.mu + ( (stat+tq)*stderr )
];
}
out = {};
setReadOnly( out, 'rejected', pval <= opts.alpha );
setReadOnly( out, 'alpha', opts.alpha );
setReadOnly( out, 'pValue', pval );
setReadOnly( out, 'statistic', stat );
setReadOnly( out, 'ci', cint );
setReadOnly( out, 'df', df );
setReadOnly( out, 'nullValue', opts.mu );
setReadOnly( out, 'mean', xmean );
setReadOnly( out, 'sd', stderr );
setReadOnly( out, 'alternative', opts.alternative );
setReadOnly( out, 'method', ( y ) ? 'Paired t-test' : 'One-sample t-test' );
setReadOnly( out, 'print', print );
return out;
}
// EXPORTS //
module.exports = ttest;
|