One-sample and paired Student's t-Test.
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> One-sample and paired Student's t-Test.
``bash`
npm install @stdlib/stats-ttest
`javascript`
var ttest = require( '@stdlib/stats-ttest' );
#### ttest( x\[, y]\[, opts] )
The function performs a one-sample t-test for the null hypothesis that the data in [array][mdn-array] or [typed array][mdn-typed-array] x is drawn from a normal distribution with mean zero and unknown variance.
`javascript
var normal = require( '@stdlib/random-base-normal' ).factory;
var rnorm;
var arr;
var out;
var i;
rnorm = normal( 0.0, 2.0, {
'seed': 5776
});
arr = new Array( 100 );
for ( i = 0; i < arr.length; i++ ) {
arr[ i ] = rnorm();
}
out = ttest( arr );
/* e.g., returns
{
'rejected': false,
'pValue': ~0.722,
'statistic': ~0.357,
'ci': [~-0.333,~0.479],
// ...
}
*/
`
When [array][mdn-array] or [typed array][mdn-typed-array] y is supplied, the function tests whether the differences x - y come from a normal distribution with mean zero and unknown variance via the paired t-test.
`javascript
var normal = require( '@stdlib/random-base-normal' ).factory;
var rnorm;
var out;
var i;
var x;
var y;
rnorm = normal( 1.0, 2.0, {
'seed': 786
});
x = new Array( 100 );
y = new Array( 100 );
for ( i = 0; i < x.length; i++ ) {
x[ i ] = rnorm();
y[ i ] = rnorm();
}
out = ttest( x, y );
/* e.g., returns
{
'rejected': false,
'pValue': ~0.191,
'statistic': ~1.315,
'ci': [ ~-0.196, ~0.964 ],
// ...
}
*/
`
The returned object comes with a .print() method which when invoked will print a formatted output of the hypothesis test results. print accepts a digits option that controls the number of decimal digits displayed for the outputs and a decision option, which when set to false will hide the test decision.
`javascript
console.log( out.print() );
/* e.g., =>
Paired t-test
Alternative hypothesis: True difference in means is not equal to 0
pValue: 0.1916
statistic: 1.3148
df: 99
95% confidence interval: [-0.1955,0.9635]
Test Decision: Fail to reject null in favor of alternative at 5% significance level
*/
`
The ttest function accepts the following options:
- alpha: number in the interval [0,1] giving the significance level of the hypothesis test. Default: 0.05.two-sided
- alternative: Either , less or greater. Indicates whether the alternative hypothesis is that the mean of x is larger than mu (greater), smaller than mu (less) or equal to mu (two-sided). Default: two-sided.number
- mu: denoting the hypothesized true mean under the null hypothesis. Default: 0.
By default, the hypothesis test is carried out at a significance level of 0.05. To choose a different significance level, set the alpha option.
`javascript
var table;
var out;
var arr;
arr = [ 2, 4, 3, 1, 0 ];
out = ttest( arr, {
'alpha': 0.01
});
table = out.print();
/* e.g., returns
One-sample t-test
Alternative hypothesis: True mean is not equal to 0
pValue: 0.0474
statistic: 2.8284
df: 4
99% confidence interval: [-1.2556,5.2556]
Test Decision: Fail to reject null in favor of alternative at 1% significance level
*/
out = ttest( arr, {
'alpha': 0.1
});
table = out.print();
/* e.g., returns
One-sample t-test
Alternative hypothesis: True mean is not equal to 0
pValue: 0.0474
statistic: 2.8284
df: 4
90% confidence interval: [0.4926,3.5074]
Test Decision: Reject null in favor of alternative at 10% significance level
*/
`
To test whether the data comes from a distribution with a mean different than zero, set the mu option.
`javascript
var out;
var arr;
arr = [ 4, 4, 6, 6, 5 ];
out = ttest( arr, {
'mu': 5
});
/* e.g., returns
{
'rejected': false,
'pValue': 1,
'statistic': 0,
'ci': [ ~3.758, ~6.242 ],
// ...
}
*/
`
By default, a two-sided test is performed. To perform either of the one-sided tests, set the alternative option to less or greater.
`javascript
var table;
var out;
var arr;
arr = [ 4, 4, 6, 6, 5 ];
out = ttest( arr, {
'alternative': 'less'
});
table = out.print();
/* e.g., returns
One-sample t-test
Alternative hypothesis: True mean is less than 0
pValue: 0.9998
statistic: 11.1803
df: 4
95% confidence interval: [-Infinity,5.9534]
Test Decision: Fail to reject null in favor of alternative at 5% significance level
*/
out = ttest( arr, {
'alternative': 'greater'
});
table = out.print();
/* e.g., returns
One-sample t-test
Alternative hypothesis: True mean is greater than 0
pValue: 0.0002
statistic: 11.1803
df: 4
95% confidence interval: [4.0466,Infinity]
Test Decision: Reject null in favor of alternative at 5% significance level
*/
`
`javascript
var normal = require( '@stdlib/random-base-normal' ).factory;
var ttest = require( '@stdlib/stats-ttest' );
var rnorm;
var arr;
var out;
var i;
rnorm = normal( 5.0, 4.0, {
'seed': 37827
});
arr = new Array( 100 );
for ( i = 0; i < arr.length; i++ ) {
arr[ i ] = rnorm();
}
// Test whether true mean is equal to zero:
out = ttest( arr );
console.log( out.print() );
/* e.g., =>
One-sample t-test
Alternative hypothesis: True mean is not equal to 0
pValue: 0
statistic: 15.0513
df: 99
95% confidence interval: [4.6997,6.127]
Test Decision: Reject null in favor of alternative at 5% significance level
*/
// Test whether true mean is equal to five:
out = ttest( arr, {
'mu': 5.0
});
console.log( out.print() );
/* e.g., =>
One-sample t-test
Alternative hypothesis: True mean is not equal to 5
pValue: 0.2532
statistic: 1.1494
df: 99
95% confidence interval: [4.6997,6.127]
Test Decision: Fail to reject null in favor of alternative at 5% significance level
*/
`
*
- [@stdlib/stats-ttest2][@stdlib/stats/ttest2]: two-sample Student's t-Test.
*
This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.
For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].
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