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{{alias}}( x, y[, options] )
Computes a two-sample Student's t test.
By default, the function performs a two-sample t-test for the null
hypothesis that the data in arrays or typed arrays `x` and `y` is
independently drawn from normal distributions with equal means.
The returned object comes with a `.print()` method which when invoked will
print a formatted output of the results of the hypothesis test.
Parameters
----------
x: Array<number>
First data array.
y: Array<number>
Second data array.
options: Object (optional)
Options.
options.alpha: number (optional)
Number in the interval `[0,1]` giving the significance level of the
hypothesis test. Default: `0.05`.
options.alternative: string (optional)
Either `two-sided`, `less` or `greater`. Indicates whether the
alternative hypothesis is that `x` has a larger mean than `y`
(`greater`), `x` has a smaller mean than `y` (`less`) or the means are
the same (`two-sided`). Default: `'two-sided'`.
options.difference: number (optional)
Number denoting the difference in means under the null hypothesis.
Default: `0`.
options.variance: string (optional)
String indicating if the test should be conducted under the assumption
that the unknown variances of the normal distributions are `equal` or
`unequal`. As a default choice, the function carries out the Welch test
(using the Satterthwaite approximation for the degrees of freedom),
which does not have the requirement that the variances of the underlying
distributions are equal. If the equal variances assumption seems
warranted, set the option to `equal`. Default: `unequal`.
Returns
-------
out: Object
Test result object.
out.alpha: number
Used significance level.
out.rejected: boolean
Test decision.
out.pValue: number
p-value of the test.
out.statistic: number
Value of test statistic.
out.ci: Array<number>
1-alpha confidence interval for the mean.
out.nullValue: number
Assumed difference in means under H0.
out.xmean: number
Sample mean of `x`.
out.ymean: number
Sample mean of `y`.
out.alternative: string
Alternative hypothesis (`two-sided`, `less` or `greater`).
out.df: number
Degrees of freedom.
out.method: string
Name of test.
out.print: Function
Function to print formatted output.
Examples
--------
// Student's sleep data:
> var x = [ 0.7, -1.6, -0.2, -1.2, -0.1, 3.4, 3.7, 0.8, 0.0, 2.0 ];
> var y = [ 1.9, 0.8, 1.1, 0.1, -0.1, 4.4, 5.5, 1.6, 4.6, 3.4 ];
> var out = {{alias}}( x, y )
{
rejected: false,
pValue: ~0.079,
statistic: ~-1.861,
ci: [ ~-3.365, ~0.205 ],
// ...
}
// Print table output:
> var table = out.print()
Welch two-sample t-test
Alternative hypothesis: True difference in means is not equal to 0
pValue: 0.0794
statistic: -1.8608
95% confidence interval: [-3.3655,0.2055]
Test Decision: Fail to reject null in favor of alternative at 5%
significance level
// Choose a different significance level than `0.05`:
> out = {{alias}}( x, y, { 'alpha': 0.1 });
> table = out.print()
Welch two-sample t-test
Alternative hypothesis: True difference in means is not equal to 0
pValue: 0.0794
statistic: -1.8608
90% confidence interval: [-3.0534,-0.1066]
Test Decision: Reject null in favor of alternative at 10% significance level
// Perform one-sided tests:
> out = {{alias}}( x, y, { 'alternative': 'less' });
> table = out.print()
Welch two-sample t-test
Alternative hypothesis: True difference in means is less than 0
pValue: 0.0397
statistic: -1.8608
df: 17.7765
95% confidence interval: [-Infinity,-0.1066]
Test Decision: Reject null in favor of alternative at 5% significance level
> out = {{alias}}( x, y, { 'alternative': 'greater' });
> table = out.print()
Welch two-sample t-test
Alternative hypothesis: True difference in means is greater than 0
pValue: 0.9603
statistic: -1.8608
df: 17.7765
95% confidence interval: [-3.0534,Infinity]
Test Decision: Fail to reject null in favor of alternative at 5%
significance level
// Run tests with equal variances assumption:
> x = [ 2, 3, 1, 4 ];
> y = [ 1, 2, 3, 1, 2, 5, 3, 4 ];
> out = {{alias}}( x, y, { 'variance': 'equal' });
> table = out.print()
Two-sample t-test
Alternative hypothesis: True difference in means is not equal to 0
pValue: 0.8848
statistic: -0.1486
df: 10
95% confidence interval: [-1.9996,1.7496]
Test Decision: Fail to reject null in favor of alternative at 5%
significance level
// Test for a difference in means besides zero:
> var rnorm = {{alias:@stdlib/random/base/normal}}.factory({ 'seed': 372 });
> x = new Array( 100 );
> for ( i = 0; i < x.length; i++ ) {
... x[ i ] = rnorm( 2.0, 3.0 );
... }
> y = new Array( 100 );
> for ( i = 0; i < x.length; i++ ) {
... y[ i ] = rnorm( 1.0, 3.0 );
... }
> out = {{alias}}( x, y, { 'difference': 1.0, 'variance': 'equal' })
{
rejected: false,
pValue: ~0.642,
statistic: ~-0.466,
ci: [ ~-0.0455, ~1.646 ],
// ...
}
See Also
--------
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