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{{alias}}( x[, y][, options] )
Computes a one-sample or paired Student's t test.
When no `y` is supplied, the function performs a one-sample t-test for the
null hypothesis that the data in array or typed array `x` is drawn from a
normal distribution with mean zero and unknown variance.
When array or 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.
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>
Data array.
y: Array<number> (optional)
Paired 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)
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'`.
options.mu: number (optional)
Hypothesized true mean under the null hypothesis. Set this option to
test whether the data comes from a distribution with the specified `mu`.
Default: `0`.
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 mean under H0 (or difference in means when `y` is supplied).
out.alternative: string
Alternative hypothesis (`two-sided`, `less` or `greater`).
out.df: number
Degrees of freedom.
out.mean: number
Sample mean of `x` or `x - y`, respectively.
out.sd: number
Standard error of the mean.
out.method: string
Name of test.
out.print: Function
Function to print formatted output.
Examples
--------
// One-sample t-test:
> var rnorm = {{alias:@stdlib/random/base/normal}}.factory( 0.0, 2.0, { 'seed': 5776 });
> var x = new Array( 100 );
> for ( var i = 0; i < x.length; i++ ) {
... x[ i ] = rnorm();
... }
> var out = {{alias}}( x )
{
rejected: false,
pValue: ~0.722,
statistic: ~0.357,
ci: [~-0.333,~0.479],
// ...
}
// Paired t-test:
> rnorm = {{alias:@stdlib/random/base/normal}}.factory( 1.0, 2.0, { 'seed': 786 });
> x = new Array( 100 );
> var y = new Array( 100 );
> for ( i = 0; i < x.length; i++ ) {
... x[ i ] = rnorm();
... y[ i ] = rnorm();
... }
> out = {{alias}}( x, y )
{
rejected: false,
pValue: ~0.191,
statistic: ~1.315,
ci: [ ~-0.196, ~0.964 ],
// ...
}
// Print formatted output:
> var table = out.print()
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
// Choose custom significance level:
> arr = [ 2, 4, 3, 1, 0 ];
> out = {{alias}}( arr, { 'alpha': 0.01 });
> table = out.print()
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
// Test for a mean equal to five:
> var arr = [ 4, 4, 6, 6, 5 ];
> out = {{alias}}( arr, { 'mu': 5 })
{
rejected: false,
pValue: 1,
statistic: 0,
ci: [ ~3.758, ~6.242 ],
// ...
}
// Perform one-sided tests:
> arr = [ 4, 4, 6, 6, 5 ];
> out = {{alias}}( arr, { 'alternative': 'less' });
> table = out.print()
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 = {{alias}}( arr, { 'alternative': 'greater' });
> table = out.print()
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
See Also
--------
|
