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|
{{alias}}( x, sigma[, options] )
Computes a one-sample z-test.
The function performs a one-sample z-test for the null hypothesis that the
data in array or typed array `x` is drawn from a normal distribution with
mean zero and standard deviation `sigma`.
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.
sigma: number
Known standard deviation.
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 mean.
out.nullValue: number
Assumed mean value under H0.
out.sd: number
Standard error.
out.alternative: string
Alternative hypothesis (`two-sided`, `less` or `greater`).
out.method: string
Name of test (`One-Sample z-test`).
out.print: Function
Function to print formatted output.
Examples
--------
// One-sample z-test:
> var rnorm = {{alias:@stdlib/random/base/normal}}.factory( 0.0, 2.0, { 'seed': 212 });
> var x = new Array( 100 );
> for ( var i = 0; i < x.length; i++ ) {
... x[ i ] = rnorm();
... }
> var out = {{alias}}( x, 2.0 )
{
alpha: 0.05,
rejected: false,
pValue: ~0.180,
statistic: ~-1.34,
ci: [ ~-0.66, ~0.124 ],
...
}
// Choose custom significance level and print output:
> arr = [ 2, 4, 3, 1, 0 ];
> out = {{alias}}( arr, 2.0, { 'alpha': 0.01 });
> table = out.print()
One-sample z-test
Alternative hypothesis: True mean is not equal to 0
pValue: 0.0253
statistic: 2.2361
99% confidence interval: [-0.3039,4.3039]
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, 1.0, { 'mu': 5 })
{
rejected: false,
pValue: 1,
statistic: 0,
ci: [ ~4.123, ~5.877 ],
// ...
}
// Perform one-sided tests:
> arr = [ 4, 4, 6, 6, 5 ];
> out = {{alias}}( arr, 1.0, { 'alternative': 'less' })
{
alpha: 0.05,
rejected: false,
pValue: 1,
statistic: 11.180339887498949,
ci: [ -Infinity, 5.735600904580115 ],
// ...
}
> out = {{alias}}( arr, 1.0, { 'alternative': 'greater' })
{
alpha: 0.05,
rejected: true,
pValue: 0,
statistic: 11.180339887498949,
ci: [ 4.264399095419885, Infinity ],
//...
}
See Also
--------
|
