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{{alias}}( x, y, sigmax, sigmay[, options] )
Computes a two-sample z-test.
By default, the function performs a two-sample z-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 and known
standard deviations `sigmax` and `sigmay`.
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.
sigmax: number
Known standard deviation of first group.
sigmay: number
Known standard deviation of second group.
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`.
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.method: string
Name of test.
out.print: Function
Function to print formatted output.
Examples
--------
// Drawn from Normal(0,2):
> var x = [ -0.21, 0.14, 1.65, 2.11, -1.86, -0.29, 1.48, 0.81, 0.86, 1.04 ];
// Drawn from Normal(1,2):
> var y = [ -1.53, -2.93, 2.34, -1.15, 2.7, -0.12, 4.22, 1.66, 3.43, 4.66 ];
> var out = {{alias}}( x, y, 2.0, 2.0 )
{
alpha: 0.05,
rejected: false,
pValue: ~0.398,
statistic: ~-0.844
ci: [ ~-2.508, ~0.988 ],
alternative: 'two-sided',
method: 'Two-sample z-test',
nullValue: 0,
xmean: ~0.573,
ymean: ~1.328
}
// Print table output:
> var table = out.print()
Two-sample z-test
Alternative hypothesis: True difference in means is not equal to 0
pValue: 0.3986
statistic: -0.8441
95% confidence interval: [-2.508,0.998]
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, 2.0, 2.0, { 'alpha': 0.4 });
> table = out.print()
Two-sample z-test
Alternative hypothesis: True difference in means is not equal to 0
pValue: 0.3986
statistic: -0.8441
60% confidence interval: [-1.5078,-0.0022]
Test Decision: Reject null in favor of alternative at 40% significance level
// Perform one-sided tests:
> out = {{alias}}( x, y, 2.0, 2.0, { 'alternative': 'less' });
> table = out.print()
Two-sample z-test
Alternative hypothesis: True difference in means is less than 0
pValue: 0.1993
statistic: -0.8441
95% confidence interval: [-Infinity,0.7162]
Test Decision: Fail to reject null in favor of alternative at 5%
significance level
> out = {{alias}}( x, y, 2.0, 2.0, { 'alternative': 'greater' });
> table = out.print()
Two-sample z-test
Alternative hypothesis: True difference in means is greater than 0
pValue: 0.8007
statistic: -0.8441
95% confidence interval: [-2.2262,Infinity]
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, 1.0 );
... }
> y = new Array( 100 );
... for ( i = 0; i < x.length; i++ ) {
... y[ i ] = rnorm( 0.0, 2.0 );
... }
> out = {{alias}}( x, y, 1.0, 2.0, { 'difference': 2.0 })
{
rejected: false,
pValue: ~0.35,
statistic: ~-0.935
ci: [ ~1.353, ~2.229 ],
// ...
}
See Also
--------
|
