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{{alias}}( x[, y][, options] )
Computes a one-sample or paired Wilcoxon signed rank test.
When no `y` is supplied, the function performs a one-sample Wilcoxon signed
rank test for the null hypothesis that the data is drawn from a symmetric
distribution around zero.
When `y` is supplied, the function tests whether the
differences `x - y` come from a symmetric distribution around zero.
If `x` has less than fifty elements, an exact p-value is computed if there
are no zero values or ties. Otherwise, a normal approximation is used.
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>|TypedArray
Data array.
y: Array<number>|TypedArray (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.correction: boolean (optional)
Determines whether to apply continuity correction adjusting the Wilcoxon
rank statistic by 0.5 towards the mean when using the normal
approximation. Default: `true`.
options.exact: boolean (optional)
Determines whether to force use of the exact distribution instead of a
normal approximation when there are more than fifty data points.
Default: `false`.
options.mu: number (optional)
Hypothesized true location under the null hypothesis. Set this option to
test whether the data comes from a distribution with the specified `mu`.
Default: `0`.
options.zeroMethod: string (optional)
Method governing how zero-differences are handled (`pratt`, `wilcox`, or
`zsplit`). When set to `pratt`, differences of zero are used to
calculate ranks but their ranks are then dropped. When set to `wilcox`,
all zero-differences are discarded. When set to `zsplit`, differences of
zero are used to rank and their ranks are then split between positive
and negative ones. Default: `'wilcox'`.
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.nullValue: number
Assumed location parameter under H0.
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
--------
// One-sample test:
> var arr = [ 6, 8, 14, 16, 23, 24, 28, 29, 41, -48, 49, 56, 60, -67, 75 ];
> var out = {{alias}}( x )
{
'rejected': true,
'alpha': 0.05,
'pValue': 0.04125976562499978,
'statistic': 96
// ...
}
// Paired test:
> runif = {{alias:@stdlib/random/base/discrete-uniform}}.factory( 1, 5, { 'seed': 786 });
> var x = new Array( 100 );
> var y = new Array( 100 );
> for ( i = 0; i < x.length; i++ ) {
... x[ i ] = runif();
... y[ i ] = runif();
... }
> out = {{alias}}( x, y )
{
'rejected': false,
'alpha': 0.05,
'pValue': 0.21759090963694638,
'statistic': 2702.5,
// ...
}
// Print formatted output:
> var table = out.print()
Paired Wilcoxon signed rank test
Alternative hypothesis: Median of the difference `x - y` is not equal to 0
pValue: 0.2176
statistic: 2702.5
Test Decision: Fail to reject null in favor of alternative at 5% significance level
// Choose custom significance level:
> out = {{alias}}( arr, { 'alpha': 0.01 });
> table = out.print()
One-Sample Wilcoxon signed rank test
Alternative hypothesis: Median of `x` is not equal to 0
pValue: 0.0413
statistic: 96
Test Decision: Fail to reject null in favor of alternative at 1% significance level
// Test for a median equal to ten:
> out = {{alias}}( arr, { 'mu': 10 })
{
'rejected': false,
'alpha': 0.05,
'pValue': 0.11169650413134602,
'statistic': 88.5,
'nullValue': 10,
// ...
}
// Perform one-sided tests:
> out = {{alias}}( arr, { 'alternative': 'less' });
> table = out.print()
One-Sample Wilcoxon signed rank test
Alternative hypothesis: Median of `x` is less than 0
pValue: 0.9823
statistic: 96
Test Decision: Fail to reject null in favor of alternative at 5% significance level
> out = {{alias}}( arr, { 'alternative': 'greater' });
> table = out.print()
One-Sample Wilcoxon signed rank test
Alternative hypothesis: Median of `x` is greater than 0
pValue: 0.0206
statistic: 96
Test Decision: Reject null in favor of alternative at 5% significance level
See Also
--------
|
