time-to-botec/squiggle/node_modules/@stdlib/stats/wilcoxon/docs/repl.txt

{{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
    --------