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

{{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
    --------