time-to-botec/squiggle/node_modules/@stdlib/stats/ttest2/docs/repl.txt

{{alias}}( x, y[, options] )
    Computes a two-sample Student's t test.

    By default, the function performs a two-sample t-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.

    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.

    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`.

    options.variance: string (optional)
        String indicating if the test should be conducted under the assumption
        that the unknown variances of the normal distributions are `equal` or
        `unequal`. As a default choice, the function carries out the Welch test
        (using the Satterthwaite approximation for the degrees of freedom),
        which does not have the requirement that the variances of the underlying
        distributions are equal. If the equal variances assumption seems
        warranted, set the option to `equal`. Default: `unequal`.

    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.df: number
        Degrees of freedom.

    out.method: string
        Name of test.

    out.print: Function
        Function to print formatted output.

    Examples
    --------
    // Student's sleep data:
    > var x = [ 0.7, -1.6, -0.2, -1.2, -0.1, 3.4, 3.7, 0.8, 0.0, 2.0 ];
    > var y = [ 1.9, 0.8, 1.1, 0.1, -0.1, 4.4, 5.5, 1.6, 4.6, 3.4 ];
    > var out = {{alias}}( x, y )
    {
        rejected: false,
        pValue: ~0.079,
        statistic: ~-1.861,
        ci: [ ~-3.365, ~0.205 ],
        // ...
    }

    // Print table output:
    > var table = out.print()
    Welch two-sample t-test

    Alternative hypothesis: True difference in means is not equal to 0

        pValue: 0.0794
        statistic: -1.8608
        95% confidence interval: [-3.3655,0.2055]

    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, { 'alpha': 0.1 });
    > table = out.print()
    Welch two-sample t-test

    Alternative hypothesis: True difference in means is not equal to 0

        pValue: 0.0794
        statistic: -1.8608
        90% confidence interval: [-3.0534,-0.1066]

    Test Decision: Reject null in favor of alternative at 10% significance level

    // Perform one-sided tests:
    > out = {{alias}}( x, y, { 'alternative': 'less' });
    > table = out.print()
    Welch two-sample t-test

    Alternative hypothesis: True difference in means is less than 0

        pValue: 0.0397
        statistic: -1.8608
        df: 17.7765
        95% confidence interval: [-Infinity,-0.1066]

    Test Decision: Reject null in favor of alternative at 5% significance level

    > out = {{alias}}( x, y, { 'alternative': 'greater' });
    > table = out.print()
    Welch two-sample t-test

    Alternative hypothesis: True difference in means is greater than 0

        pValue: 0.9603
        statistic: -1.8608
        df: 17.7765
        95% confidence interval: [-3.0534,Infinity]

    Test Decision: Fail to reject null in favor of alternative at 5%
    significance level

    // Run tests with equal variances assumption:
    > x = [ 2, 3, 1, 4 ];
    > y = [ 1, 2, 3, 1, 2, 5, 3, 4 ];
    > out = {{alias}}( x, y, { 'variance': 'equal' });
    > table = out.print()
    Two-sample t-test

    Alternative hypothesis: True difference in means is not equal to 0

        pValue: 0.8848
        statistic: -0.1486
        df: 10
        95% confidence interval: [-1.9996,1.7496]

    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, 3.0 );
    ... }
    > y = new Array( 100 );
    > for ( i = 0; i < x.length; i++ ) {
    ...     y[ i ] = rnorm( 1.0, 3.0 );
    ... }
    > out = {{alias}}( x, y, { 'difference': 1.0, 'variance': 'equal' })
    {
        rejected: false,
        pValue: ~0.642,
        statistic: ~-0.466,
        ci: [ ~-0.0455, ~1.646 ],
        // ...
    }

    See Also
    --------