@stdlib/stats-binomial-test
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    0.0.7 • Public • Published

    Binomial Test

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    Exact test for the success probability in a Bernoulli experiment.

    Installation

    npm install @stdlib/stats-binomial-test

    Usage

    var binomialTest = require( '@stdlib/stats-binomial-test' );

    binomialTest( x[, n][, opts] )

    When supplied nonnegative integers x (number of successes in a Bernoulli experiment) and n (total number of trials), the function computes an exact test for the success probability in a Bernoulli experiment. Alternatively, x may be a two-element array containing the number of successes and failures, respectively.

    var out = binomialTest( 550, 1000 );
    /* returns
        {
            'rejected': true,
            'pValue': ~0.001,
            'statistic': 0.55,
            'ci': [ ~0.519, ~0.581 ],
            // ...
        }
    */
    
    out = binomialTest( [ 550, 450 ] );
    /* returns
        {
            'rejected': true,
            'pValue': ~0.001,
            'statistic': 0.55,
            'ci': [ ~0.519, ~0.581 ],
            // ...
        }
    */

    The returned object comes with a .print() method which when invoked will print a formatted output of the results of the hypothesis test. print accepts a digits option that controls the number of decimal digits displayed for the outputs and a decision option, which when set to false will hide the test decision.

    console.log( out.print() );
    /* e.g., =>
        Exact binomial test
    
        Alternative hypothesis: True correlation coefficient is not equal to 0.5
    
            pValue: 0.0017
            statistic: 0.55
            95% confidence interval: [0.5186,0.5811]
    
        Test Decision: Reject null in favor of alternative at 5% significance level
    */

    The function accepts the following options:

    • alpha: number in the interval [0,1] giving the significance level of the hypothesis test. Default: 0.05.
    • alternative: Either two-sided, less or greater. Indicates whether the alternative hypothesis is that the true ratio of variances is greater than one (greater), smaller than one (less), or that the variances are the same (two-sided). Default: two-sided.
    • p: success probability under the null hypothesis. Default: 0.5.

    By default, the hypothesis test is carried out at a significance level of 0.05. To choose a different significance level, set the alpha option.

    var out = binomialTest( 59, 100, {
        'alpha': 0.1
    });
    /* returns
        {
            'rejected': true,
            'pValue': ~0.089,
            'statistic': 0.59,
            'ci': [ ~0.487, ~0.687 ],
            // ...
        }
    */

    By default, a two-sided test is performed. To perform either of the one-sided tests, set the alternative option to less or greater.

    out = binomialTest( 550, 1000, {
        'alternative': 'greater'
    });
    table = out.print();
    /** e.g., returns
        Exact binomial test
    
        Alternative hypothesis: True correlation coefficient is greater than 0.5
    
            pValue: 0.0009
            statistic: 0.55
            95% confidence interval: [0.5235,1]
    
        Test Decision: Reject null in favor of alternative at 5% significance level
    */
    
    out = binomialTest( 550, 1000, {
        'alternative': 'less'
    });
    table = out.print();
    /* e.g., returns
        Exact binomial test
    
        Alternative hypothesis: True correlation coefficient is less than 0.5
    
            pValue: 0.9993
            statistic: 0.55
            95% confidence interval: [0,0.5762]
    
        Test Decision: Fail to reject null in favor of alternative at 5% significance level
    */

    To test whether the success probability in the population is equal to some other value than 0.5, set the p option.

    var out = binomialTest( 23, 100, {
        'p': 0.2
    });
    /* returns
        {
            'rejected': false,
            'pValue': ~0.453,
            'statistic': 0.23,
            'ci': [ ~0.152, ~0.325 ],
            // ...
        }
    */
    
    var table = out.print();
    /* e.g., returns
        Exact binomial test
    
        Alternative hypothesis: True correlation coefficient is not equal to 0.2
    
            pValue: 0.4534
            statistic: 0.23
            95% confidence interval: [0.1517,0.3249]
    
        Test Decision: Fail to reject null in favor of alternative at 5% significance level
    */

    Examples

    var binomialTest = require( '@stdlib/stats-binomial-test' );
    
    var out = binomialTest( 682, 925 );
    /* returns
        {
            'rejected': true,
            'pValue': ~3.544e-49,
            'statistic': 0.737,
            'ci': [ ~0.708, ~0.765 ],
            // ...
        }
    */
    
    out = binomialTest( [ 682, 925 - 682 ] );
    /* returns
        {
            'rejected': true,
            'pValue': ~3.544e-49,
            'statistic': 0.737,
            'ci': [ ~0.708, ~0.765 ],
            // ...
        }
    */
    
    out = binomialTest( 682, 925, {
        'p': 0.75,
        'alpha': 0.05
    });
    /* returns
        {
            'rejected': false,
            'pValue': ~0.382
            'statistic': 0.737,
            'ci': [ ~0.708, ~0.765 ],
            // ...
        }
    */
    
    out = binomialTest( 21, 40, {
        'p': 0.4,
        'alternative': 'greater'
    });
    /* returns
        {
            'rejected': false,
            'pValue': ~0.382,
            'statistic': 0.737,
            'ci': [ ~0.385, 1.0 ],
            // ...
        }
    */

    Notice

    This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

    For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

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    License

    See LICENSE.

    Copyright

    Copyright © 2016-2022. The Stdlib Authors.

    Install

    npm i @stdlib/stats-binomial-test

    Homepage

    stdlib.io

    DownloadsWeekly Downloads

    60

    Version

    0.0.7

    License

    Apache-2.0

    Unpacked Size

    59.4 kB

    Total Files

    11

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