time-to-botec

README.md (5875B)

---

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 # Binomial Test
 
 > Exact test for the success probability in a Bernoulli experiment.
 
 <section class="usage">
 
 ## Usage
 
 ```javascript
 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.
 
 ```javascript
 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.
 
 <!-- run-disable -->
 
 ```javascript
 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.
 
 ```javascript
 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`.
 
 ```javascript
 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.
 
 ```javascript
 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
 */
 ```
 
 </section>
 
 <!-- /.usage -->
 
 <section class="examples">
 
 ## Examples
 
 <!-- eslint no-undef: "error" -->
 
 ```javascript
 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 ],
         // ...
     }
 */
 ```
 
 </section>
 
 <!-- /.examples -->
 
 <section class="links">
 
 </section>
 
 <!-- /.links -->