time-to-botec

README.md (4585B)

---

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 # Levene's Test
 
 > Compute Levene's test for equal variances.
 
 <section class="intro">
 
 Levene's test is used to test the null hypothesis that the variances of `k` groups are equal against the alternative that at least two of them are different.
 
 </section>
 
 <!-- /.intro -->
 
 <section class="usage">
 
 ## Usage
 
 ```javascript
 var leveneTest = require( '@stdlib/stats/levene-test' );
 ```
 
 #### leveneTest( x\[, y, ..., z]\[, opts] )
 
 Calculates Levene's test for input arrays `x`, `y`, ..., `z` holding numeric observations. 
 
 ```javascript
 // Data from Hollander & Wolfe (1973), p. 116:
 var x = [ 2.9, 3.0, 2.5, 2.6, 3.2 ];
 var y = [ 3.8, 2.7, 4.0, 2.4 ];
 var z = [ 2.8, 3.4, 3.7, 2.2, 2.0 ];
 
 var out = leveneTest( x, y, z );
 /* returns
     {
         'rejected': false,
         'alpha': 0.05,
         'df': [ 2, 11 ],
         'pValue': ~0.1733,
         'statistic': ~2.0638,
         ...
     }
 */
 ```
 
 The function accepts the following `options`:
 
 -   **alpha**: `number` on the interval `[0,1]` giving the significance level of the hypothesis test. Default: `0.05`.
 -   **groups**: an `array` of group indicators. Only applicable when providing a single numeric array holding all observations.
 
 By default, the test is carried out at a significance level of `0.05`. To test at a different significance level, set the `alpha` option.
 
 ```javascript
 var x = [ 2.9, 3.0, 2.5, 2.6, 3.2 ];
 var y = [ 3.8, 2.7, 4.0, 2.4 ];
 var z = [ 2.8, 3.4, 3.7, 2.2, 2.0 ];
 
 var out = leveneTest( x, y, z, {
     'alpha': 0.01
 });
 /* returns
     {
         'rejected': false,
         'alpha': 0.01,
         'df': [ 2, 11 ],
         'pValue': ~0.1733,
         'statistic': ~2.0638,
         ...
     }
 */
 ```
 
 In addition to providing multiple arrays, the function supports providing a single numeric array holding all observations along with an array of group indicators.
 
 <!-- eslint-disable array-element-newline -->
 
 ```javascript
 var arr = [
     2.9, 3.0, 2.5, 2.6, 3.2,
     3.8, 2.7, 4.0, 2.4,
     2.8, 3.4, 3.7, 2.2, 2.0
 ];
 var groups = [
     'a', 'a', 'a', 'a', 'a',
     'b', 'b', 'b', 'b',
     'c', 'c', 'c', 'c', 'c'
 ];
 var out = leveneTest( arr, {
     'groups': groups
 });
 ```
 
 The returned object comes with a `.print()` method which, when invoked, prints a formatted output of test results. The method accepts the following options:
 
 -   **digits**: number of decimal digits displayed for the outputs. Default: `4`.
 -   **decision**: `boolean` indicating whether to print the test decision. Default: `true`.
 
 ```javascript
 var x = [ 2.9, 3.0, 2.5, 2.6, 3.2 ];
 var y = [ 3.8, 2.7, 4.0, 2.4 ];
 var z = [ 2.8, 3.4, 3.7, 2.2, 2.0 ];
 
 var out = leveneTest( x, y, z );
 console.log( out.print() );
 /* =>
     Levene's test for Homogeneity of Variance
 
     Null hypothesis: The variances in all groups are the same.
 
         df 1: 2
         df 2: 11
         F score: 2.0638
         P Value: 0.1733
 
     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 leveneTest = require( '@stdlib/stats/levene-test' );
 
 // Data from Hollander & Wolfe (1973), p. 116:
 var x = [ 2.9, 3.0, 2.5, 2.6, 3.2 ];
 var y = [ 3.8, 2.7, 4.0, 2.4 ];
 var z = [ 2.8, 3.4, 3.7, 2.2, 2.0 ];
 
 var out = leveneTest( x, y, z );
 /* returns
     {
         'rejected': false,
         'alpha': 0.05,
         'df': [ 2, 11 ],
         'pValue': ~0.1733,
         'statistic': ~2.0638,
         ...
     }
 */
 
 var table = out.print();
 /* returns
     Levene's test for Homogeneity of Variance
 
     Null hypothesis: The variances in all groups are the same.
 
         df 1: 2
         df 2: 11
         F score: 2.0638
         P Value: 0.1733
 
     Test Decision: Fail to reject null in favor of alternative at 5% significance level
 */
 ```
 
 </section>
 
 <!-- /.examples -->
 
 <section class="references">
 
 </section>
 
 <!-- /.references -->
 
 <section class="links">
 
 </section>
 
 <!-- /.links -->