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# Chi-square independence test

> Perform a chi-square independence test.

<section class="usage">

## Usage

```javascript
var chi2test = require( '@stdlib/stats/chi2test' );
```

#### chi2test( x\[, opts] )

Computes a chi-square independence test for the **null hypothesis** that the joint distribution of the cell counts in two-dimensional `ndarray` or `array` of `arrays` `x` is the product of the row and column marginals, i.e. that the row and column variables are independent.

```javascript
// 2x2 table
var x = [
    [ 20, 30 ],
    [ 30, 20 ]
];

var out = chi2test( x );
/* returns
    {
        'rejected': false,
        'alpha': 0.05,
        'pValue': ~0.072,
        'df': 1,
        'statistic': 3.24,
        ...
    }
*/
```

The function accepts the following `options`:

-   **alpha**: significance level of the hypothesis test. Must be on the interval `[0,1]`. Default: `0.05`.
-   **correct**: `boolean` indicating whether to use Yates' continuity correction when provided a 2x2 contingency table. Default: `true`.

By default, the test is performed at a significance level of `0.05`. To adjust the significance level, set the `alpha` option.

```javascript 
var x = [
    [ 20, 30 ],
    [ 30, 20 ]
];
var opts = {
    'alpha': 0.1
};
var out = chi2test( x, opts );
/* returns
    {
        'rejected': true,
        'alpha': 0.1,
        'pValue': ~0.072,
        'df': 1,
        'statistic': 3.24,
        ...
    }
*/
```

For 2x2 contingency tables, the function by default applies Yates' continuity correction. To disable the continuity correction, set `correct` to `false`.

```javascript 
var x = [
    [ 20, 30 ],
    [ 30, 20 ]
];
var opts = {
    'correct': false
};
var out = chi2test( x, opts );
/* returns
    {
        'rejected': true,
        'alpha': 0.05,
        'pValue': ~0.046,
        'df': 1,
        'statistic': 4,
        ...
    }
*/
```

The function returns an `object` having the following properties:

-   **alpha**: significance level.
-   **rejected**: `boolean` indicating the test decision.
-   **pValue**: test p-value.
-   **statistic**: test statistic.
-   **df**: degrees of freedom.
-   **expected**: expected cell counts.
-   **method**: test name.
-   **print**: method for printing formatted test output.

To print formatted test output, invoke the `print` method. `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
var x = [
    [ 20, 30 ],
    [ 30, 20 ]
];
var out = chi2test( x );
console.log( out.print() );
/* =>
*    Chi-square independence test
*
*    Null hypothesis: the two variables are independent
*
*        pValue: 0.0719
*        statistic: 3.24
*        degrees of freedom: 1
*
*    Test Decision: Fail to reject null in favor of alternative at 5% significance level
*/

console.log( out.print({
    'digits': 6
}) );
/* =>
* Chi-square independence test
*
* Null hypothesis: the two variables are independent
*
*     pValue: 0.071861
*     statistic: 3.24
*     degrees of freedom: 1
*
* Test Decision: Fail to reject null in favor of alternative at 5% significance level
*/
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   The chi-square approximation may be incorrect if the observed or expected frequencies in each category are too small. Common practice is to require frequencies greater than five. The Yates' continuity correction is enabled by default for 2x2 tables to account for this, although it tends to over-correct.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var array = require( '@stdlib/ndarray/array' );
var chi2test = require( '@stdlib/stats/chi2test' );

var table;
var out;

/*
* Data from students in grades 4-6 on whether good grades, athletic ability, or popularity are most important to them:
*
* Source: Chase, M.A and Dummer, G.M. (1992), "The Role of Sports as a Social Determinant for Children"
*/
table = array([
    /* Grades Popular Sports */
    [ 63, 31, 25 ], // 4th
    [ 88, 55, 33 ], // 5th
    [ 96, 55, 32 ] // 6th
]);

// Assess whether the grade level and the students' goals are independent of each other:
out = chi2test( table );
// returns {...}

console.log( out.print() );
```

</section>

<!-- /.examples -->

<section class="links">

</section>

<!-- /.links -->
