# One Way ANOVA
> Perform a one-way analysis of variance.
## Usage
```javascript
var anova1 = require( '@stdlib/stats/anova1' );
```
#### anova1( x, factor\[, opts] )
For an [array][mdn-array] or [typed array][mdn-typed-array] of numeric values `x` and an [array][mdn-array] of classifications `factor`, a one-way analysis of variance is performed. The hypotheses are given as follows:
The function returns an object containing the treatment and error squared errors, degrees of freedom, mean squared errors, and both the p-value and F score.
```javascript
var out;
var x;
var y;
x = [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 ];
y = [ 'Treatment A', 'Treatment B', 'Treatment C', 'Control', 'Treatment A', 'Treatment B', 'Treatment C', 'Control', 'Treatment A', 'Treatment B', 'Treatment C', 'Control' ];
out = anova1( x, y );
/* returns
{
'treatment': { 'df': 11, 'ss': 15, 'ms': 5 },
'error': { 'df': 8, 'ss': 128, 'ms': 16 },
'statistic': 0.3125,
'pValue': 0.81607947904798,
'means':
{ 'Treatment A': { 'mean': 5, 'sampleSize': 3, 'SD': 4 },
'Treatment B': { 'mean': 6, 'sampleSize': 3, 'SD': 4 },
'Treatment C': { 'mean': 7, 'sampleSize': 3, 'SD': 4 },
'Control': { 'mean': 8, 'sampleSize': 3, 'SD': 4 } },
'method': 'One-Way ANOVA'
}
*/
```
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.
```javascript
var out;
var x;
var y;
x = [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 ];
y = [ 'Treatment A', 'Treatment B', 'Treatment C', 'Control', 'Treatment A', 'Treatment B', 'Treatment C', 'Control', 'Treatment A', 'Treatment B', 'Treatment C', 'Control' ];
out = anova1( x, y );
console.log( out.print() );
/* =>
One-Way ANOVA
Null Hypothesis: All Means Equal
Alternate Hypothesis: At Least one Mean not Equal
df SS MS F Score P Value
Treatment 3 15 5 0.3125 0.8161
Errors 8 128 16
Fail to Reject Null: 0.8161 >= 0.05
*/
```
The function accepts the following `options`:
- **alpha**: `number` in the interval `[0,1]` giving the significance level of the hypothesis test. Default: `0.05`.
- **decision**: a `boolean` value indicating if function is to return a decision of either _rejection of the null hypothesis_ or _failure to reject the null hypothesis_. Default: `false`
By default, the test is carried out at a significance level of `0.05`. To choose a custom significance level, set the `alpha` option.
```javascript
var x = [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 ];
var y = [ 'Treatment A', 'Treatment B', 'Treatment C', 'Control', 'Treatment A', 'Treatment B', 'Treatment C', 'Control', 'Treatment A', 'Treatment B', 'Treatment C', 'Control' ];
var out = anova1( x, y );
var table = out.print();
/* e.g., returns
One-Way ANOVA
Null Hypothesis: All Means Equal
Alternate Hypothesis: At Least one Mean not Equal
df SS MS F Score P Value
Treatment 3 15 5 0.3125 0.8161
Errors 8 128 16
Fail to Reject Null: 0.8161 >= 0.05
*/
out = anova1( x, y, {
'alpha': 0.9
});
table = out.print();
/* e.g., returns
One-Way ANOVA
Null Hypothesis: All Means Equal
Alternate Hypothesis: At Least one Mean not Equal
df SS MS F Score P Value
Treatment 3 15 5 0.3125 0.8161
Errors 8 128 16
Reject Null: 0.8161 <= 0.9
*/
```
## Notes
- The calculation for the p value is based on [an F distribution][anova-nist].
## Examples
```javascript
var anova1 = require( '@stdlib/stats/anova1' );
var x = [ 3, 4, 5, 6, 2, 5, 10, 12, 8, 10 ];
var f = [ 'control', 'treatA', 'treatB', 'control', 'treatA', 'treatB', 'control', 'treatA', 'treatB', 'control' ];
var out = anova1( x, f, {
'decision': true
});
console.log( out.print() );
out = anova1( x, f, {
'alpha': 0.9
});
console.log( out.print() );
```
[mdn-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array
[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Typed_arrays
[anova-nist]: https://www.itl.nist.gov/div898/handbook/ppc/section2/ppc231.htm
