197 lines
6.0 KiB
Markdown
197 lines
6.0 KiB
Markdown
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@license Apache-2.0
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Copyright (c) 2018 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# One Way ANOVA
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> Perform a one-way analysis of variance.
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<section class="usage">
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## Usage
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```javascript
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var anova1 = require( '@stdlib/stats/anova1' );
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```
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#### anova1( x, factor\[, opts] )
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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:
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<!-- <equation class="equation" label="eq:hypotheses" align="center" raw="\begin{align*} H_{0}:& \; \mu_{1} = \mu_{2} = \dots = \mu_{k} \\ H_{a}:& \; \text{at least one} \; \mu_{i} \; \text{not equal to the others} \end{align*}" alt="Hypotheses of ANOVA"> -->
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<div class="equation" align="center" data-raw-text="\begin{align*} H_{0}:& \; \mu_{1} = \mu_{2} = \dots = \mu_{k} \\ H_{a}:& \; \text{at least one} \; \mu_{i} \; \text{not equal to the others} \end{align*}" data-equation="eq:hypotheses">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@7e0a95722efd9c771b129597380c63dc6715508b/lib/node_modules/@stdlib/stats/anova1/docs/img/equation_hypotheses.svg" alt="Hypotheses of ANOVA">
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<br>
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</div>
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<!-- </equation> -->
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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.
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```javascript
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var out;
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var x;
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var y;
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x = [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 ];
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y = [ 'Treatment A', 'Treatment B', 'Treatment C', 'Control', 'Treatment A', 'Treatment B', 'Treatment C', 'Control', 'Treatment A', 'Treatment B', 'Treatment C', 'Control' ];
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out = anova1( x, y );
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/* returns
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{
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'treatment': { 'df': 11, 'ss': 15, 'ms': 5 },
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'error': { 'df': 8, 'ss': 128, 'ms': 16 },
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'statistic': 0.3125,
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'pValue': 0.81607947904798,
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'means':
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{ 'Treatment A': { 'mean': 5, 'sampleSize': 3, 'SD': 4 },
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'Treatment B': { 'mean': 6, 'sampleSize': 3, 'SD': 4 },
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'Treatment C': { 'mean': 7, 'sampleSize': 3, 'SD': 4 },
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'Control': { 'mean': 8, 'sampleSize': 3, 'SD': 4 } },
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'method': 'One-Way ANOVA'
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}
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*/
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```
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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.
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```javascript
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var out;
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var x;
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var y;
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x = [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 ];
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y = [ 'Treatment A', 'Treatment B', 'Treatment C', 'Control', 'Treatment A', 'Treatment B', 'Treatment C', 'Control', 'Treatment A', 'Treatment B', 'Treatment C', 'Control' ];
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out = anova1( x, y );
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console.log( out.print() );
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/* =>
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One-Way ANOVA
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Null Hypothesis: All Means Equal
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Alternate Hypothesis: At Least one Mean not Equal
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df SS MS F Score P Value
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Treatment 3 15 5 0.3125 0.8161
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Errors 8 128 16
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Fail to Reject Null: 0.8161 >= 0.05
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*/
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```
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The function accepts the following `options`:
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- **alpha**: `number` in the interval `[0,1]` giving the significance level of the hypothesis test. Default: `0.05`.
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- **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`
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By default, the test is carried out at a significance level of `0.05`. To choose a custom significance level, set the `alpha` option.
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```javascript
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var x = [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 ];
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var y = [ 'Treatment A', 'Treatment B', 'Treatment C', 'Control', 'Treatment A', 'Treatment B', 'Treatment C', 'Control', 'Treatment A', 'Treatment B', 'Treatment C', 'Control' ];
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var out = anova1( x, y );
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var table = out.print();
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/* e.g., returns
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One-Way ANOVA
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Null Hypothesis: All Means Equal
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Alternate Hypothesis: At Least one Mean not Equal
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df SS MS F Score P Value
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Treatment 3 15 5 0.3125 0.8161
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Errors 8 128 16
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Fail to Reject Null: 0.8161 >= 0.05
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*/
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out = anova1( x, y, {
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'alpha': 0.9
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});
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table = out.print();
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/* e.g., returns
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One-Way ANOVA
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Null Hypothesis: All Means Equal
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Alternate Hypothesis: At Least one Mean not Equal
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df SS MS F Score P Value
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Treatment 3 15 5 0.3125 0.8161
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Errors 8 128 16
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Reject Null: 0.8161 <= 0.9
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*/
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```
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</section>
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<!-- /.usage -->
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<section class="notes">
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## Notes
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- The calculation for the p value is based on [an F distribution][anova-nist].
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</section>
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<!-- /.notes -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var anova1 = require( '@stdlib/stats/anova1' );
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var x = [ 3, 4, 5, 6, 2, 5, 10, 12, 8, 10 ];
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var f = [ 'control', 'treatA', 'treatB', 'control', 'treatA', 'treatB', 'control', 'treatA', 'treatB', 'control' ];
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var out = anova1( x, f, {
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'decision': true
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});
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console.log( out.print() );
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out = anova1( x, f, {
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'alpha': 0.9
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});
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console.log( out.print() );
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```
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</section>
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<!-- /.examples -->
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<section class="links">
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[mdn-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array
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[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Typed_arrays
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[anova-nist]: https://www.itl.nist.gov/div898/handbook/ppc/section2/ppc231.htm
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</section>
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<!-- /.links -->
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