One Way ANOVA

Perform a one-way analysis of variance.

Installation

npm install @stdlib/stats-anova1

Usage

var anova1 = require( '@stdlib/stats-anova1' );

anova1( x, factor[, opts] )

For an array or typed array of numeric values x and an 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.

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.

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.

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.

Examples

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() );

Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

Community

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.