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Perform a one-way analysis of variance.
npm install @stdlib/stats-anova1Alternatively,
- To load the package in a website via a
scripttag without installation and bundlers, use the ES Module available on theesmbranch (see README). - If you are using Deno, visit the
denobranch (see README for usage intructions). - For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the
umdbranch (see README).
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To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.
var anova1 = require( '@stdlib/stats-anova1' );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:
numberin the interval[0,1]giving the significance level of the hypothesis test. Default:0.05. - decision: a
booleanvalue 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
*/- The calculation for the p value is based on an F distribution.
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() );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.
See LICENSE.
Copyright © 2016-2024. The Stdlib Authors.
