Perform a chi-square goodness-of-fit test.
APACHE-2.0 License
Perform a chi-square goodness-of-fit test.
npm install @stdlib/stats-chi2gof
Alternatively,
script
tag without installation and bundlers, use the ES Module available on the esm
branch (see README).deno
branch (see README for usage intructions).umd
branch (see README).The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.
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 chi2gof = require( '@stdlib/stats-chi2gof' );
Computes a chi-square goodness-of-fit test for the null hypothesis that the values of x
come from the discrete probability distribution specified by y
.
// Observed counts:
var x = [ 30, 20, 23, 27 ];
// Expected counts:
var y = [ 25, 25, 25, 25 ];
var res = chi2gof( x, y );
var o = res.toJSON();
/* returns
{
'rejected': false,
'alpha': 0.05,
'pValue': ~0.5087,
'df': 3,
'statistic': ~2.32,
...
}
*/
The second argument can either be an array-like object (or 1-dimensional ndarray
) of expected frequencies, an array-like object (or 1-dimensional ndarray
) of population probabilities summing to one, or a discrete probability distribution name to test against.
// Observed counts:
var x = [ 89, 37, 30, 28, 2 ];
// Expected probabilities:
var y = [ 0.40, 0.20, 0.20, 0.15, 0.05 ];
var res = chi2gof( x, y );
var o = res.toJSON();
/* returns
{
'rejected': true,
'alpha': 0.05,
'pValue': ~0.0187,
'df': 3,
'statistic': ~9.9901,
...
}
*/
When specifying a discrete probability distribution name, distribution parameters must be provided as additional arguments.
var Int32Array = require( '@stdlib/array-int32' );
var discreteUniform = require( '@stdlib/random-base-discrete-uniform' );
var res;
var x;
var v;
var i;
// Simulate expected counts...
x = new Int32Array( 100 );
for ( i = 0; i < x.length; i++ ) {
v = discreteUniform( 0, 99 );
x[ v ] += 1;
}
res = chi2gof( x, 'discrete-uniform', 0, 99 );
// returns {...}
The function accepts the following options
:
[0,1]
. Default: 0.05
.0
.boolean
indicating whether to calculate p-values by Monte Carlo simulation. Default: false
.500
.By default, the test is performed at a significance level of 0.05
. To adjust the significance level, set the alpha
option.
var x = [ 89, 37, 30, 28, 2 ];
var p = [ 0.40, 0.20, 0.20, 0.15, 0.05 ];
var res = chi2gof( x, p );
var table = res.toString();
/* e.g., returns
Chi-square goodness-of-fit test
Null hypothesis: population probabilities are equal to those in p
pValue: 0.0186
statistic: 9.9901
degrees of freedom: 3
Test Decision: Reject null in favor of alternative at 5% significance level
*/
res = chi2gof( x, p, {
'alpha': 0.01
});
table = res.toString();
/* e.g., returns
Chi-square goodness-of-fit test
Null hypothesis: population probabilities are equal to those in p
pValue: 0.0186
statistic: 9.9901
degrees of freedom: 3
Test Decision: Fail to reject null in favor of alternative at 1% significance level
*/
By default, the p-value is computed using a chi-square distribution with k-1
degrees of freedom, where k
is the length of x
. If provided distribution arguments are estimated (e.g., via maximum likelihood estimation), the degrees of freedom should be corrected. Set the ddof
option to use k-1-n
degrees of freedom, where n
is the degrees of freedom adjustment.
var x = [ 89, 37, 30, 28, 2 ];
var p = [ 0.40, 0.20, 0.20, 0.15, 0.05 ];
var res = chi2gof( x, p, {
'ddof': 1
});
var o = res.toJSON();
// returns { 'pValue': ~0.0186, 'statistic': ~9.9901, 'df': 3, ... }
Instead of relying on chi-square approximation to calculate the p-value, one can use Monte Carlo simulation. When the simulate
option is true
, the simulation is performed by re-sampling from the discrete probability distribution specified by y
.
var x = [ 89, 37, 30, 28, 2 ];
var p = [ 0.40, 0.20, 0.20, 0.15, 0.05 ];
var res = chi2gof( x, p, {
'simulate': true,
'iterations': 1000 // explicitly set the number of Monte Carlo simulations
});
// returns {...}
The function returns a results object
having the following properties:
boolean
indicating the test decision.To print formatted test output, invoke the toString
method. The method accepts the following options:
4
.boolean
indicating whether to show the test decision. Default: true
.var x = [ 89, 37, 30, 28, 2 ];
var p = [ 0.40, 0.20, 0.20, 0.15, 0.05 ];
var res = chi2gof( x, p );
var table = res.toString({
'decision': false
});
/* e.g., returns
Chi-square goodness-of-fit test
Null hypothesis: population probabilities are equal to those in p
pValue: 0.0186
statistic: 9.9901
degrees of freedom: 3
*/
var poisson = require( '@stdlib/random-base-poisson' );
var Int32Array = require( '@stdlib/array-int32' );
var chi2gof = require( '@stdlib/stats-chi2gof' );
var N = 400;
var lambda = 3.0;
var rpois = poisson.factory( lambda );
// Draw samples from a Poisson distribution:
var x = [];
var i;
for ( i = 0; i < N; i++ ) {
x.push( rpois() );
}
// Generate a frequency table:
var freqs = new Int32Array( N );
for ( i = 0; i < N; i++ ) {
freqs[ x[ i ] ] += 1;
}
// Assess whether the simulated values come from a Poisson distribution:
var out = chi2gof( freqs, 'poisson', lambda );
// returns {...}
console.log( out.toString() );
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.
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See LICENSE.
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