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incrmgrubbs
Moving Grubbs' test for outliers.
Grubbs' test (also known as the maximum normalized residual test or extreme studentized deviate test) is a statistical test used to detect outliers in a univariate dataset assumed to come from a normally distributed population. Grubbs' test is defined for the hypothesis:
 H_0: the dataset does not contain outliers.
 H_1: the dataset contains exactly one outlier.
For a window of size W
, the Grubbs' test statistic for a twosided alternative hypothesis is defined as
where s
is the sample standard deviation. The Grubbs test statistic is thus the largest absolute deviation from the sample mean in units of the sample standard deviation.
The Grubbs' test statistic for the alternative hypothesis that the minimum value is an outlier is defined as
The Grubbs' test statistic for the alternative hypothesis that the maximum value is an outlier is defined as
For a twosided test, the hypothesis that a dataset does not contain an outlier is rejected at significance level α if
where t
denotes the upper critical value of the tdistribution with W2
degrees of freedom and a significance level of α/(2W)
.
For a onesided test, the hypothesis that a dataset does not contain an outlier is rejected at significance level α if
where t
denotes the upper critical value of the tdistribution with W2
degrees of freedom and a significance level of α/W
.
Installation
npm install @stdlib/statsincrmgrubbs
Usage
var incrmgrubbs = require( '@stdlib/statsincrmgrubbs' );
incrmgrubbs( window[, options] )
Returns an accumulator function
which incrementally performs Grubbs' test for outliers. The window
parameter defines the number of values over which to perform Grubbs' test.
var accumulator = incrmgrubbs( 20 );
The function accepts the following options
:

alpha: significance level. Default:
0.05
. 
alternative: alternative hypothesis. The option may be one of the following values:

'twosided'
: test whether the minimum or maximum value is an outlier. 
'min'
: test whether the minimum value is an outlier. 
'max'
: test whether the maximum value is an outlier.
Default:
'twosided'
. 
accumulator( [x] )
If provided an input value x
, the accumulator function returns updated test results. If not provided an input value x
, the accumulator function returns the current test results.
var rnorm = require( '@stdlib/randombasenormal' );
var accumulator = incrmgrubbs( 3 );
var results = accumulator( rnorm( 10.0, 5.0 ) );
// returns null
results = accumulator( rnorm( 10.0, 5.0 ) );
// returns null
results = accumulator( rnorm( 10.0, 5.0 ) );
// returns <Object>
results = accumulator();
// returns <Object>
The accumulator function returns an object
having the following fields:
 rejected: boolean indicating whether the null hypothesis should be rejected.
 alpha: significance level.
 criticalValue: critical value.
 statistic: test statistic.
 df: degrees of freedom.
 mean: sample mean.
 sd: corrected sample standard deviation.
 min: minimum value.
 max: maximum value.
 alt: alternative hypothesis.
 method: method name.
 print: method for prettyprinting test output.
The print
method accepts the following options:

digits: number of digits after the decimal point. Default:
4
. 
decision:
boolean
indicating whether to print the test decision. Default:true
.
Notes
 Grubbs' test assumes that data is normally distributed. Accordingly, one should first verify that the data can be reasonably approximated by a normal distribution before applying the Grubbs' test.
 The minimum
window
size is3
. In general, the larger thewindow
, the more robust outlier detection will be. However, larger windows entail increased memory consumption.  Until
window
values have been provided, the accumulator returnsnull
.  Input values are not type checked. If provided
NaN
or a value which, when used in computations, results inNaN
, the accumulated test statistic isNaN
for at leastW1
future invocations. If nonnumeric inputs are possible, you are advised to type check and handle accordingly before passing the value to the accumulator function.
Examples
var sensorData = require( '@stdlib/datasetssuthaharansinglehopsensornetwork' );
var incrmgrubbs = require( '@stdlib/statsincrmgrubbs' );
var data;
var opts;
var acc;
var N;
var r;
var i;
// Get a test dataset:
data = sensorData();
N = 0;
for ( i = 0; i < data.length; i++ ) {
if ( data[ i ].mote_id === 1 ) {
N += 1;
data[ i ] = data[ i ].temperature;
}
}
data.length = N;
// Create a new accumulator which analyzes the last 5 minutes of data:
opts = {
'alternative': 'twosided'
};
acc = incrmgrubbs( 60, opts );
// Update the accumulator:
for ( i = 0; i < data.length; i++ ) {
r = acc( data[ i ] );
if ( r && r.rejected ) {
console.log( 'Index: %d', i );
console.log( '' );
console.log( r.print() );
}
}
References
 Grubbs, Frank E. 1950. "Sample Criteria for Testing Outlying Observations." The Annals of Mathematical Statistics 21 (1). The Institute of Mathematical Statistics: 27–58. doi:10.1214/aoms/1177729885.
 Grubbs, Frank E. 1969. "Procedures for Detecting Outlying Observations in Samples." Technometrics 11 (1). Taylor & Francis: 1–21. doi:10.1080/00401706.1969.10490657.
See Also

@stdlib/statsincr/grubbs
: grubbs' test for outliers.
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.
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License
See LICENSE.
Copyright
Copyright © 20162024. The Stdlib Authors.