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dsempn
Calculate the standard error of the mean of a doubleprecision floatingpoint strided array using a twopass algorithm.
The standard error of the mean of a finite size sample of size n
is given by
where σ
is the population standard deviation.
Often in the analysis of data, the true population standard deviation is not known a priori and must be estimated from a sample drawn from the population distribution. In this scenario, one must use a sample standard deviation to compute an estimate for the standard error of the mean
where s
is the sample standard deviation.
Installation
npm install @stdlib/statsbasedsempn
Usage
var dsempn = require( '@stdlib/statsbasedsempn' );
dsempn( N, correction, x, stride )
Computes the standard error of the mean of a doubleprecision floatingpoint strided array x
using a twopass algorithm.
var Float64Array = require( '@stdlib/arrayfloat64' );
var x = new Float64Array( [ 1.0, 2.0, 2.0 ] );
var N = x.length;
var v = dsempn( N, 1, x, 1 );
// returns ~1.20185
The function has the following parameters:
 N: number of indexed elements.

correction: degrees of freedom adjustment. Setting this parameter to a value other than
0
has the effect of adjusting the divisor during the calculation of the standard deviation according toNc
wherec
corresponds to the provided degrees of freedom adjustment. When computing the standard deviation of a population, setting this parameter to0
is the standard choice (i.e., the provided array contains data constituting an entire population). When computing the corrected sample standard deviation, setting this parameter to1
is the standard choice (i.e., the provided array contains data sampled from a larger population; this is commonly referred to as Bessel's correction). 
x: input
Float64Array
. 
stride: index increment for
x
.
The N
and stride
parameters determine which elements in x
are accessed at runtime. For example, to compute the standard error of the mean of every other element in x
,
var Float64Array = require( '@stdlib/arrayfloat64' );
var floor = require( '@stdlib/mathbasespecialfloor' );
var x = new Float64Array( [ 1.0, 2.0, 2.0, 7.0, 2.0, 3.0, 4.0, 2.0 ] );
var N = floor( x.length / 2 );
var v = dsempn( N, 1, x, 2 );
// returns 1.25
Note that indexing is relative to the first index. To introduce an offset, use typed array
views.
var Float64Array = require( '@stdlib/arrayfloat64' );
var floor = require( '@stdlib/mathbasespecialfloor' );
var x0 = new Float64Array( [ 2.0, 1.0, 2.0, 2.0, 2.0, 2.0, 3.0, 4.0 ] );
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var N = floor( x0.length / 2 );
var v = dsempn( N, 1, x1, 2 );
// returns 1.25
dsempn.ndarray( N, correction, x, stride, offset )
Computes the standard error of the mean of a doubleprecision floatingpoint strided array using a twopass algorithm and alternative indexing semantics.
var Float64Array = require( '@stdlib/arrayfloat64' );
var x = new Float64Array( [ 1.0, 2.0, 2.0 ] );
var N = x.length;
var v = dsempn.ndarray( N, 1, x, 1, 0 );
// returns ~1.20185
The function has the following additional parameters:

offset: starting index for
x
.
While typed array
views mandate a view offset based on the underlying buffer
, the offset
parameter supports indexing semantics based on a starting index. For example, to calculate the standard error of the mean for every other value in x
starting from the second value
var Float64Array = require( '@stdlib/arrayfloat64' );
var floor = require( '@stdlib/mathbasespecialfloor' );
var x = new Float64Array( [ 2.0, 1.0, 2.0, 2.0, 2.0, 2.0, 3.0, 4.0 ] );
var N = floor( x.length / 2 );
var v = dsempn.ndarray( N, 1, x, 2, 1 );
// returns 1.25
Notes
 If
N <= 0
, both functions returnNaN
.  If
N  c
is less than or equal to0
(wherec
corresponds to the provided degrees of freedom adjustment), both functions returnNaN
.
Examples
var randu = require( '@stdlib/randombaserandu' );
var round = require( '@stdlib/mathbasespecialround' );
var Float64Array = require( '@stdlib/arrayfloat64' );
var dsempn = require( '@stdlib/statsbasedsempn' );
var x;
var i;
x = new Float64Array( 10 );
for ( i = 0; i < x.length; i++ ) {
x[ i ] = round( (randu()*100.0)  50.0 );
}
console.log( x );
var v = dsempn( x.length, 1, x, 1 );
console.log( v );
References
 Neely, Peter M. 1966. "Comparison of Several Algorithms for Computation of Means, Standard Deviations and Correlation Coefficients." Communications of the ACM 9 (7). Association for Computing Machinery: 496–99. doi:10.1145/365719.365958.
 Schubert, Erich, and Michael Gertz. 2018. "Numerically Stable Parallel Computation of (Co)Variance." In Proceedings of the 30th International Conference on Scientific and Statistical Database Management. New York, NY, USA: Association for Computing Machinery. doi:10.1145/3221269.3223036.
See Also

@stdlib/statsbase/dsem
: calculate the standard error of the mean for a doubleprecision floatingpoint strided array. 
@stdlib/statsbase/dstdevpn
: calculate the standard deviation of a doubleprecision floatingpoint strided array using a twopass algorithm.
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 © 20162024. The Stdlib Authors.