# @stdlib/stats-base-dsemyc Release 0.0.7

Calculate the standard error of the mean for a double-precision floating-point strided array using a one-pass algorithm proposed by Youngs and Cramer.

Keywords
stdlib, stdmath, statistics, stats, mathematics, math, standard error of the mean, standard error, standard deviation, estimation, estimate, mean, stdev, std, strided, strided array, typed, array, float64, double, float64array, javascript, node, node-js, nodejs, standard-deviation, standard-error, standard-error-of-the-mean, strided-array
Apache-2.0
Install
``` npm install @stdlib/stats-base-dsemyc@0.0.7 ```

# dsemyc

Calculate the standard error of the mean of a double-precision floating-point strided array using a one-pass algorithm proposed by Youngs and Cramer.

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/stats-base-dsemyc`

## Usage

`var dsemyc = require( '@stdlib/stats-base-dsemyc' );`

#### dsemyc( N, correction, x, stride )

Computes the standard error of the mean of a double-precision floating-point strided array `x` using a one-pass algorithm proposed by Youngs and Cramer.

```var Float64Array = require( '@stdlib/array-float64' );

var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
var N = x.length;

var v = dsemyc( 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 to `N-c` where `c` corresponds to the provided degrees of freedom adjustment. When computing the standard deviation of a population, setting this parameter to `0` 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 to `1` 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/array-float64' );
var floor = require( '@stdlib/math-base-special-floor' );

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 = dsemyc( 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/array-float64' );
var floor = require( '@stdlib/math-base-special-floor' );

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 = dsemyc( N, 1, x1, 2 );
// returns 1.25```

#### dsemyc.ndarray( N, correction, x, stride, offset )

Computes the standard error of the mean of a double-precision floating-point strided array using a one-pass algorithm proposed by Youngs and Cramer and alternative indexing semantics.

```var Float64Array = require( '@stdlib/array-float64' );

var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
var N = x.length;

var v = dsemyc.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/array-float64' );
var floor = require( '@stdlib/math-base-special-floor' );

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 = dsemyc.ndarray( N, 1, x, 2, 1 );
// returns 1.25```

## Notes

• If `N <= 0`, both functions return `NaN`.
• If `N - c` is less than or equal to `0` (where `c` corresponds to the provided degrees of freedom adjustment), both functions return `NaN`.

## Examples

```var randu = require( '@stdlib/random-base-randu' );
var round = require( '@stdlib/math-base-special-round' );
var Float64Array = require( '@stdlib/array-float64' );
var dsemyc = require( '@stdlib/stats-base-dsemyc' );

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 = dsemyc( x.length, 1, x, 1 );
console.log( v );```

## References

• Youngs, Edward A., and Elliot M. Cramer. 1971. "Some Results Relevant to Choice of Sum and Sum-of-Product Algorithms." Technometrics 13 (3): 657–65. doi:10.1080/00401706.1971.10488826.

## 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 