Calculates the Welch-Satterthwaite approximation to the 'effective degrees of freedom' by using the samples' uncertainties and degrees of freedoms, as described in Welch (1947) and Satterthwaite (1946). External sensitivity coefficients can be supplied optionally.

WelchSatter

Propagation of uncertainty using higher-order Taylor expansion and Monte Carlo simulation. Calculations of propagated uncertainties are based on matrix calculus including covariance structure according to Arras 1998 <doi:10.3929/ethz-a-010113668> (first order), Wang & Iyer 2005 <doi:10.1088/0026-1394/42/5/011> (second order) and BIPM Supplement 1 (Monte Carlo) <doi:10.59161/JCGM101-2008>.

Andrej-Nikolai Spiess

propagate

Propagation of Uncertainty

WelchSatter function

Welch-Satterthwaite approximation to the 'effective degrees of freedom' — WelchSatter

<dl>

 <dt>ui</dt>
<dd>the uncertainties \(u_i\) for each variable \(x_i\).</dd>

 <dt>ci</dt>
<dd>the sensitivity coefficients \(c_i = \partial y/\partial x_i\).</dd>
 
 <dt>df</dt>
<dd>the degrees of freedom for the samples, \(\nu_i\).</dd>

 <dt>df.tot</dt>
<dd>an optional known total degrees of freedom for the system, \(\nu_{\mathrm{tot}}\). Overrides the internal calculation of \(\nu_{\mathrm{ws}}\).</dd>
 
 <dt>uc</dt>
<dd>the combined uncertainty, u(y).</dd>

 <dt>alpha</dt>
<dd>the significance level for the t-statistic. See 'Details'.</dd>

 <dt>k</dt>
<dd>an external coverage factor, say 2, that overrides the one obtained from defining <code>alpha</code>.</dd>

</dl>

WelchSatter: Welch-Satterthwaite approximation to the 'effective degrees of freedom'

Description

Usage

Arguments

Value

Details

References

Examples