Description Usage Arguments Details Value Author(s) References See Also Examples

Provides the Welch-Satterthwaite effective degrees of freedom given standard uncertainties and associated degrees of freedom.

w.s is an alias for welch.satterthwaite.

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`ui` |
Standard uncertainties |

`df` |
Degrees of freedom |

`ci` |
Sensitivity coefficients |

`uc` |
Combined standard uncertainty |

Implements the Welch-Satterthwaite equation as provided in the ISO Guide to the expression of
uncertainty in measurement (1995) (See JCGM 100:2008). This assumes that `uc`

is the
uncertainty in a measurement result *y*, where *y=f(x_1, x_2, …)*, `ci`

are
the partial derivatives *dy/dx[i]* and `ui`

is the standard uncertainty associated with `xi`

.

The implementation assumes that the combined uncertainty `uc`

is equal to
`sqrt(sum((ci*ui)^2)`

. An independent estimate of `uc`

can be provided.

The `ci`

are 'sensitivity coefficients'; the default is 1, so that the `ui`

can be given either as standard uncertainties in the values of influence quantities *x_i*,
together with the associated `ci`

, or as contributions `ci*ui`

to the uncertainty in *y*.

Correlation is not supported, because the Welch-Satterthwaite equation is only valid for independent variances.

The calculated effective degrees of freedom associated with `uc`

.

S. L. R. Ellison s.ellison@lgc.co.uk

JCGM 100 (2008) *Evaluation of measurement data - Guide to the expression
of uncertainty in measurement*. http://www.bipm.org/utils/common/documents/jcgm/JCGM_100_2008_E.pdf.
(JCGM 100:2008 is a public domain copy of ISO/IEC *Guide to the expression
of uncertainty in measurement* (1995) ).

Satterthwaite, F. E. (1946), An Approximate Distribution of Estimates of Variance Components.,
Biometrics Bulletin **2**, 110-114, doi:10.2307/3002019

Welch, B. L. (1947), The generalization of "Student's" problem when several different
population variances are involved., Biometrika **34** 28-35

None, yet.

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