Description Usage Arguments Details Value Author(s) References Examples

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.

1 |

`ui` |
the uncertainties |

`ci` |
the sensitivity coefficients |

`df` |
the degrees of freedom for the samples, |

`dftot` |
an optional known total degrees of freedom for the system, |

`uc` |
the combined uncertainty, u(y). |

`alpha` |
the significance level for the t-statistic. See 'Details'. |

*ν_{\rm{eff}} \approx \frac{u(y)^4}{∑_{i = 1}^n \frac{(c_iu_i)^4}{ν_i}}, \quad k = t(1 - (α/2), ν_{\rm{eff}}), \quad u_{\rm{exp}} = ku(y)*

A list with the following items:

`ws.df` |
the 'effective degrees of freedom'. |

`k` |
the coverage factor for calculating the expanded uncertainty. |

`u.exp` |
the expanded uncertainty |

Andrej-Nikolai Spiess

An Approximate Distribution of Estimates of Variance Components.

Satterthwaite FE.

*Biometrics Bulletin* (1946), **2**: 110-114.

The generalization of "Student's" problem when several different population variances are involved.

Welch BL.

*Biometrika* (1947), **34**: 28-35.

1 2 | ```
## Taken from GUM H.1.6, 4).
WelchSatter(ui = c(25, 9.7, 2.9, 16.6), df = c(18, 25.6, 50, 2), uc = 32, alpha = 0.01)
``` |

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.