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

‘Algorithm S’ calculates a robust estimate of pooled standard deviation from a set of standard deviations

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`s` |
A vector of standard deviations or, if |

`degfree` |
Scalar number of degrees of freedom associated with all
values in |

`na.rm` |
a logical value indicating whether 'NA' values should be stripped before the computation proceeds. |

`prob.eta` |
prob.eta is set to specify the lower tail area of the chi-squared distribution used as a cut-off. |

`is.range` |
if is.range is TRUE, s is interpreted as a vector of positive differences of duplcate observations and degfree is set to 1 |

`tol` |
Convergence tolerance Iteration continues until the relative
change in estimated pooled sd drops below |

`maxiter` |
Maximum number of iterations permitted. |

`verbose` |
Controls information displayed during iteration; see Details. |

Algorithm S is suggested by ISO 5725-5:1998 as a robust estimator of
pooled standard deviation *s.pool* from standard deviations of
groups of size *degfree*.

The algorithm calculates a ‘limit factor’, *eta*, set to
`qchisq(prob.eta, degfree)`

. Following an initial estimate of
*s.pool* as `median(s)`

, the standard deviations *s{i}*
are replaced with *w[i]=min(eta*s.pool, s[i])*
and an updated value for *s.pool* calculated as

*xi*sqrt(sum(w)^2)/p*

where *p* is the number of standard deviations and *ξ* is calculated as

*
xi = 1/sqrt(pchisq(degfree*eta^2, degfree + 2) + (1-prob.eta)*eta^2)*

If the *s[i]* are ranges of two values, ISO 5725 recommends
carrying out the above iteration on the ranges and then dividing by
*sqrt{degfree+1}*; in the implementation here, this
is done prior to returning the estimate.

If `verbose`

is non-zero, the current iteration number
and estimate are printed; if `verbose>1`

, the current set
of truncated values *w* is also printed.

A scalar estimate of poooled standard deviation.

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

ISO 5725-5:1998 Accuracy (trueness and precision) of measurement methods and results - Part 5: Alternative methods for the determination of the precision of a standard measurement method

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