algS: 'Algorithm S' - robust estimate of pooled standard deviation
In metRology: Support for Metrological Applications

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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	algS(s, degfree, na.rm = FALSE, prob.eta = 0.9, 
		is.range = FALSE, tol = .Machine$double.eps^0.25, 
		maxiter = 25, verbose = FALSE)

`s`	A vector of standard deviations or, if `is.range` is `TRUE`, ranges.
`degfree`	Scalar number of degrees of freedom associated with all values in `s`. If a vector is supplied, `median(degfree)` will be used.
`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 `tol`.
`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

algA

#example from ISO 5725-5:1998 (cell ranges for percent creosote)

cdiff <- c(0.28, 0.49, 0.40, 0.00, 0.35, 1.98, 0.80, 0.32, 0.95)

algS(cdiff, is.range=TRUE)
	

#Compare with the sd of the two values (based on the range)
c.sd <- cdiff/sqrt(2)
algS(c.sd, degfree=1, verbose=TRUE)