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metRology (version 0.9-29-2)

welch.satterthwaite: Welch-Satterthwaite effective degrees of freedom

Description

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

w.s is an alias for welch.satterthwaite.

Usage

w.s(ui, df, ci = rep(1, length(ui)), uc=sqrt(sum((ci*ui)^2)))

welch.satterthwaite(ui, df, ci = rep(1, length(ui)), uc=sqrt(sum((ci*ui)^2)))

Value

The calculated effective degrees of freedom associated with uc.

Arguments

ui

Standard uncertainties

df

Degrees of freedom

ci

Sensitivity coefficients dy/dxi

uc

Combined standard uncertainty

Author

S. L. R. Ellison s.ellison@lgcgroup.com

Details

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(x1,x2,), ci are the partial derivatives y/xi 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 xi, 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.

References

JCGM 100 (2008) Evaluation of measurement data - Guide to the expression of uncertainty in measurement. tools:::Rd_expr_doi("10.59161/JCGM100-2008E"). (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

See Also

None, yet.

Examples

Run this code

u <- c(0.1, 0.3, 0.2, 1.1)
ci <- c(1.0, 2.0, 3.0, 0.5)
degfree <- c(Inf,6,8,3)

w.s(ui=u,df=degfree, ci=ci)

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