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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Degrees of freedom
Sensitivity coefficients dy/dx_i
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, …),
the partial derivatives dy/dx[i] and
ui is the standard uncertainty associated with
The implementation assumes that the combined uncertainty
uc is equal to
sqrt(sum((ci*ui)^2). An independent estimate of
uc can be provided.
ci are 'sensitivity coefficients'; the default is 1, so that the
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
S. L. R. Ellison firstname.lastname@example.org
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
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