Page:NIOSH Manual of Analytical Methods - Chapter P.pdf/17

 Thus, the coverage factor k is approximated as: ,

which is less than and close to 3.0, if the effective number of degrees of freedom and .

,

In summary, the bias uncertainty is pooled together with the uncertainty components in

.

It should be remembered, however, that only refers to quantities, which vary at each of the future measurements following the initial evaluation.

Note 3: For statisticians. Characterizing effects of uncorrected bias: If the systematic error (bias) is non-zero, confidence limits on the accuracy range A may be approximated as follows. The Smith-Satterthwaite approximation is generalized in approximating estimates in Eq 6 by:

in terms of a chi-square random variable

for the two cases

The effective number of degrees of freedom υ is determined by forcing the variance of

to reproduce the estimated variance of

or

in their

respective cases:

Calculation of or is generally straightforward and depends on specifics of the evaluation experiment and on significant influence parameters. The confidence limit A95% is then determined as in Eq 9:

This expression has been found [12] quite accurate, exhibiting negligible effects from the discontinuity: The chi-square approximation is expected to be worst when is large relative 3/15/03

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NIOSH Manual of Analytical Methods