Several generalizations and variations of the material presented in this chapter are possible. The relative standard deviation and relative bias sometimes depend on the concentration sampled in a complicated way, requiring special attention. See, for example Ref. [24]. Also, asymmetric confidence intervals are sometimes required. Single-sided intervals are useful in some instances, e.g., alarm systems, as well as in quantifying limits of detection or quantitation, described briefly above. Ways to handle environmental influence parameters may also be complicated. See, for example Ref. [9]. In any case, despite the complexities possible, the examples given in this chapter may help to characterize method uncertainty in a reasonable manner.
6.
TECHNICAL NOTES
Note 1: Mainly for the statistically minded. Example of accuracy range confidence limit: Suppose it is known that the bias is zero. For example, an exposure standard may be set that specifies a given sampling and analytical method. In this case, the hazardous concentration may be said to be operationally defined. Operationally defined methods include NIOSH Methods 7400 and NIOSH 5040. If the bias is zero, Eq. 6 simplifies to: . Furthermore, if the relative standard deviation is estimated as with υ degrees of freedom (computed using the Smith-Satterthwaite approximation [1,13-14] if TRSD has more than one component), then the 95% confidence limit on TRSD is: , where is a 5% quantile value for the chi-square distribution, which can be read from a table in most elementary statistics texts. This determines the 95% confidence limit on the accuracy range itself as: .
If
= 15,
giving coverage factor k = 2.8 (Eq. 11).
Note that can be interpreted as a conservative estimate of TRSD and therefore can be treated as a Type B uncertainty with infinite number of degrees of freedom as described following Table 1.
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