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 complicated cases generally have specific difficulties that are best be approached by a statistician. With these assumptions, in terms of the combined uncertainty uc the limit of detection is traditionally [23, 24] taken to be: ,

(12)

and the detection limit may be defined as.

(13)

Note that uc includes the uncertainty associated with correction, if any, with blank subtractions. See Ref. [5] for a detailed example. After LOD and LD have been determined for a method they may be used as follows. A substance may be asserted as present if an estimate exceeds LOD. Moreover, if unknown (true) concentration X exceeds LD, an estimate is likely to exceed LOD. Given the above definitions and assumptions, the false positive rate r on asserting presence is closely equal to the non-detection rate. Note: If the combined uncertainty uc is determined from a method evaluation providing an effective number υ (as in Technical Note 2) degrees of freedom, then at 95% confidence in the method evaluation, the false positive rate is limited by: (14) where

5.

is the cumulative normal function. For example, if

, then

.

DISCUSSION The approach presented here to document method accuracy range and uncertainty relates to the statistical theory [11, 16-22] of tolerance or prediction intervals. This theory was originally developed in simplified form to predict the range of future measurements of a normally distributed random variable on the basis of n initial measurements. The initial measurements are analogous to the method evaluation, whereas the future measurements represent method application subsequent to evaluation. Because of measurement cost, workplace assessments cannot at present be conducted in such a way that continual re-evaluation is done at each measurement. The prediction interval approach given here shows a less costly way to document measurement uncertainty in those cases where a method has been initially evaluated and then used many times without reevaluation. The approach closely follows ISO GUM. Of course, for such an approach to actually make sense, an adequate quality control program must be instituted so that the measurement method remains stable during the time of its application following evaluation.

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NIOSH Manual of Analytical Methods