Page:NIOSH Manual of Analytical Methods - Chapter P.pdf/16

 where the constant K is to be determined so that . First of all, the distribution of

is approximated as chi-square:

,

where

is determined as with the Smith-Satterthwaite [23-24] approximation, forcing

variances to agree; often

.

Now, , or, in other words: .

[Note that

, unlike Note 3.]

Remembering that a2 depends on the estimate following integral equation:

, K is given as a solution of the

,

where the correction O[1/n2 ] is easily proved by expanding the integrand about in

. Therefore, the following simple asymptotic expression for

results:

.

3/15/03

223

NIOSH Manual of Analytical Methods