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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
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NIOSH Manual of Analytical Methods
