Statistical Sampling Strategies for Survey of Soil Contamination - Dealing with Contaminated Sites: From Theory Towards Practical Application - page 184

locations can then simply be obtained by rewriting Eqs. ( 4.4 ) and ( 4.16 ), and sub-
stituting the prior estimate of the spatial variance of y or the indicator i in the area,
S 2 (.), for the estimated spatial variance, S 2 (.)

S 2 (.)
V max

n = . (4.28)

In case of a constraint on the coefficient of variation, the same procedure can
be used. It requires a prior estimate of the mean, which is used to compute the
maximum value of the sampling variance of the mean, V max .
For STSI, prior estimates of the spatial variances within strata can be used to
compute the optimal allocation, i.e. the numbers of sampling locations per stratum
that result in the minimum sampling variance of the estimated mean or areal frac-
tion, given the total number of sampling locations (de Gruijter et al. 2006 , p. 94).
The required total number of sampling locations for a specified maximum allowable
sampling variance of the estimated mean (areal fraction) can then be calculated with

L

a h S h (.) 2

1
V max ·

n = , (4.29)

h = 1

where S h (.) is the prior estimate of the spatial standard deviation of y or i within
stratum h . Equation ( 4.29 ) assumes equal cost per sampling location for the strata.
I refer to de Gruijter et al. ( 2006 , p. 95) if these costs are unequal for the strata. For
proportional allocation, the required number of sampling locations can be calculated
with

h = 1

L

a h S h (.)

n = . (4.30)

V max

4.2.5.2 Constraint on Probability of Error

This section describes how to calculate the required number of sampling locations
if the quality constraint is formulated in terms of the probability of occurrence of
the error in the estimated mean or the areal fraction. If an absolute error d has been
specified with an allowed probability of exceedance

α , then the maximum allowable

sampling variance can be derived from d and α as

d
u 1 − α/ 2

2

V max = , (4.31)

where u 1 − α/ 2 is the (1 2) quantile of the standard normal distribution. The

derived value of V max is then inserted in Eq. ( 4.28 ), Eq. ( 4.29 )orEq.( 4.30 )to
obtain the required number of sampling locations.

− α/