Statistical Sampling Strategies for Survey of Soil Contamination - Dealing with Contaminated Sites: From Theory Towards Practical Application - page 169

proportional to a prior estimate of the concentration. However, for other contam-
inants poorly correlated with the first contaminant, this so-called pps-sampling
design can be rather inefficient, see Brus et al. ( 2006 ) for an example. Finally, ancil-
lary information either can be used at the sampling stage, or at the estimation stage,
see Section 4.2.3 . The latter is more flexible: we can use this information to estimate
the mean concentration of some contaminants but not for others.
Many of the sampling designs described hereafter are supported by Visual
Sample Plan (VSP) software for designing environmental sampling plans. VSP can
be downloaded free at http://vsp.pnl.gov , along with a user's guide (Matzke et al.
2007 ).
4.2.1.1 Simple Random Sampling
The simplest way of selecting sampling locations randomly is simple random sam-
pling (SI). In SI all sampling locations are selected with equal probability and
independently from each other. In general, the sampling locations are slightly clus-
tered by chance. This makes SI rather inefficient in general: the sampling variance
(standard deviation) of the estimated target parameter (mean, median, areal propor-
tion et cetera.) is large compared to other sampling designs with the same number of
sampling locations. An advantage of SI is that it is easy to implement, see de Gruijter
et al. ( 2006 , p. 80), and the estimation of the target parameter and its sampling
variance is relatively simple (see Section 4.2.2 ).
4.2.1.2 Stratified Simple Random Sampling
In stratified simple random sampling (STSI) the area is divided into sub-areas, called
'strata', in each of which a predetermined number of sampling locations is selected
by SI, see previous section. There are two possible reasons for stratification. First,
by stratifying the area we may aim at increasing the efficiency compared to SI. So,
due to the stratification we hope that the sampling variance of the estimated target
parameter is smaller than with simple random sampling at the same costs (same
number of sampling locations), or vice versa, we hope that the costs of STSI are
smaller (we need fewer sampling locations) compared to SI with the same sam-
pling variance. The more homogeneous the strata, the larger the gain in efficiency.
A homogeneous stratum is a stratum in which the soil contaminant concentration
varies only slightly compared to the spatial variation within the area as a whole. A
pitfall in stratified sampling is to use too many strata. This is no problem as long as
the number of sampling locations per stratum is nearly proportional to the surface
area. However, if this detailed stratification leads to numbers of sampling locations
per stratum that are strongly disproportional to the surface areas, this may lead to a
loss rather than a gain in precision.
The second reason for stratification is that we want to have separate estimates for
the sub-areas, see Section 4.3 . By using the sub-areas as strata in random sampling,
we can control the number of sampling locations within the sub-areas, and related to