Statistical Sampling Strategies for Survey of Soil Contamination - Dealing with Contaminated Sites: From Theory Towards Practical Application - page 177

where L is the number of strata, a h are the relative areas of the strata (stratum
weights), and ¯ y h is the estimated mean of stratum h estimated by Eq. ( 4.3 ).

Provided all numbers of sampling locations are larger than 1, the sampling
variance of ¯ y STSI can be estimated by

V

y STSI a h V y h ,

L

¯ ¯

= (4.8)

h = 1

y h is the estimated sampling variance of ¯

where V

¯

y h

V

y h

S h ( y )
n h

¯

= , (4.9)

with S h ( y )the spatial variance of y within stratum h , that can be estimated by
(compare with Eq. ( 4.5 ))

n h

y hi − ¯

y h 2

1
( n h −

S 2 h ( y )

= , (4.10)

1)

i = 1

and n h is the number of sampling locations in stratum h .
If only one location per stratum is selected, the sampling variance can be
approximated by the collapsed strata estimator (Cochran 1977 ).
The 100(1 − α )% confidence interval for y is given by ¯

V

y STSI ,

t ( df )
1

¯ ¯

y STSI ±

2 ·

(4.11)

− α/

where t ( df )
1

2) quantile of the Student distribution with df degrees
of freedom. For df we can either take simply n

is the (1 − α/

− α/ 2

L (Lohr 1999 , p. 101), or it can be
approximated by Sattherwaites method (Nanthakumar and Selvavel 2004 )

−

h = 1 a h S 2 h ( y ) 2

n h

df ≈ (4.12)

S 2 h ( y )
n h

2

h = 1 a h

1
n h − 1

Random Grid Sampling

Similar to SI, for SY the spatial mean is estimated by the unweighted mean of the
measurements in the sample

n

1
n

¯

y SY = y i . (4.13)

i = 1