Geoscience Reference
In-Depth Information
TABLE 2.3
Strata Means, Standard Deviations (SD), and Standard Errors (SE) for Means when
the Observations for TCE Shown in Figure 2.4 Are Poststratified into Ten Strata
Based on Treating Each of the Columns of Data in the Figure as Consisting of Two
Strata of Four Observations Each
Stratum
Mean
SD
SE
1
10
10
64
542
156.5
258.3
129.1
2
346
191
850
30
354.3
354.8
177.4
3
12
23
187
164
96.5
91.8
45.9
4
701
2,130
1,860
622
1,328.3
778.4
389.2
5
40
42
655
21,600
5,584.3
10,681.1
5,340.5
6
67,700
38,900
584
2,540
27,431.0
32111.5
16,055.8
7
600
663
3,750
8,760
3,443.3
3,837.4
1,918.7
8
14,000
16,100
12,800
763
10,915.8
6,904.5
3,452.3
9
11
1,160
4,270
9,870
3,827.8
4,411.7
2,205.8
10
7,320
4,030
273
190
2,953.3
3,418.0
1,709.0
Overall
a
5,609.1
1,760.4
a
The overall mean is the mean of the values for the individual strata because the strata sizes are
all four and each has the same weight. The overall standard error is the estimated standard error
of the overall mean based on the variance calculated using Equation (2.24), with
N
i
/
N
= 1/10.
An alternative analysis involves poststratification of the sample. For
example, each of the columns of observations can be divided into two
strata of four observations each based on the top four and the bottom
four observations. There are then ten strata, with means, standard devia-
tions, and standard errors of the means as shown in Table 2.3. The esti-
mated mean TCE concentration is 5609.1, which is the same as obtained
by treating the data as coming from a random sample. The estimated
standard error of the mean is 1760.4, which is less than the value of 1996.8
that was obtained assuming a random sample. The approximate 95%
confidence interval for the true mean based on the stratified sample is
given by 5609.1 ± 1.96(1760.4), that is, 2158.7 to 9059.4 is therefore nar-
rower than the interval calculated assuming a random sample.
In this example, the TCE concentrations are assumed to be effectively
made at a point in the sample area. There is then an infinite number of pos-
sible sample points in each of the strata so that the standard errors shown in
Table 2.3 are just
SD/4
, without any finite population corrections.
2.11 Some Other Design Strategies
So far in this chapter, the sample designs considered are simple random sam-
pling, stratified random sampling, and systematic sampling. There are also a
number of other design strategies that are sometimes useful. Here, a few of
