Russel-Research-Method-in-Anthropology

Sampling Theory 175
TABLE 7.2
All Samples of 2 from 5 Elements
Sample Mean Cumulative Mean
Guinea-Bissau and Nepal (100 197)/2 148.5 148.5
Guinea-Bissau and Moldova (100 374)/2 237.0 385.5
Guinea-Bissau and Zambia (100 413)/2 256.5 642.0
Guinea-Bissau and Haiti (100 443)/2 271.5 913.5
Nepal and Moldova (197 374)/2 285.5 1199.0
Nepal and Zambia (197 413)/2 305.0 1504.0
Nepal and Haiti (197 443)/2 320.0 1824.0
Moldova and Zambia (374 413)/2 393.5 2217.5
Moldova and Haiti (374 443)/2 408.5 2626.0
Zambia and Haiti (413 443)/2 428.0 3054.0
x 3054/10 305.4
parameter we want to estimate—is $294.16. There are 2,118,760 samples of
size 5 that can be taken from 50 elements. I used a random-number generator
to select 15 samples of size 5 from the data in table 7.1 and calculated the
mean of each sample. Table 7.3 shows the results.
Even in this small set of 15 samples, the mean is $284.12—quite close to
the actual mean of $294.16. Figure 7.6a shows the distribution of these samples.
It has the look of a normal distribution straining to happen. Figure 7.6b
shows 50 samples of five from the 50 countries in table 7.1. The strain toward
the normal curve is unmistakable and the mean of those 50 samples is $293.98
3
6
5
Number of Cases
2
1
Number of Cases
4
3
2
1
0
0 100 200 300 400 500
0
100 200 300 400 500
a.
PCGDP
b.
Samples of Two
Figure 7.4. Five cases and the distribution of samples of size 2 from those cases.