Stratified sampling examples

From AWF-Wiki
(Difference between revisions)
Jump to: navigation, search
(Example 1)
(Example 1)
Line 68: Line 68:
 
|
 
|
 
|'''7.0667'''
 
|'''7.0667'''
 +
|}
 +
 +
'''Table 3''' Calculation of parametric error variance of the estimated mean of the population for <math>n=10</math>.
 +
 +
{| class="wikitable"
 +
|-
 +
!''Stratum''
 +
!''fpc''
 +
!''<math>\sigma_h^2/n</math>''
 +
!''var per stratum<math>fpc\sigma_h^2/n''
 +
!''var*<math>W_h^2</math>''
 +
|-
 +
|1
 +
|0.769230769
 +
|0.87244898
 +
|0.67111461
 +
|0.146154
 +
|-
 +
|2
 +
|0.714285714
 +
|1.61979167
 +
|1.15699405
 +
|0.082275
 +
|-
 +
|3
 +
|0.714285714
 +
|0.82812500
 +
|0.59151786
 +
|0.042063
 +
|-
 +
|
 +
|
 +
|<math>var(\hat y)=</math>
 +
|'''0.270492'''
 
|}
 
|}
  

Revision as of 20:19, 16 December 2010

Example 1

This example shows stratified sampling by the example population from figure 1.

Figure 1 Example population (deVries 1986)

Imagine the example population of \(N=30\) elements be subdivided into three strata as in figure 2. Here, stratification has been done arbitrarily into three strata of size 14, 8 and 8. From this stratified population, we wish to take a sample of \(n=10\), taking \(n_1=4\) from the first stratum and \(n_2=n_3=3\) from the other two strata. The stratum parametric means and variances are given in table 1.

Table 1 Stratum parameters for the stratified example population.

Stratum \(N_h\,\) \(n_h\,\) \(\mu_h\,\) \(\sigma_h^2\,\)
1 14 4 6.29 3.49
2 8 3 10.13 4.86
3 8 3 5.38 2.48
Figure 2 Subdividing the example population (arbitrarily) in three strata, for illustration purposes

Calculation in stratified sampling is best done in tabular format, first per stratum and then combining the per-stratum results to the values / estimations for the entire population. The estimation of the mean is illustrated in Table 2 and results – as expected – in the parametric mean without stratification. Table 3 presents the calculation of the parametric error variance for \(n=10\) and the defined allocation of samples to the three strata.

Table 2 Calculation of parametric population mean from the parametric strata means.

Stratum Stratum mean Weight \((W_h)\) mean*weight
1 6.29 0.466667 2.9333
2 10.13 0.266667 2.7000
3 5.38 0.266667 1.4333
7.0667

Table 3 Calculation of parametric error variance of the estimated mean of the population for \(n=10\).

Stratum fpc \(\sigma_h^2/n\) var per stratum\(fpc\sigma_h^2/n'' !''var*<math>W_h^2\)
1 0.769230769 0.87244898 0.67111461 0.146154
2 0.714285714 1.61979167 1.15699405 0.082275
3 0.714285714 0.82812500 0.59151786 0.042063
\(var(\hat y)=\) 0.270492
Construction.png sorry: 

This section is still under construction! This article was last modified on 12/16/2010. If you have comments please use the Discussion page or contribute to the article!

Personal tools
Namespaces

Variants
Actions
Navigation
Development
Toolbox
Print/export