Stratified sampling examples
(→Example 1) |
(→Example 1) |
||
| Line 9: | Line 9: | ||
'''Table 1''' Stratum parameters for the stratified example population. | '''Table 1''' Stratum parameters for the stratified example population. | ||
| − | <div style="float:left; margin-right:2em"> | + | :<div style="float:left; margin-right:2em"> |
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
| Line 36: | Line 36: | ||
|2.48 | |2.48 | ||
|} | |} | ||
| − | </div> | + | :</div> |
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 <math>n=10</math> and the defined allocation of samples to the three strata. | 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 <math>n=10</math> and the defined allocation of samples to the three strata. | ||
| Line 42: | Line 42: | ||
'''Table 2''' Calculation of parametric population mean from the parametric strata means. | '''Table 2''' Calculation of parametric population mean from the parametric strata means. | ||
| − | <div style="float:left; margin-right:2em"> | + | :<div style="float:left; margin-right:2em"> |
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
| Line 70: | Line 70: | ||
|'''7.0667''' | |'''7.0667''' | ||
|} | |} | ||
| − | </div> | + | :</div> |
Revision as of 19:07, 16 December 2010
Example 1
This example shows stratified sampling by the example population from figure 1.
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
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
 |
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! |
