Table 4 Bias (%) in estimates of standard errors of estimates of the population mean for the various methods considered here
Example | Methods with complete enumeration of N sampling units as first phase | Methods with first-phase sample size = f | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|
Ratio of means | Mean of ratios | Model-assisted | PPS sampling | QPPS sampling | Simple random sampling | Ratio of means | Mean of ratios | Model-assisted | QPPS sampling | |
Second-phase sample size = 100 | ||||||||||
 1 | − 0.7 | − 0.8 | − 0.9 | − 0.7 | − 1.7 | − 0.2 | − 0.8 | − 0.9 | − 0.9 | − 1.3 |
 2 | − 0.7 | − 0.9 | − 0.7 | − 0.7 | − 0.5 | − 0.9 | − 1.0 | − 0.9 | − 1.1 | − 0.9 |
 3 | − 1.1 | − 2.1 | − 0.7 | − 1.1 | − 0.8 | − 0.7 | − 1.1 | − 1.2 | − 1.3 | − 0.9 |
 4 | − 1.2 | − 1.3 | − 1.2 | − 1.0 | − 0.9 | − 0.2 | − 0.7 | − 1.0 | − 0.8 | − 0.8 |
 5 | − 0.6 | − 0.3 | − 0.3 | − 0.9 | − 0.5 | 0.1 | − 0.2 | − 0.2 | − 0.3 | − 0.4 |
Second-phase sample size = 40 | ||||||||||
 1 | − 1.5 | − 2.7 | − 2.2 | − 0.7 | − 1.8 | − 1.1 | − 2.0 | − 2.1 | − 1.9 | − 1.6 |
 2 | − 1.2 | − 2.3 | − 1.4 | − 1.4 | − 2.2 | − 1.2 | − 1.9 | − 2.2 | − 1.5 | − 2.3 |
 3 | − 1.5 | − 2.4 | − 1.9 | − 1.1 | − 2.0 | − 1.5 | − 2.3 | − 2.4 | − 2.0 | − 1.9 |
 4 | − 0.9 | − 2.1 | − 1.9 | − 1.4 | − 1.5 | − 0.8 | − 1.6 | − 1.8 | − 1.6 | − 1.6 |
 5 | − 1.1 | − 2.3 | − 1.9 | − 0.7 | − 1.8 | − 1.4 | − 2.2 | − 2.4 | − 2.1 | − 1.6 |
Second-phase sample size = 10 | ||||||||||
 1 | − 2.7 | − 8.1 | − 1.0 | − 2.6 | − 8.2 | − 2.6 | − 6.8 | − 7.3 | − 2.3 | − 7.4 |
 2 | − 3.5 | − 8.3 | 35.4 | − 3.6 | − 8.5 | − 3.4 | − 7.0 | − 7.5 | 21.4 | − 7.4 |
 3 | − 3.4 | − 8.4 | − 1.2 | − 3.0 | − 8.2 | − 3.8 | − 7.7 | − 7.9 | − 2.6 | − 7.5 |
 4 | − 3.5 | − 8.3 | 4.0 | − 3.0 | − 8.0 | − 2.8 | − 6.9 | − 7.3 | − 1.2 | − 7.1 |
 5 | − 3.4 | − 8.3 | 8.6 | − 3.1 | − 7.8 | − 2.8 | − 7.2 | − 7.6 | 1.5 | − 7.3 |