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Table 5 Sampling efficiency (%) of the various methods considered here relative to simple random sampling

From: Simulation studies to examine bias and precision of some estimators that use auxiliary information in design-based sampling in forest inventory

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

Ratio of means

Mean of ratios

Model-assisted

QPPS sampling

Second-phase sample size = 100

 1

− 59

− 53

− 58

− 58

− 57

− 28

− 25

− 28

− 29

 2

− 55

− 47

− 55

− 63

− 52

− 31

− 26

− 31

− 27

 3

− 57

− 55

− 56

− 58

− 56

− 28

− 27

− 28

− 29

 4

− 59

− 52

− 59

− 62

− 57

− 28

− 24

− 28

− 29

 5

− 61

− 52

− 61

− 65

− 58

− 29

− 24

− 29

− 30

Second-phase sample size = 40

 1

− 59

− 54

− 58

− 58

− 58

− 28

− 26

− 28

− 29

 2

− 54

− 47

− 54

− 63

− 52

− 31

− 26

− 31

− 28

 3

− 57

− 56

− 56

− 58

− 57

− 28

− 27

− 28

− 29

 4

− 59

− 53

− 59

− 62

− 57

− 29

− 25

− 28

− 29

 5

− 61

− 53

− 60

− 65

− 58

− 29

− 24

− 29

− 29

Second-phase sample size = 10

 1

− 58

− 56

− 55

− 58

− 59

− 31

− 28

− 29

− 33

 2

− 53

− 49

− 22

− 62

− 53

− 31

− 27

− 14

− 30

 3

− 56

− 57

− 52

− 57

− 58

− 30

− 29

− 26

− 31

 4

− 59

− 55

− 52

− 62

− 59

− 31

− 28

− 28

− 33

 5

− 60

− 55

− 51

− 65

− 61

− 31

− 27

− 27

− 33

  1. Each value in the table was determined as the difference between the mean of the simulation estimates of the standard error of estimates of the population mean for the estimator concerned and the mean when simple random sampling was used, as a proportion of the mean in the simple random sampling case. Each value in the table was the mean of 5000 simulations when the target-auxiliary variable correlation level was 0.9. Otherwise, the structure of the table is similar to that of Table 2. The results in the first row of the table are repeated in Fig. 3