What is the difference between Neyman allocation and optimum allocation?

What is the difference between Neyman allocation and optimum allocation?

A Neyman allocation scheme provides the most precision for estimating a population mean given a fixed total sample size. Of note, Neyman allocation is a special case of optimal allocation whose objective in sample allocation is to minimize variance of an estimator for a population mean for a given total cost.

What is proportionate allocation?

Proportional allocation is a procedure for dividing a sample among the strata in a stratified sample survey. A sample survey collects data from a population in order to estimate population characteristics. With roughly equal per-unit data collection costs, a budget amount $B corresponds to a total sample size n.

What is the formula for proportional allocation?

Proportional allocation sets the sample size in each stratum equal to be proportional to the number of sampling units in that stratum. That is, nh/n = Wh. Proportional allocation yields a self weighted sample (no additional weighting is required to estimate unbiased population parameters).

What is the advantage of doing proportional allocation?

Another advantage of proportional allocation is that it produces a sample size that is representative of the size of the stratum within the population. If, for instance, one stratum consists of 1,000 people and another of 2,000 people, a proportional allocation could draw a sample of 1 percent from each stratum.

What is optimal allocation?

Optimal allocation is a procedure for dividing the sample among the strata in a stratified sample survey. A stratified sample selects separate samples from subgroups (called “strata”) of the population and can often increase the accuracy of survey results.

What constitutes an optimal allocation of resources?

theory of allocation combination is called the “optimal” or “efficient” combination. As a rule, the optimal allocation equalizes the returns of the marginal (or last) unit to be transferred between all the possible uses.

Where is the optimal allocation of resources found?

The optimal allocation of resources is found: where the marginal cost is at its lowest. at every point along a production possibilities curve.

Which is an example of a proportional allocation?

Proportional allocation sets the sample size in each stratum equal to be proportional to the number of sampling units in that stratum. That is, nh/n = Wh. Proportional allocation yields a self weighted sample (no additional weighting is required to estimate unbiased population parameters). For example, ȳ st = ȳ, as previously discussed.

What is the efficiency of the Neyman allocation?

The relative efficiency of Neyman and optimum allocations are Vprop Vney × 100 = 115.23 % and Vprop Vopt × 100 = 118.26 %, respectively. Consider a population stratified into L strata.

What is variance estimate for Stratum 1 Neyman allocation?

For example, a variance estimate for stratum 1 would be S ^ 1 2 = p ^ 1 q ^ 1 = ( 0.47) ( 0.53). and then calculate each n h = n W h, rounding where required. Neyman Allocation ignores costs for these calculations as well because we assume they are equal.

How to calculate relative efficiencies of proportional allocation?

Compute the relative efficiencies of the Neyman and optimum allocation with respect to the proportional allocation for estimating the population mean when samples from each stratum are selected by SRSWOR method. where C = 50,000 and Co = 10,000.