Question

Parts a-d involve working with the data set and a random sample, but parts e and f are more general and about the comparison between optimal allocation and proportional allocation as well as stratification in general for this population. In what situations does optimal allocation perform better than proportional, and how does stratification affect the estimate for a given variable

Answer 1

Proportion allocation:

In this case samples are allocated on the basis of size of the strata. If the size of the strata is large then we take larger sample from that strat and vice versa.

Optimum allocation:

In this case samples are drawn

i) directly proportion to the size of the strata

ii) directly proportional to the variability of the strata , that is larger samples are taken from the strata who have larger in variation.

iii) inversly proportion to the cost of collecting information from each units.

that is smaller the samples are collected from the strata on which information of units that is costly.

So that optimum allocation is better when there is large variability within the different strata. Also it is better if the cost required collecting information of the units are vary from strata to strata.