Proportional Stratification Component of Design Effect

Abstract

This paper is concerned with Stratification as a component of design effect (Deff). There is a need to determine the pattern and magnitude of this component when the sample allocation is proportional, and to see how such component behaves when parameters like strata means, strata variances, strata proportions and sample size of each stratum vary. Factorial analysis is carried out, to determine the effects of those various factors on the design effect and to form some idea about its expected magnitude when faced with a design of a specific given structure. Also, an attempt will be made to arrive at the expressions, which are believed original, for the design effect in the case of a population consisting of two strata. It is shown that the different combinations of strata means and strata variances affect significantly the design effect. The Deff values increase with the increase in the levels of variances of strata, and as differences in strata means become less. But decrease as strata sizes tend to equality. The precision of proportionate stratified sampling is investigated and examined, and consequently, it is confirmed that it is the same as that of simple random sampling (SRS) when strata means are equal.