On linear stratification of skewed and normal populations

Abstract

Strata boundary determination is one of the technical operations in Stratified Sampling. Maximized precision dominated
the literature in the appraisal of the performance of methods of strata construction which fails to account for the bias
associated with each method because the most precise method may not actually be the most efficient. This study
develops Linear Stratification (LS) as a new and simple approach to strata boundary determination. Strata boundaries
were established with LS, cumulative square root of frequency method and Geometric Stratification. Samples were selected
randomly without replacement from each stratum and estimates of the population parameters obtained. These estimates
were compared i.e. LS with that of the two existing methods using four sets of real life data with varying degrees of
skewness. With the Mean Square Error (MSE) value rather than minimum variance commonly used for appraisal, the
results show that LS provides minimum MSE value in both skewed and normal populations, hence the most efficient when
compared with the two competing methods in strata boundary determination.