Obtaining Stratum Breaks in Skewed Populations Using a Simple Method

• Activity Number: 278
• Type: Contributed
• Date/Time: Tuesday, August 10, 2004 : 2:00 PM to 3:50 PM
• Sponsor: Section on Survey Research Methods
• Author(s): Patricia M. Gunning*+ and Jane M. Horgan and Gary Keogh
• Companies: Dublin City University and Dublin City University and Dublin City University
• Keywords: efficiency ; geometric progression ; optimum allocation ; stratification

Abstract

Dalenius (1950) derived equations for determining boundaries when stratifying continuous variables so as to minimise the variance of the estimates with optimum allocation. No exact solution of these equations exists, and implementation of optimum stratification is usually based on approximation methods. This paper derives a new algorithm for the construction of stratum boundaries in positively skewed populations, which is easier to implement than current methods. The algorithm is based on an observation by Cochran (1961) that, with near optimum boundaries, the coefficients of variation are often found to be approximately the same in all strata. We show that, when the populations are positively skewed, the stratum breaks may be obtained using the geometric progression. Tests on four real populations show that the suggested method of stratum construction compares favorably with the commonly used cumulative root frequency approximation method of Dalenius and Hodges (1957), and the method of Lavallée and Hidiroglou (1988), which is specifically designed for skewed populations, in terms of the precision of the estimator of the mean and total.