An integration of stratified sampling designs and Geographic Information Systems

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An integration of stratified sampling designs and Geographic Information Systems - An application in Educational Research

Satharasinghe A,Ranjith Premalal De Silva
E-mail: rpdesilva@pdn.ac.lk

Thattil R.O., Samitha S.
Postgraduate Institute of Agriculture, University of Peradeniya, Sri Lanka
Tel: +94-777-801712, Fax: +94-8-387216

Abstract
In demographic and socio-economic surveys, stratified sampling designs are frequently used and regions (geographical administrative units) are generally used as strata. Assuming causal mechanisms are localized and ignoring impacts from the bordering regions, sampling units within geographic regions are considered to be homogeneous in these surveys. However, sampling units within geographic regions may not be homogeneous and therefore, sample may not be representative, if the variation of spatial variables affecting the study variables were not considered in stratification. The values of the spatial variables cannot assumed to be fixed and random at every point within geographic regions. Therefore, sampling units drawn from strata based on administrative boundaries cannot be thought to be representative of wider areas and hence do not offer scope for the generalization or extrapolation of research results.

In certain situations, use of one or two variables may not be sufficient to do a proper stratification of a population, as the population is heterogeneous due to the variations of several variables. Therefore, it may be necessary to take all such important variables into consideration. In this study, a new stratification method is introduced to overcome these problems.

In this study, the stratification is achieved using sufficient number of both non-spatial variables and spatial variables computed in GIS. To be able to utilize sufficient number of variables, stratification is done by two multivariate techniques namely factor analysis and cluster analysis, and by the Extended Ekman Rule (EER).

The new stratification method was tested by applying it to estimate parameters on the academic performance of year 5 students of public schools of the Southern Province of Sri Lanka. Academic performance was estimated by a two-stage and one-stage stratified sampling designs using strata constructed under the new methods. Area was stratified using the spatial variables on the infrastructure facilities thus forming first stage strata and schools were stratified by using non-spatial variables on the facilities available in schools and these school strata were used as second stage strata in two-stage stratified sampling designs. Schools were also stratified by spatial as well as non-spatial variables and resulting strata were used in one stage stratified sampling design.

The one-stage stratified sampling design, using strata constructed under Extended Ekman Rule using linear combination of several factors, yielded the highest precision of the estimate. The strata constructed by this facility-based classification of schools can be used to grade schools and such a grading system can be used to determine cut-off marks for university entrance and national level examinations.

Almost all-important features of sampling such as randomness, homogeneity of strata as well as the findings can be visualized by digital thematic maps and can be verified against field conditions easily, by user-friendly facilities available in GIS. Further, under this methodology once the system is established, samples could be drawn according to the desired requirements quickly and easily without any manual work including drawing of new geographic sub-regional boundaries and drawing sampling units according to random numbers manually.