Approximate Methods to Obtain the Optimum Stratum Boundaries: A Comparative Study

Authors: Ghadah A. Alsakkal ¹ & Mowafaq Muhammed Al Kassab^2
1Department of Computer Engineering, Tishk International University, Erbil, Iraq
²Department of Mathematics Education, Tishk International University, Erbil, Iraq

Abstract: In this article, we shall present an approximately optimal method for constructing stratum boundary points when the sample is allocated proportionally. The method is based on an equal partitioning of the cumulative f^(6⁄(7 )), where f is the distribution of the stratification variable. We show that in many practical situations, this technique compares favorably with approximately optimal stratification and allocation methods of previously suggested.

Keywords: Proportional Allocation, Stratification, Optimum Strata Boundaries, Cumulative Frequency Distribution, Efficiency

Download the PDF Document

doi: 10.23918/eajse.v7i1p197

References

Al-kassab M.M.T. and Aldaghestani, T.H. (1997). Using the Linear Model to Find Stratum Boundaries Based on the Proportional Allocation: A comparative Study. Mutah Journal for Research and Studies, 1294), 195-209.

Al-kassab M.M.T. (1993). Approximately Optimal Stratification Using Proportional Allocation. Tanmeat Alrafideen Journal, 41.

Cochran, W. (1963). Sampling techniques. Wiley, N.Y.

Cochran, W. (1961). Comparison of methods for determining stratum boundaries. Bull. Int. Statist. Inst. 3pt, (2), 345-358.

Dalenius, T. (1957). Sampling in Sweden. Almqvist & Wiksell, Stockholm.

Dalenius, T. and Hodges, J. L. (1959). Minimum variance stratification. J. Amer Statist. Ass., 54, 88-101.

Ekman, G. (1959). An approximation useful in univariate stratification. J. Amer. Statist. Ass., 30, 219-229.

Hess, I. Sethi, V. K. and Balakrishnan, T. R. (1966) Stratification: A practical investigation. J. Amer. Statist. Ass. 613 74-90.
Kish L. (1965). Survey Sampling. New York 1965.

Serfling, R. J. (1968). Approximately optimal stratification. J. Amer. Statist. Ass. 63, 1298-1309.

Singh, R. (1971). Approximately optimal stratification on the auxiliary variable. J. Amer. Statist. Ass. 66, 829-833.

Thomson, I. (1976). Comparison of approximately optimal stratification given proportional allocation with other methods of stratification and allocation. Metrika, Band 23, Seite 15-25, 1976.

Valliant, R., Dorfman, A.H., & Royall, R.M. (2000). Finite Population Sampling and Inference: A Prediction Approach. Wiley, New York.

Wackerly, D. D., Mendenhall, W., & Scheaffer, R. L. (2008). Mathematical Statistics with Applications (Seventh ed.). Belmont.

Wasan, A.A. (2017). Approximate optimal strata based on proportional allocation. Postgraduate Diploma Thesis. University of Mosul.