PENENTUAN TITIK-TITIK BATAS OPTIMUM STRATA PADA PENARIKAN CONTOH ACAK BERLAPIS DENGAN PEMROGRAMAN DINAMIK (Kasus : Pengeluaran per Kapita Propinsi Jawa Timur Tahun 2008)

Abstract

Optimum stratification is the method of choosing the best boundaries that make strata internally homogeneous, given some sample allocation. In order to make the strata internally homogenous, the strata should be constructed in such a way that the strata variances for the characteristic under study be as small as possible. This could be achieved effectively by having the distribution of the main study variable known and create strata by cutting the range of the distribution at suitable points. The problem of finding Optimum Strata Boundaries (OSB) is considered as the problem of determining Optimum Strata Widths (OSW). The problem is formulated as a Mathematical Programming Problem (MPP), which minimizes the variance of the estimated population parameter under Neyman allocation subject to the restriction that sum of the widths of all the strata is equal to the total range of the distribution. The distributions of the study variable are considered as continuous with standard normal density functions. The formulated MPPs, which turn out to be multistage decision problems, can then be solved using dynamic programming technique proposed by Buhler and Deutler (1975). After the counting process using C++ program received the width of each stratum. From these results the optimal boundary point can be determined for each stratum. For the two strata to get the optimal point on the boundary x 1 = 0.002. For the formation of three strata obtained the optimal point on the boundary x 1 = -0.546 and x 2 = 0.552. For the formation of four strata obtained optimal boundary point is x 1 = -0.869, x 2 = 0.003 and x 3 = 0.878. In forming five strata obtained optimal boundary point x 1 = -1.096, x 2 = -0.331, x 3 = 0.339 and x 4 = 1.107. The establishment of a total of six strata obtained the optimal point on the boundary x 1 = -1.267, x 2 = -0.569, x 3 = 0.005, x 4 = 0.579 and x 5 = 1.281.