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 Bühler 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 x1 =
0.002. For the formation of three strata obtained the optimal point on the
boundary x1 = -0.546 and x2 = 0.552. For the formation of
four strata obtained optimal boundary point is x1 = -0.869, x2
= 0.003 and x3 = 0.878. In forming five strata obtained optimal
boundary point x1 = -1.096, x2 = -0.331, x3 =
0.339 and x4 = 1.107. The establishment of a total of six strata
obtained the optimal point on the boundary x1 = -1.267, x2
= -0.569, x3 = 0.005, x4 = 0.579 and x5 =
1.281.