Simple Latin Cubic Sampling +1 and -k Sampling Designs

Abstract

In this study we presented a new class of probability sampling designs, simple latin cubic sampling +1 sampling designs that were developed from simple latin square sampling designs by focus on three-dimensional, with the specific goals of deriving an estimator of the population total, true variances of these estimators, and estimators of these variances.  And the Horvitz-Thompson estimation method will be the primary method used to generate these estimator. These designs when compared with simple random, stratified, and systematic sampling will provide estimator with smaller variance for simulation population with spatial correlation and assume that the survey region can be partitioned into three-dimensional grid of d³ equalized three-dimensional.