Abstract
Evaluating the statistical properties of a semi-Latin square, and in general, an incomplete block design, is vital in determining the usefulness of the design for experimentation. Improving the procedures for obtaining these statistical properties has been the subject of some research studies and software developments. Many available statistical software that evaluate incomplete block designs do so at the level of analysis of variance but not for the popular A-, D-, E-, and MV-efficiency properties of these designs to determine their adequacy for experimentation. This study presents a program written in the MATLAB environment using MATLAB codes and syntaxes which is capable of computing the A-, D-, E-, and MV-efficiency properties of any n×n/k semi-Latin square and any incomplete block design via their incidence matrices, where N is the number of rows and columns and k is the number of plots. The only input required for the program to compute the four efficiency criteria is the incidence matrix of the incomplete block design. The incidence matrix is the binary representation of an incomplete block design. The program automatically generates the efficiency values of the design once the incidence matrix has been provided, as shown in the examples.
Highlights
Evaluating the statistical properties of a semi-Latin square, and in general, an incomplete block design, is vital in determining the usefulness of the design for experimentation
Given a semi-Latin square, Ξ, with t = nk treatments arranged in b = n2 blocks, the incidence matrix, N, emanating from Ξ or that of any other t-treatment incomplete block design, Σ, in b blocks, is a t × b matrix of 1’s and 0’s
We provide some illustrative examples of the performances of the MATLAB program in evaluating semi-Latin squares
Summary
Evaluating the statistical properties of a semi-Latin square, and in general, an incomplete block design, is vital in determining the usefulness of the design for experimentation. Many available statistical software that evaluate incomplete block designs do so at the level of analysis of variance but not for the popular A-, D-, E-, and MV-efficiency properties of these designs to determine their adequacy for experimentation. This study presents a program written in the MATLAB environment using MATLAB codes and syntaxes which is capable of computing the A-, D-, E-, and MV-efficiency properties of any (n × n)/k semi-Latin square and any incomplete block design via their incidence matrices, where N is the number of rows and columns and k is the number of plots. Bailey [4] listed some methods for the construction of semi-Latin squares, such as the inflation method, interleaving method, Trojan method, superposition method, etc. According to John [8], incomplete block designs with equal block sizes often differ in the precision with which treatment effects are estimated, and efficiency factors of the incomplete block designs provide useful measures of these differences
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