Symmetric and Unsymmetric Balanced Incomplete Block Designs: A Comparative Analysis

Acha Chigozie Kelechi

doi:10.5923/j.statistics.20120204.02

Abstract

This paperdiscusses a comparative analysis on balanced incomplete block designs by using the classical analysis of variance (ANOVA) method. Fortunately, the data collected for the analysis were in two groups of the balanced incomplete-block designs (BIBDâs), that is, symmetric, and unsymmetric (BIBDâs). In this paper, the basic interest is to apply classical ANOVA on the two types of BIBDâs and check whether they are significant and also minimizes error. A secondary data from N.R.C.R.I, Umudike, Abia State was used. To achieve this, we shall consider treatment (adjusted), block (adjusted) treatment (not adjusted) in the classical ANOVA method on the available data. Though, symmetric balanced incomplete block design (SBIBD) and unsymmetric balanced incomplete block design (USBIBD) are significant, it is pertinent to note that the SBIBD classical ANOVA method is found to be preferable to the USBIBD with reference to their variances at different level of significance.

Highlights

The basic concepts of the statistical design of e xperiments and data analysis were discovered in the early part of the 20th century as a cost effective research design tool to help improve y ields in farming
The objective of this study is to check if there is any significance of the relationship between the variables at 0.01 and 0.05 levels with reference to minimu m variance on symmetric balanced incomp lete block design (SBIBD) and unsymmetric balanced inco mplete b lock design (USBIBD)
On the basis of comparison, using min imization of error in balance inco mplete block design (BIBD), we have that SBIBD leads to a minimu m error than unsymmetric balanced incomp lete block design (USBIBD) whether the treatment is adjusted or not

Summary

Introduction

The basic concepts of the statistical design of e xperiments and data analysis were discovered in the early part of the 20th century as a cost effective research design tool to help improve y ields in farming. Many types of designs experiments and analysis techniques have been developed to meet the diverse needs of researchers and engineers. One of such experimental designs is called the balance inco mplete block design (BIBD). To the best of my knowledge complete b lock design is widely used by researchers more than the balanced incomp lete block designs because the missing data are computed before analysis. The objective of this study is to check if there is any significance of the relationship between the variables at 0.01 and 0.05 levels with reference to minimu m variance on symmetric balanced incomp lete block design (SBIBD) and unsymmetric balanced inco mplete b lock design (USBIBD).

Literature

Symmetric Bal anced Incomplete-bl ock Design

Summary and Conclusions