Measure of overall regression sum of squares of symmetric randomized complete block design with a lost observation

Abstract

A randomized complete block design (RCBD) is useful for analyzing a treatment variable and one block variable under the condition where experimental units are limited. The RCBD is assumed that there is no interaction between the treatment variable and the block variable. This paper considered the symmetric randomized complete block design (SRCBD) with t treatments and t blocks, when a lost value occurs in the experiments. For the analysis of variance for the unbalanced data, the ready-made formulae were not provided in the past. The SRCBD with a lost value was analyzed by means of the fundamental underlying linear regression model in order to determine the reliable mathematical formulae for the fitted parameters and the overall regression sum of squares of experimental data. It is noted that all possible parameters are considered in the overall regression sum of squares which will be helpful for the analysis of variance through the exact approach (the model comparison approach) at a later stage.