Full-model regression sum of squares of randomized complete block design having one unrecorded observation

Abstract

In the classical design of experiment, a randomized complete block design (RCBD) is a helpful experimental design because this design uses a small number of experimental units. The randomized complete block design is comprised of two factors, i.e., a nuisance factor and a potential factor. In many real experiments, some data might be missing or unrecorded. The instant formulae were not provided for an analysis of variance in this case. This paper took into account the randomized complete block design (RCBD) with a treatments and b blocks. In this contribution, the RCBD with an unrecorded value was analyzed by means of the exact scheme with the model comparison approach. The advantages of the exact scheme are that the unrecorded value for the unfilled cell is not estimated and the treatment sum of squares is unbiased. It is important to note that there is no ready-made formula for RCBD in the past. Hence, this research paper provided the mathematical formulae for the fitted parameters and the overall regression sum of squares (ORSS) for the full model of experimental data. It is also noted that the ORSS is imperative for the analysis of the variance by means of the exact scheme.