Abstract
When faced with unbalanced data, it is often necessary to estimate the necessary missing values before the application of the analysis of variance technique. Previous studies have shown that different designs require different missing value estimators. With the introduction of some relatively new statistical designs, it has become expedient to derive missing value estimators for such designs. In this study, least squares estimators of missing values in a three-factor nested-factorial design are derived. Properties of the estimators are equally determined. A numerical example is given to show the application of the theoretical results obtained in this paper. Our empirical results establish the appropriateness of the missing value estimation method presented in this study.
Highlights
Comparative experiments are often inevitable in many scientific studies
Theorem 1 provides the estimators of s missing values within the same cell in nested-factorial design
The theoretical results obtained in this paper are predicated on several cases of missing values
Summary
Comparative experiments are often inevitable in many scientific studies. They serve as the means of generating data. Before carrying out a comparative experiment, an experimenter may have to adopt a suitable experimental(statistical) design. Several statistical designs have been proposed for use under certain experimental conditions[1,2]. Data collected in the course of a well design experiment need to be analysed in order to provide answers to research questions under consideration. If quantitative data are classified according to three or more treatments or levels of at least two factors, an analysis of variance (ANOVA) tech-nique may be applied. Different statistical designs require different analysis of variance techniques. One-way ANOVA is applicable to data collected using the completely randomised design
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