Methods and Applications of Statistics in Clinical Trials, Volume 2: Planning, Analysis, and Inferential Methods

Chapter 2

Analysis of Variance (ANOVA)

Jörg Kaufman

2.1 Introduction

The development of analysis of variance (ANOVA) methodology has in turn had an influence on the types of experimental research being carried out in many fields. ANOVA is one of the most commonly used statistical techniques, with applications across the full spectrum of experiments in agriculture, biology, chemistry, toxicology, pharmaceutical research, clinical development, psychology, social science, and engineering. The procedure involves the separation of total observed variation in the data into individual components attributable to various factors as well as those caused by random or chance fluctuation. It allows performing hypothesis tests of significance to determine which factors influence the outcome of the experiment. However, although hypothesis testing is certainly a very useful feature of the ANOVA, it is by no means the only aspect. The methodology was originally developed by Sir Ronald A. Fisher [1], the pioneer and innovator of the use and applications of statistical methods in experimental design, who coined the name “Analysis of Variance—ANOVA.”

For most biological phenomena, inherent variability exists within the response processes of treated subjects as well as among the conditions under which treatment is received, which results in sampling variability, meaning that results for a subject included in a study will differ to some extent from those of other subjects in the affected population. ...