An introduction to analysis of variance (ANOVA) with special reference to data from clinical experiments in optometry

Abstract

This article is aimed primarily at eye care practitioners who are undertaking advanced clinical research, and who wish to apply analysis of variance (ANOVA) to their data. ANOVA is a data analysis method of great utility and flexibility. This article describes why and how ANOVA was developed, the basic logic which underlies the method and the assumptions that the method makes for it to be validly applied to data from clinical experiments in optometry. The application of the method to the analysis of a simple data set is then described. In addition, the methods available for making planned comparisons between treatment means and for making post hoc tests are evaluated. The problem of determining the number of replicates or patients required in a given experimental situation is also discussed.

The application of analysis of variance (ANOVA) to different experimental designs in optometry

“…In a previous article (Armstrong et al, 2000), we described a commonly used notation to describe the basic model of an ANOVA. The subscript 'i' is used to denote the group or class (i.e.…”

“…In our previous article (Armstrong et al, 2000), we described a one-way ANOVA in a randomised design which compared the reading rates of three groups of subjects, viz., young normal subjects, elderly normal subjects and subjects with age-related macular degeneration. This ANOVA is described as a 'fixed effects' model in which the objective is to estimate the differences between the subject groups and these are regarded as 'fixed' or discrete effects.…”

“…In the one-way, 'fixed' effects ANOVA described previously (Armstrong et al, 2000), each observation was classified in only one way, i.e. in which treatment or subject group the observation fell.…”

“…In addition to the assumptions made in the randomised design, i.e. homogeneity of variance, additive class effects and normal distribution of errors (Armstrong et al, 2000), this type of design makes the additional assumption that the difference between two treatments is consistent across all replications.…”

“…A previous article (Armstrong et al, 2000) described the origin of ANOVA, the logic which underlies the method and the assumptions necessary to apply it to data. In addition, the simplest form of the analysis, the one-way ANOVA in a randomised design, was described and illustrated using a clinical experiment drawn from optometric research.…”