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

Richard A. Armstrong*, Frank Eperjesi, Bernard Gilmartin

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

Analysis of variance (ANOVA) is the most efficient method available for the analysis of experimental data. Analysis of variance is a method of considerable complexity and subtlety, with many different variations, each of which applies in a particular experimental context. Hence, it is possible to apply the wrong type of ANOVA to data and, therefore, to draw an erroneous conclusion from an experiment. This article reviews the types of ANOVA most likely to arise in clinical experiments in optometry including the one-way ANOVA ('fixed' and 'random effect' models), two-way ANOVA in randomised blocks, three-way ANOVA, and factorial experimental designs (including the varieties known as 'split-plot' and 'repeated measures'). For each ANOVA, the appropriate experimental design is described, a statistical model is formulated, and the advantages and limitations of each type of design discussed. In addition, the problems of non-conformity to the statistical model and determination of the number of replications are considered. © 2002 The College of Optometrists.

Original languageEnglish
Pages (from-to)248-256
Number of pages9
JournalOphthalmic and Physiological Optics
Volume22
Issue number3
DOIs
Publication statusPublished - May 2002

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Optometry
Analysis of Variance
Research Design
Statistical Models

Keywords

  • analysis of variance (ANOVA)
  • experimental design
  • factorial experimental design
  • random effect factor
  • randomised blocks
  • repeated measures design
  • split-plot design

Cite this

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title = "The application of analysis of variance (ANOVA) to different experimental designs in optometry",
abstract = "Analysis of variance (ANOVA) is the most efficient method available for the analysis of experimental data. Analysis of variance is a method of considerable complexity and subtlety, with many different variations, each of which applies in a particular experimental context. Hence, it is possible to apply the wrong type of ANOVA to data and, therefore, to draw an erroneous conclusion from an experiment. This article reviews the types of ANOVA most likely to arise in clinical experiments in optometry including the one-way ANOVA ('fixed' and 'random effect' models), two-way ANOVA in randomised blocks, three-way ANOVA, and factorial experimental designs (including the varieties known as 'split-plot' and 'repeated measures'). For each ANOVA, the appropriate experimental design is described, a statistical model is formulated, and the advantages and limitations of each type of design discussed. In addition, the problems of non-conformity to the statistical model and determination of the number of replications are considered. {\circledC} 2002 The College of Optometrists.",
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The application of analysis of variance (ANOVA) to different experimental designs in optometry. / Armstrong, Richard A.; Eperjesi, Frank; Gilmartin, Bernard.

In: Ophthalmic and Physiological Optics, Vol. 22, No. 3, 05.2002, p. 248-256.

Research output: Contribution to journalArticle

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