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

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. Copyright (C) 2000 The College of Optometrists.

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

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.

Statnote 23: Non-parametric analysis of variance (ANOVA)

To carry out an analysis of variance, several assumptions are made about the nature of the experimental data which have to be at least approximately true for the tests to be valid. One of the most important of these assumptions is that a measured quantity must be a parametric variable, i.e., a member of a normally distributed population. If the data are not normally distributed, then one method of approach is to transform the data to a different scale so that the new variable is more likely to be normally distributed. An alternative method, however, is to use a non-parametric analysis of variance. There are a limited number of such tests available but two useful tests are described in this Statnote, viz., the Kruskal-Wallis test and Friedmann’s analysis of variance.

Statnote 11: the two-factor analysis of variance

Experiments combining different groups or factors are a powerful method of investigation in applied microbiology. ANOVA enables not only the effect of individual factors to be estimated but also their interactions; information which cannot be obtained readily when factors are investigated separately. In addition, combining different treatments or factors in a single experiment is more efficient and often reduces the number of replications required to estimate treatment effects adequately. Because of the treatment combinations used in a factorial experiment, the degrees of freedom (DF) of the error term in the ANOVA is a more important indicator of the ‘power’ of the experiment than simply the number of replicates. A good method is to ensure, where possible, that sufficient replication is present to achieve 15 DF for each error term of the ANOVA. Finally, in a factorial experiment, it is important to define the design of the experiment in detail because this determines the appropriate type of ANOVA. We will discuss some of the common variations of factorial ANOVA in future statnotes. If there is doubt about which ANOVA to use, the researcher should seek advice from a statistician with experience of research in applied microbiology.

Statnote 13: a more complex analysis of variance incorporating a 'repeated measures' factor

Experiments combining different groups or factors and which use ANOVA are a powerful method of investigation in applied microbiology. ANOVA enables not only the effect of individual factors to be estimated but also their interactions; information which cannot be obtained readily when factors are investigated separately. In addition, combining different treatments or factors in a single experiment is more efficient and often reduces the sample size required to estimate treatment effects adequately. Because of the treatment combinations used in a factorial experiment, the degrees of freedom (DF) of the error term in the ANOVA is a more important indicator of the ‘power’ of the experiment than the number of replicates. A good method is to ensure, where possible, that sufficient replication is present to achieve 15 DF for the error term of the ANOVA testing effects of particular interest. Finally, it is important to always consider the design of the experiment because this determines the appropriate ANOVA to use. Hence, it is necessary to be able to identify the different forms of ANOVA appropriate to different experimental designs and to recognise when a design is a split-plot or incorporates a repeated measure. If there is any doubt about which ANOVA to use in a specific circumstance, the researcher should seek advice from a statistician with experience of research in applied microbiology.

The use of analysis of variance (ANOVA) in applied microbiology

Experiments combining different groups or factors and which use ANOVA are a powerful method of investigation in applied microbiology. ANOVA enables not only the effect of individual factors to be estimated but also their interactions; information which cannot be obtained readily when factors are investigated separately. In addition, combining different treatments or factors in a single experiment is more efficient and often reduces the number of replications required to estimate treatment effects adequately. Because of the treatment combinations used in a factorial experiment, the DF of the error term in the ANOVA is a more important indicator of the ‘power’ of the experiment than the number of replicates. A good method is to ensure, where possible, that sufficient replication is present to achieve 15 DF for each error term of the ANOVA. Finally, it is important to consider the design of the experiment because this determines the appropriate ANOVA to use. Some of the most common experimental designs used in the biosciences and their relevant ANOVAs are discussed by. If there is doubt about which ANOVA to use, the researcher should seek advice from a statistician with experience of research in applied microbiology.

The relationship between measurement method and corneal structure on apparent intraocular pressure in glaucoma and ocular hypertension

Purpose: To analyse the relationship between measured intraocular pressure (IOP) and central corneal thickness (CCT), corneal hysteresis (CH) and corneal resistance factor (CRF) in ocular hypertension (OHT), primary open-angle (POAG) and normal tension glaucoma (NTG) eyes using multiple tonometry devices. Methods: Right eyes of patients diagnosed with OHT (n=47), normal tension glaucoma (n=17) and POAG (n=50) were assessed, IOP was measured in random order with four devices: Goldmann applanation tonometry (GAT); Pascal(R) dynamic contour tonometer (DCT); Reichert(R) ocular response analyser (ORA); and Tono-Pen(R) XL. CCT was then measured using a hand-held ultrasonic pachymeter. CH and CRF were derived from the air pressure to corneal reflectance relationship of the ORA data. Results: Compared to the GAT, the Tonopen and ORA Goldmann equivalent (IOPg) and corneal compensated (IOPcc) measured higher IOP readings (F=19.351, p<0.001), particularly in NTG (F=12.604, p<0.001). DCT was closest to Goldmann IOP and had the lowest variance. CCT was significantly different (F=8.305, p<0.001) between the 3 conditions as was CH (F=6.854, p=0.002) and CRF (F=19.653, p<0.001). IOPcc measures were not affected by CCT. The DCT was generally not affected by corneal biomechanical factors. Conclusion: This study suggests that as the true pressure of the eye cannot be determined non-invasively, measurements from any tonometer should be interpreted with care, particularly when alterations in the corneal tissue are suspected.