Recommendations for analysis of repeated-measures designs: testing and correcting for sphericity and use of manova and mixed model analysis

Abstract

Purpose: A common experimental design in ophthalmic research is the repeated-measures design in which at least one variable is a within-subject factor. This design is vulnerable to lack of 'sphericity' which assumes that the variances of the differences among all possible pairs of within-subject means are equal. Traditionally, this design has been analysed using a repeated-measures analysis of variance (RM-anova) but increasingly more complex methods such as multivariate anova (manova) and mixed model analysis (MMA) are being used. This article surveys current practice in the analysis of designs incorporating different factors in research articles published in three optometric journals, namely Ophthalmic and Physiological Optics (OPO), Optometry and Vision Science (OVS), and Clinical and Experimental Optometry (CXO), and provides advice to authors regarding the analysis of repeated-measures designs.

Recent findings: Of the total sample of articles, 66% used a repeated-measures design. Of those articles using a repeated-measures design, 59% and 8% analysed the data using RM-anova or manova respectively and 33% used MMA. The use of MMA relative to RM-anova has increased significantly since 2009/10. A further search using terms to select those papers testing and correcting for sphericity ('Mauchly's test', 'Greenhouse-Geisser', 'Huynh and Feld') identified 66 articles, 62% of which were published from 2012 to the present.

Summary: If the design is balanced without missing data then manova should be used rather than RM-anova as it gives better protection against lack of sphericity. If the design is unbalanced or with missing data then MMA is the method of choice. However, MMA is a more complex analysis and can be difficult to set up and run, and care should be taken first, to define appropriate models to be tested and second, to ensure that sample sizes are adequate.

Keywords: Greenhouse-Geisser; Huynh-Feldt; Mauchly's test; mixed model analysis; repeated-measures design; sphericity.