Review Article

A review of multivariate methods of analysing refractive data with dioptric power matrices

Elizabeth Chetty, Alan Rubin
African Vision and Eye Health | Vol 81, No 1 | a714 | DOI: | © 2022 Elizabeth Chetty, Alan Rubin | This work is licensed under CC Attribution 4.0
Submitted: 18 October 2021 | Published: 08 November 2022

About the author(s)

Elizabeth Chetty, Department of Optometry, Faculty of Health Sciences, University of Johannesburg, Johannesburg, South Africa
Alan Rubin, Department of Optometry, Faculty of Health Sciences, University of Johannesburg, Johannesburg, South Africa


Background: There are three components to refractive state, namely sphere, cylinder and axis. Similarly, central corneal power is also composed of three components, namely the power along the flat meridian, the power along the steep meridian and the axis of the flat meridian. Most studies that investigate refractive data and corneal power analyse each of the three components individually rather than as a trivariate entity. In doing so, pertinent information may inadvertently be omitted.

Aim: The purpose of this review is to provide a brief overview of the multivariate statistics that are available to analyse multivariate data such as dioptric power. This will enable readers to better understand research that is analysed using these methods.

Method: An extensive review of databases such as Google Scholar, Science Direct and ResearchGate was done to gather publications on the topic of multivariate statistical analysis. Keywords such as multivariate statistical analysis, dioptric power, stereo-pairs, polar profiles and hypothesis testing were used to conduct the search.

Results: The debate for the need to analyse dioptric power using multivariate statistical methods has been a long-standing one. For this review, more than 40 publications were analysed to provide a simplified overview of the multivariate statistical methods that can be used to analyse dioptric power.

Conclusion: The use of multivariate statistical methods is a valuable tool in analysing and understanding dioptric power holistically and may provide more insights for research involving refractive error and corneal power.



multivariate statistical analysis; dioptric power space; dioptric power; stereo-pairs; polar profiles; hypothesis testing


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Crossref Citations

1. Multivariate analysis of refractive state in eyes with keratoconus
Elizabeth Chetty
BMJ Open Ophthalmology  vol: 8  issue: 1  first page: e001344  year: 2023  
doi: 10.1136/bmjophth-2023-001344