Multivariate analysis of refractive data: mathematics and statistics of spherocylinders

Abstract

Purpose: To develop methods for multivariate statistical analysis of spherocylinders and to use these methods to compare autorefraction and manifest subjective refraction in 50 healthy eyes.

Setting: Department of Ophthalmology, Arhus University Hospital, Arhus, Denmark.

Methods: A method was developed to transform a spherocylinder to a suitable format as a spherical equivalent power (SEP) and 2 polar values, separated by an arch of 45 degrees, a so-called power-vector format. The accuracy of autorefraction was defined as the difference between autorefraction and manifest refraction, using the described power vector. These entities were subjected to multivariate analysis using the Hotelling T2 test. A method of graphic analysis was developed, using matrix algebra and computation of eigenvectors and eigenvalues.

Results: For individual data, the variation was considerably larger for the SEP than for the astigmatism. For aggregate data, univariate, bivariate, and trivariate statistical analysis did not demonstrate significant average differences between the 2 refraction methods. No refractive components and no combinations of refractive components displayed significant mean differences.

Conclusions: The study confirmed our clinical experience that the astigmatism derived from autorefraction is nearly identical to manifest refraction, while the sphere needs some adjustment. In groups of healthy eyes, autorefraction can be used as a substitute for manifest refraction. Statistical analysis of spherocylinders, including evaluation of refractive procedures, can be performed in an exact manner with multivariate statistics.