Application of parametric statistics to visual acuity data

ETDRS charts with logarithmic notation are widely used for measuring visual acuity in clinical studies worldwide. However, the distribution of measurement results often deviates from normal, limiting the applicability of parametric statistical methods, which are more powerful than the non-parametric ones. In cases of significant skewness, raw data can undergo power transformation with varying exponents (λ), as described by J.W. Tukey. The optimal transformation is considered the one that best normalizes the data. The formulas for common visual acuity notations coincide with specific members of Tukey’s power function family to within a sign (decimal: λ=–1.0; logarithmic: λ=0). Purpose. This study uses Tukey’s power transformations to identify the visual acuity notation most suitable for parametric statistical methods. Material and methods. The study analyzed both original measurement results and reconstructed visual acuity data from several large multicenter studies: the Central India Eye and Medical Study (CIEMS) — 4711 participants; the Early Treatment Diabetic Retinopathy Study (ETDRS) — 3710 participants; the Age-related Eye Disease Study 2 (AREDS2) — 4203 participants. Original data were obtained by measuring visual acuity in both eyes of 100 healthy volunteers using the ETDRS protocol. Visual acuity distribution for each multicenter study was reconstructed from histograms in the corresponding publications. Results. In all cases, the exponent for the optimal transformation was closer to that for decimal notation (–1.0) than logarithmic notation (0): CIEMS — λ=–1.31; ETDRS — λ=–0.8; AREDS2 — λ=–0.88; original data — λ=–1.66. The optimal transformation did not pass the Shapiro-Wilk test for normality in any of the cases. The distribution closest to normal was obtained when analyzing the original data, likely due to the Shapiro-Wilk test’s sensitivity to repeating values. Conclusion. The authors recommend using decimal notation for the statistical processing and presentation of visual acuity data, as it is more appropriate for parametric statistical methods.