SOME STATISTICAL CONCEPTS IN THE ANALYSIS OF VISION AND VISUAL ACUITY

Abstract— As conventionally recorded, visual acuity data constitute an ordinal scale of measurement. An investigation of four different clinical samples shows that visual acuity is not normally distributed amongst these populations. Furthermore, acuity is often measured on charts which, by the inherent restriction of the stimulus size, have the effect of truncating the upper limit of the scale producing, in statistical terms, an incomplete distribution. The distribution of acuity for each sample is found to be adequately described in terms of the equation: F(x) =Axα(T‐x)β, where F(x) is the cumulative distribution of the statistical population, T is the truncation level (known), x is the Snellen decimal acuity (known) and A, α and β are parameters. Alternative analytical procedures based upon this model, which overcome these limitations, are discussed.