Abstract
M.Phil. (Optometry)
Different representations of dioptric power and their relative coordinate systems are summarised. The transition matrices required to switch from one coordinate system to another are provided. Three sets of data are analysed; a sample of 205 refractions, a sample of 205 keratometric readings and a sample of 790 autorefractive excesses of 790 autorefractions over 790 subjective refractions. Brief mention is made of emmetropisation. In the event that such a driving force exists, the possible effects on the distributional characteristics of refractive error are noted. Normality and the assessment thereof are discussed qualitatively and quantitatively. The univariate marginal and multivariate joint distributions .of the samples are examined using the coordinate system introduced by Deal and Toop (1993): their vector is represented by d=(d 1 d 2 d3)~ Departure from normality is determined in three ways; assessment of
the linearity of the chi-square probability plots, measures of skewness and measures of kurtosis. Marginal normal probability plots are included for completeness. The statistical procedures and some of the theory involved in the implementation of these techniques are described briefly to assist in the interpretation of the distribution analysis. Marginal transformations are employed to improve the normality of the marginal distributions in an attempt to reduce the multivariate departure from normality. Power transformations and shifted power transformations are described and applied to
the data.