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Revista Cubana de Oftalmología

Print version ISSN 0864-2176On-line version ISSN 1561-3070


BALDAQUIN RODRIGUEZ, Waldemar  and  LAPIDO POLANCO. Statistical analysis of refractive data. Rev Cubana Oftalmol [online]. 2014, vol.27, n.2, pp.212-236. ISSN 0864-2176.

Objective: to describe the decomposition technique into Cartesian coordinates for the statistical analysis of refractive data and the proposal and exemplification of a methodology. Method: the Cartesian decomposition technique for the statistical analysis of refractive data was reviewed. Sample data were used to exemplify the algorithm. In the statistical analysis, summary measures and hypothesis tests were applied by using Student's t statistic and Hotelling's T2 for univariate and multivariate data, respectively. Results: a method that allows transforming data from one spherocylinder into a point in the three-dimensional space was described and exemplified, by means of the conversion of refraction into three independent orthogonal components of a Cartesian coordinate system. Unlike other mathematically equivalent methods, this technique brought about three components with optical significance to describe the sphere and the cylinder (the spherical equivalent and two Jackson crossed cylinders), thus eliminating the directional characteristics of data. In this system of Cartesian coordinates, the operations in real numbers are defined (addition, multiplication by scalars, among others), allowing mathematical and statistical analysis based on 3 x 1 matrices. The most common clinical measures that can be estimated with such a method are astigmatism variation, induced astigmatism, refractive surprise or error of the refractive procedure, mean astigmatism, comparison of population means, correlations, etc. Conclusions: the Cartesian representation of refraction is a non-polar notation that facilitates the graphical representation and statistical analysis of individual and population data.

Keywords : induced astigmatism; decomposition of refractive data.

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