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      Dioptric power and refractive behaviour: a review of methods and applications

      review-article
      , ,
      BMJ Open Ophthalmology
      BMJ Publishing Group
      optics and refraction, vision, public health

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          Abstract

          Myopia is a global healthcare concern and effective analyses of dioptric power are important in evaluating potential treatments involving surgery, orthokeratology, drugs such as low-dose (0.05%) atropine and gene therapy. This paper considers issues of concern when analysing refractive state such as data normality, transformations, outliers and anisometropia. A brief review of methods for analysing and representing dioptric power is included but the emphasis is on the optimal approach to understanding refractive state (and its variation) in addressing pertinent clinical and research questions.

          Although there have been significant improvements in the analysis of refractive state, areas for critical consideration remain and the use of power matrices as opposed to power vectors is one such area. Another is effective identification of outliers in refractive data. The type of multivariate distribution present with samples of dioptric power is often not considered. Similarly, transformations of samples (of dioptric power) towards normality and the effects of such transformations are not thoroughly explored. These areas (outliers, normality and transformations) need further investigation for greater efficacy and proper inferences regarding refractive error. Although power vectors are better known, power matrices are accentuated herein due to potential advantages for statistical analyses of dioptric power such as greater simplicity, completeness, and improved facility for quantitative and graphical representation of refractive state.

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          Measures of multivariate skewness and kurtosis with applications

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            Power vectors: an application of Fourier analysis to the description and statistical analysis of refractive error.

            The description of sphero-cylinder lenses is approached from the viewpoint of Fourier analysis of the power profile. It is shown that the familiar sine-squared law leads naturally to a Fourier series representation with exactly three Fourier coefficients, representing the natural parameters of a thin lens. The constant term corresponds to the mean spherical equivalent (MSE) power, whereas the amplitude and phase of the harmonic correspond to the power and axis of a Jackson cross-cylinder (JCC) lens, respectively. Expressing the Fourier series in rectangular form leads to the representation of an arbitrary sphero-cylinder lens as the sum of a spherical lens and two cross-cylinders, one at axis 0 degree and the other at axis 45 degrees. The power of these three component lenses may be interpreted as (x,y,z) coordinates of a vector representation of the power profile. Advantages of this power vector representation of a sphero-cylinder lens for numerical and graphical analysis of optometric data are described for problems involving lens combinations, comparison of different lenses, and the statistical distribution of refractive errors.
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              Nonparametric statistical tests for the continuous data: the basic concept and the practical use

              Conventional statistical tests are usually called parametric tests. Parametric tests are used more frequently than nonparametric tests in many medical articles, because most of the medical researchers are familiar with and the statistical software packages strongly support parametric tests. Parametric tests require important assumption; assumption of normality which means that distribution of sample means is normally distributed. However, parametric test can be misleading when this assumption is not satisfied. In this circumstance, nonparametric tests are the alternative methods available, because they do not required the normality assumption. Nonparametric tests are the statistical methods based on signs and ranks. In this article, we will discuss about the basic concepts and practical use of nonparametric tests for the guide to the proper use.
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                Author and article information

                Journal
                BMJ Open Ophthalmol
                BMJ Open Ophthalmol
                bmjophth
                bmjophth
                BMJ Open Ophthalmology
                BMJ Publishing Group (BMA House, Tavistock Square, London, WC1H 9JR )
                2397-3269
                2022
                1 April 2022
                : 7
                : 1
                : e000929
                Affiliations
                [1] departmentDepartment of Optometry , University of Johannesburg - Doornfontein Campus , Johannesburg, Gauteng, South Africa
                Author notes
                [Correspondence to ] Professor Alan Rubin; arubin@ 123456uj.ac.za
                Author information
                http://orcid.org/0000-0001-6217-7862
                http://orcid.org/0000-0001-8307-2912
                http://orcid.org/0000-0002-4105-5513
                Article
                bmjophth-2021-000929
                10.1136/bmjophth-2021-000929
                8977790
                38a4159a-badd-4073-81f2-99d6392a52e5
                © Author(s) (or their employer(s)) 2022. Re-use permitted under CC BY-NC. No commercial re-use. See rights and permissions. Published by BMJ.

                This is an open access article distributed in accordance with the Creative Commons Attribution Non Commercial (CC BY-NC 4.0) license, which permits others to distribute, remix, adapt, build upon this work non-commercially, and license their derivative works on different terms, provided the original work is properly cited, appropriate credit is given, any changes made indicated, and the use is non-commercial. See:  http://creativecommons.org/licenses/by-nc/4.0/.

                History
                : 19 October 2021
                : 16 February 2022
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                optics and refraction,vision,public health
                optics and refraction, vision, public health

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