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Ophthalmic statistics note 9: parametric versus non-parametric methods for data analysis
  1. Simon S Skene1,
  2. Catey Bunce2,
  3. Nick Freemantle3,
  4. Caroline J Doré1
  5. On behalf of the Ophthalmic Statistics Group
    1. 1Comprehensive Clinical Trials Unit, University College London, London, UK
    2. 2NIHR Biomedical Research Centre at Moorfields Eye Hospital NHS Foundation Trust and UCL Institute of Ophthalmology, London, UK
    3. 3Department of Primary Care and Population Health, University College London, London, UK
    1. Correspondence to Dr Simon S Skene, Comprehensive Clinical Trials Unit, University College London, Gower Street, London, WC1E 6BT, UK; s.skene{at}

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    Distributions of measured data are often well modelled by known probability distributions, which provide a useful description of their underlying properties such as location (average), spread (variation) and shape. Statisticians use probability distributions to interpret and attribute meaning, draw conclusions and answer research questions using the measurements or data that researchers gather during their studies. Different types of data follow different probability distributions, and these distributions are characterised by certain features called parameters. Even the most statistically averse of researchers is likely to have heard of the normal distribution, which is often used to approximate the distribution of continuous or measurement data such as intraocular pressure, central retinal thickness and degree of proptosis. The normal distribution follows a ‘bell-shaped curve’ (although with a rim stretching to ±infinity) the shape of which is specified by the mean and SD, with different values of each, giving rise to different bell-shaped curves (see figure 1).

    Figure 1

    Examples of the normal N (µ, σ) distributions parameterised by different values of mean (µ) and SD (σ).

    Other distributions such as the binomial and Poisson probability distributions are less commonly reported in ophthalmic research and are characterised by different parameters. The binomial distribution is used for dichotomous data and is characterised by the probability of success, that is, the number of ‘successes’ out of a total number of observed events, for example, the proportion of graft transplants that fail within 6 months of transplantation. The Poisson distribution is used for counts data and is characterised by the mean number of events, for example, endophthalmitis rates.

    The assumption that the observed data follow such probability distributions allows a statistician to apply appropriate statistical tests, which are known as parametric tests. The normal distribution is a powerful tool provided the data plausibly arise from that distribution or can be …

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    • Collaborators Valentina Cipriani, Jonathan Cook, David Crabb, Phillippa Cumberland, Gabriela Czanner, Paul Donachie, Andrew Elders, Marta Garcia Finana, Rachel Nash, Ana Quartilho, Chris Rogers, Luke Saunders, John Stephenson, Irene Stratton, Wen Xing, Haogang Zhu.

    • Contributors SSS drafted the paper, CB reviewed and revised the paper, NF and CJD conducted an internal peer review and provided additional comment.

    • Funding The post of CB is partly funded by the National Institute for Health Research Biomedical Research Centre based at Moorfields Eye Hospital National Health Service Foundation Trust and UCL Institute of Ophthalmology.

    • Disclaimer The views expressed in this article are those of the authors and not necessarily those of the National Health Service, the National Institute for Health Research or the Department of Health.

    • Competing interests None declared.

    • Provenance and peer review Not commissioned; externally peer reviewed.

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