Non-normally distributed data and non-parametric statistics

Richard A. Armstrong

Research output: Contribution to journalArticle

Abstract

Different types of numerical data can be collected in a scientific investigation and the choice of statistical analysis will often depend on the distribution of the data. A basic distinction between variables is whether they are ‘parametric’ or ‘non-parametric’. When a variable is parametric, the data come from a symmetrically shaped distribution known as the ‘Gaussian’ or ‘normal distribution’ whereas non-parametric variables may have a distribution which deviates markedly in shape from normal. This article describes several aspects of the problem of non-normality including: (1) how to test for two common types of deviation from a normal distribution, viz., ‘skew’ and ‘kurtosis’, (2) how to fit the normal distribution to a sample of data, (3) the transformation of non-normally distributed data and scores, and (4) commonly used ‘non-parametric’ statistics which can be used in a variety of circumstances.
Language English 26 1 Optometry Today 51 16 Published - 19 Aug 2011

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Nonparametric Statistics
Gaussian distribution
Skew-normal Distribution
Non-normality
Kurtosis
Statistical Analysis
Deviation

Keywords

• numerical data
• scientific investigation
• choice
• statistical analysis
• distribution of data
• parametric
• distribution

Cite this

Armstrong, Richard A. / Non-normally distributed data and non-parametric statistics. In: Optometry Today. 2011 ; Vol. 51, No. 16. pp. 26.
title = "Non-normally distributed data and non-parametric statistics",
abstract = "Different types of numerical data can be collected in a scientific investigation and the choice of statistical analysis will often depend on the distribution of the data. A basic distinction between variables is whether they are ‘parametric’ or ‘non-parametric’. When a variable is parametric, the data come from a symmetrically shaped distribution known as the ‘Gaussian’ or ‘normal distribution’ whereas non-parametric variables may have a distribution which deviates markedly in shape from normal. This article describes several aspects of the problem of non-normality including: (1) how to test for two common types of deviation from a normal distribution, viz., ‘skew’ and ‘kurtosis’, (2) how to fit the normal distribution to a sample of data, (3) the transformation of non-normally distributed data and scores, and (4) commonly used ‘non-parametric’ statistics which can be used in a variety of circumstances.",
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Non-normally distributed data and non-parametric statistics. / Armstrong, Richard A.

In: Optometry Today, Vol. 51, No. 16, 19.08.2011, p. 26.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Non-normally distributed data and non-parametric statistics

AU - Armstrong, Richard A.

PY - 2011/8/19

Y1 - 2011/8/19

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AB - Different types of numerical data can be collected in a scientific investigation and the choice of statistical analysis will often depend on the distribution of the data. A basic distinction between variables is whether they are ‘parametric’ or ‘non-parametric’. When a variable is parametric, the data come from a symmetrically shaped distribution known as the ‘Gaussian’ or ‘normal distribution’ whereas non-parametric variables may have a distribution which deviates markedly in shape from normal. This article describes several aspects of the problem of non-normality including: (1) how to test for two common types of deviation from a normal distribution, viz., ‘skew’ and ‘kurtosis’, (2) how to fit the normal distribution to a sample of data, (3) the transformation of non-normally distributed data and scores, and (4) commonly used ‘non-parametric’ statistics which can be used in a variety of circumstances.

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KW - scientific investigation

KW - choice

KW - statistical analysis

KW - distribution of data

KW - parametric

KW - distribution

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