Transformation of arbitrary distributions to the normal distribution with application to EEG test-retest reliability Export

@article{citeulike:3102832, abstract = {Many variables in the social, physical, and biosciences, including neuroscience, are non-normally distributed. To improve the statistical properties of such data, or to allow parametric testing, logarithmic or logit transformations are often used. Box-Cox transformations or ad hoc methods are sometimes used for parameters for which no transformation is known to approximate normality. However, these methods do not always give good agreement with the Gaussian. A transformation is discussed that maps probability distributions as closely as possible to the normal distribution, with exact agreement for continuous distributions. To illustrate, the transformation is applied to a theoretical distribution, and to quantitative electroencephalographic (qEEG) measures from repeat recordings of 32 subjects which are highly non-normal. Agreement with the Gaussian was better than using logarithmic, logit, or Box-Cox transformations. Since normal data have previously been shown to have better test-retest reliability than non-normal data under fairly general circumstances, the implications of our transformation for the test-retest reliability of parameters were investigated. Reliability was shown to improve with the transformation, where the improvement was comparable to that using Box-Cox. An advantage of the general transformation is that it does not require laborious optimization over a range of parameters or a case-specific choice of form.}, author = {van Albada, S. J. and Robinson, P. A.}, citeulike-article-id = {3102832}, citeulike-linkout-0 = {http://dx.doi.org/10.1016/j.jneumeth.2006.11.004}, citeulike-linkout-1 = {http://www.sciencedirect.com/science/article/B6T04-4MR7D3V-1/2/a47b3dda47a4aaff0ae704b3a56844b8}, day = {15}, doi = {10.1016/j.jneumeth.2006.11.004}, journal = {Journal of Neuroscience Methods}, keywords = {normal\_distribution, probability\_distributions, transformations}, month = {April}, number = {2}, pages = {205--211}, posted-at = {2009-09-25 14:39:51}, priority = {0}, title = {Transformation of arbitrary distributions to the normal distribution with application to EEG test-retest reliability}, url = {http://dx.doi.org/10.1016/j.jneumeth.2006.11.004}, volume = {161}, year = {2007} }

TY - JOUR ID - citeulike:3102832 L3 - citeulike-article-id:3102832 N2 - Many variables in the social, physical, and biosciences, including neuroscience, are non-normally distributed. To improve the statistical properties of such data, or to allow parametric testing, logarithmic or logit transformations are often used. Box-Cox transformations or ad hoc methods are sometimes used for parameters for which no transformation is known to approximate normality. However, these methods do not always give good agreement with the Gaussian. A transformation is discussed that maps probability distributions as closely as possible to the normal distribution, with exact agreement for continuous distributions. To illustrate, the transformation is applied to a theoretical distribution, and to quantitative electroencephalographic (qEEG) measures from repeat recordings of 32 subjects which are highly non-normal. Agreement with the Gaussian was better than using logarithmic, logit, or Box-Cox transformations. Since normal data have previously been shown to have better test-retest reliability than non-normal data under fairly general circumstances, the implications of our transformation for the test-retest reliability of parameters were investigated. Reliability was shown to improve with the transformation, where the improvement was comparable to that using Box-Cox. An advantage of the general transformation is that it does not require laborious optimization over a range of parameters or a case-specific choice of form. IS - 2 JF - Journal of Neuroscience Methods EP - 211 TI - Transformation of arbitrary distributions to the normal distribution with application to EEG test-retest reliability VL - 161 SP - 205 KW - normal_distribution KW - probability_distributions KW - transformations AU - van Albada, SJ AU - Robinson, PA PY - 2007/04/15/ UR - http://dx.doi.org/10.1016/j.jneumeth.2006.11.004 ER -