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Nonparametric and Distribution-Free Statistics (1).docx

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Aaron Childs

November 27 , 2012 Stats 2B03: Statistical Methods for Science Nonparametric and Distribution-Free Statistics (1) 13.1 Introduction - nonparametric procedures are those that do not make any assumptions about the type of distribution (e.g. normal) or about the parameters (e.g. σ 1σ ) 2f the sampled population. They can be used in place of the parametric procedures whenever such assumptions are not satisfied - notes:  in general, nonparametric procedures do not use all of the available information in the sample. Therefore if the assumptions of the parametric test are satisfied then for a given significance level α the nonparametric procedures have a higher probability of type II error (or lower power) than the corresponding parametric procedure  if any of the parametric assumptions are not satisfied, then the significance level of the parametric procedure is not known (it is not equal to the α value that you choose when you use the procedure). Therefore the parametric procedure cannot be used 13.4 The Wilcoxon signed-rank test - non parametric alternative to a z- or t-test for a single population mean μ - we want to test:  H A μ>μ 0  H A μ
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