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Chapter 13

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McMaster University
Aaron Childs

Stats 2B03: Statistical Methods for Science Chapter 13: Nonparametric and Distribution-Free Statistics 13.1 Introduction - Only those procedures that test hypotheses that are not statements about population parameters are classified as nonparametric, while those that make no assumption about the sampled population are distribution-free procedures - They allow for the testing of hypotheses that are not statements about population parameter values. Some of the chi-square tests of goodness-of-fit and the tests of independence are examples of tests possessing this advantage - Nonparametric tests may be used when the form of the sampled population is unknown - Nonparametric procedures tend to be computationally easier and consequently more quickly applied than parametric procedures. This can be a desirable feature in certain cases, but when time is not at a premium, it merits a low priority as a criterion for choosing a nonparametric test. - Nonparametric procedures may be applied when the data being analyzed consist merely of rankings or classifications. That is, the data may not be based on a measurement scale strong enough to allow the arithmetic operations necessary for carrying out parametric procedures. - The use of nonparametric procedures with data that can be handled with a parametric procedure results in a waste of data - The application of some of the nonparametric tests may be laborious for large samples 13.4 The Wilcoxon Signed-Rank Test for Location - Assumptions:  The sample is random  The variable is continuous  The population is symmetrically distributed about its mean μ  The measurement scale is at least interval - Hypotheses:  Subtract the hypothesized mean μ from ea0h observation x, to obtain i d i x i μ .0If any x ii equal to the mean, so that d = 0,ieliminate that d i from the calculations and reduce n accordingly  Rank the usable d from the smallest to the largest without regard to i the sign of d,ithat is consider only the absolute value of the d, i designated |d|, ihen ranking them. If two or more of the |d| are i equal, assign each tied value of the mean of the rank positions the tied values occupy. If, for example, the three smallest |d | are ill equal, place them in rank pos
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