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Chapter Fourteen

Chapter Fourteen - Lecture Notes Chapter Fourteen...

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Lecture Notes Chapter Fourteen: Nonparametric Statistics Randall Miller 1 | P a g e 1. Introduction: Distribution-Free Tests Definition 14.1 Distribution-free tests are statistical that do not rely on any underlying assumptions about the probability distribution of the sampled population. Definition 14.2 The branch of inferential statistics devoted to distribution-free test is call nonparametrics . Definition 14.3 Nonparametric statistics (or test) based on the ranks of measurements are called rank statistics (or rank test ). 2. Single-Population Inferences Sign Test for a Population Median η One-Tailed Test [ ] 0 0 0 0 : : or : a a H H H η η η η η η = > < Test statistic : S = Number of sample measurements greater than 0 η [or S = number of measurements less than 0 η ] Two-Tailed Test 0 0 0 : : a H H η η η η = Test Statistic : S = Larger of 1 2 and S S where 1 S is the number of measurements less than 0 η and 2 S is the number of measurements greater than 0 η [ Note : Eliminate observation from the analysis that are exactly equal to the hypothesized median, 0 η .] Observed significance level : p -value = ( ) P x S Observed significance level : p -value = ( ) 2 P x S where x has a binomial distribution with parameter n and p = .5. (Use Table II, Appendix A.) Rejection region : z z α > Rejection region : /2 z z α > Where tabulated z 0values can be found in Table IV, Appendix A.
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