Lecture Notes Chapter Fourteen: Nonparametric Statistics Randall Miller 1 | P a g e 1.Introduction: Distribution-Free TestsDefinition 14.1 Distribution-free testsare 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 InferencesSign Test for a Population Median ηOne-Tailed Test 0000::or :aaHHHηηηηηη=><Test statistic: S= Number of sample measurements greater than 0η[or S= number of measurements less than 0η] Two-Tailed Test 000::aHHηηηη=≠Test Statistic: S= Larger of 12and SSwhere 1Sis the number of measurements less than 0ηand 2Sis the number of measurements greater than 0η[Note: Eliminate observation from the analysis that are exactly equal to the hypothesized median, 0η.] Observed significance level: p-value = ()P xS≥Observed significance level: p-value = ()2P xS≥where xhas a binomial distribution with parameter nand p= .5. (Use Table II, Appendix A.) Rejection region: zzα>Rejection region: /2zzα>Where tabulated z0values can be found in Table IV, Appendix A.
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