Chapter 14 formulas

# Chapter 14 formulas - Lecture Notes Chapter Fourteen:...

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Lecture Notes Chapter Fourteen: Nonparametric Statistics Randall Miller Key Symbols o η Population median o S Test statistic for sign test o 1 T Sum of ranks of observations in sample 1 o 2 T Sum of ranks of observations in sample 2 o L T Critical lower Wilcoxon rank sum value o U T Critical upper Wilcoxon rank sum value o T + Sum of ranks of positive differences of paired observations o T Sum of ranks of negative differences of paired observations o 0 T Critical value of Wilcoxon signed ranks test o j R Rank sum of observations in sample j o H Test statistic for Kruskal – Wallis test o r F Test statistic for Friedman test o s r Spearman’s rank correlation coefficient o ρ Population correlation coefficient Formulas Sign Test for a Population Median One-Tailed Test [ ] 00 : : or : aa H HH ηη = >< Test statistic : S = Number of sample measurements greater than 0 [or S = number of measurements less than 0 ] Two-Tailed Test 0 : : a H H = Test Statistic : S = Larger of 12 and SS where 1 S is the number of measurements less than 0 and 2 S is the number of measurements greater than 0 [ Note : Eliminate observation from the analysis that are exactly equal to the hypothesized median, 0 .] Observed significance level : p -value = ( ) Px S Observed significance level : p -value = ( ) 2 where x has a binomial distribution with parameter n and p = .5. (Use Table II, Appendix A.)

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Lecture Notes Chapter Fourteen: Nonparametric Statistics Randall Miller Rejection region : zz α > Rejection region : /2 > Where tabulated z -values can be found in Table IV, Appendix A. Large Sample Sign Test for a Population Median η One-Tailed Test [ ] 00 : : or : aa H HH ηη = >< Two-Tailed Test 0 : : a H H = Test statistic : ( ) .5 .5 .5 Sn z n −− = [ Note : S is calculated as shown above. We subtract .5 from S as the “correction for continuity.” The null-hypothesized mean value is .5 np n = , and the standard deviation is ( )( ) .5 .5 .5 npq n n = = (See Chapter 5 for details on the normal approximation to the binomial distribution.)] Rejection region : > Rejection region : > where tabulated z -values can be found in Table IV, Appendix A.
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## This note was uploaded on 07/23/2011 for the course STA 3123 taught by Professor Staff during the Fall '08 term at FIU.

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Chapter 14 formulas - Lecture Notes Chapter Fourteen:...

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