When you have completed this chapter, you will be able to: Conduct the sign test for single and dependent samples using the binomial and standard normal distributions as the test statistics, conduct a test of hypothesis for dependent samples using the Wilcoxon signed-rank test, conduct and interpret the Wilcoxon rank-sum test for independent samples,. | Chapter 16 Analysis of Ranked Data 1. Conduct the sign test for single and dependent samples using the binomial and standard normal distributions as the test statistics 2. Conduct a test of hypothesis for dependent samples using the Wilcoxon signed-rank test Chapter Goals When you have completed this chapter, you will be able to: and. 3. Conduct and interpret the Wilcoxon rank-sum test for independent samples Chapter Goals 4. 5. 6. Conduct and interpret the Kruskal-Wallis test for several independent samples Compute and interpret Spearman’s coefficient of rank correlation Conduct a test of hypothesis to determine whether the correlation among the ranks in the population is different from zero Terminology Range is the difference between the largest and the smallest value Only two values are used in its calculation It is influenced by an extreme value It is easy to compute and understand The Sign Test The Sign Test is based on the sign of a difference between two related observations | Chapter 16 Analysis of Ranked Data 1. Conduct the sign test for single and dependent samples using the binomial and standard normal distributions as the test statistics 2. Conduct a test of hypothesis for dependent samples using the Wilcoxon signed-rank test Chapter Goals When you have completed this chapter, you will be able to: and. 3. Conduct and interpret the Wilcoxon rank-sum test for independent samples Chapter Goals 4. 5. 6. Conduct and interpret the Kruskal-Wallis test for several independent samples Compute and interpret Spearman’s coefficient of rank correlation Conduct a test of hypothesis to determine whether the correlation among the ranks in the population is different from zero Terminology Range is the difference between the largest and the smallest value Only two values are used in its calculation It is influenced by an extreme value It is easy to compute and understand The Sign Test The Sign Test is based on the sign of a difference between two related observations . no assumption is necessary regarding the shape of the population of differences the binomial distribution is the test statistic for small samples and the standard normal (z) for large samples the test requires dependent (related) samples Determine the sign of the difference between related pairs Determine the number of usable pairs Compare the number of positive (or negative) differences to the critical value n is the number of usable pairs (without ties), x is the number of pluses or minuses, and the binomial probability p=.5 The Sign Test continued Procedure to conduct the test: if the number of pluses or minuses is more than n/2, then if the number of pluses or minuses is less than n/2, then Normal Approximation z x n n = - - ( . ) . . 5 5 5 z x n n = + - ( . ) . . 5 5 5 if both and are greater than 5, the z distribution is appropriate n p n ( ) 1 - p Example The Gagliano Research Institute for Business Studies is comparing the Research and Development expense (R&D) as
