Chapter 11.4（课件）- 《统计学基础（英文版）》同步教学（人民大学版）

Chapter Nonparametric Tests 11 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 1 Larson/Farber 6th ed Chapter 1 Chapter Outline 11.1 The Sign Test 11.2 The Wilcoxon Tests 11.3 The Kruskal-Wallis Test 11.4 Rank Correlation 11.5 The Runs Test . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Section 11.4 Rank Correlation . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Section 11.4 Objectives How to use the Spearman rank correlation coefficient to determine whether the correlation between two variables is significant. . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. The Spearman Rank Correlation Coefficient Spearman Rank Correlation Coefficient A measure of the strength of the relationship between two variables. The Spearman rank correlation coefficient is calculated using the ranks of paired sample data entries. If there are no ties in the ranks of either variable, then the formula for the Spearman rank correlation coefficient is rs = 1 − where n is the number of paired data entries and d is the difference between the ranks of a paired data entry. If there are ties in the ranks and the number of ties is small relative to the number of data pairs, then the formula can still be used to approximate rs. . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. The Spearman Rank Correlation Coefficient The values of rs range from 1 to 1, inclusive. When the ranks of corresponding data pairs are identical, rs is equal to +1. When the ranks are in “reverse” order, rs is equal to −1. When there is no relationship, rs is equal to 0. To determine whether the correlation between variables is significant, you can perform a hypothesis test for the population correlation coefficient ρs. . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. The Spearman Rank Correlation Coefficient The null and alternative hypotheses for this test are as follows. H0: ρs = 0 (There is no correlation between variables.) Ha: ρs  0 (There is a significant correl