Chapter 11.3（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 11.3 The Kruskal-Wallis Test . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Section 11.3 Objectives How to use the Kruskal-Wallis test to determine whether three or more samples were selected from populations having the same distribution. . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. The Kruskal-Wallis Test Kruskal-Wallis test A nonparametric test that can be used to determine whether three or more independent samples were selected from populations having the same distribution. The null and alternative hypotheses for the Kruskal-Wallis test are always similar to these statements. H0: All of the populations have the same distribution. Ha: At least one population has a distribution that is different from the others. . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. The Kruskal-Wallis Test Two conditions for using the Kruskal-Wallis test are Samples must be random and independent. The size of each sample must be at least 5. If these conditions are met, then the sampling distribution for the Kruskal-Wallis test is approximated by a chi-square distribution with k – 1 degrees of freedom, where k is the number of samples. . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. The Kruskal-Wallis Test Test Statistic for the Kruskal-Wallis Test For three or more independent samples, the test statistic, H, for the Kruskal-Wallis test is where k represent the number of samples, ni is the size of the ith sample, N is the sum of the sample sizes, and Ri is the sum of the ranks of the ith sample. . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Performing a Kruskal-Wallis Test Verify that the samples are random and independe