Nonparametric Statistics

Greg W. Corder is Adjunct Instructor in the Department of Physics and Astronomy at James Madison University.  He is also Adjunct Instructor of graduate education at Mary Baldwin College. Dale I. Foreman is Professor Emeritus in the School of Education and Human Development at Shenandoah University.

• Preface ixList of Variables xiiiChapter 1 Nonparametric Statistics: An Introduction 11.1 Objectives 11.2 Introduction 11.3 The Nonparametric Statistical Procedures Presented in This Book 31.3.1 State the Null and Research Hypotheses 41.3.2 Set the Level of Risk (or the Level of Significance) Associated with the Null Hypothesis 41.3.3 Choose the Appropriate Test Statistic 51.3.4 Compute the Test Statistic 51.3.5 Determine the Value Needed for Rejection of the Null Hypothesis Using the Appropriate Table of Critical Values for the Particular Statistic 51.3.6 Compare the Obtained Value with the Critical Value 61.3.7 Interpret the Results 61.3.8 Reporting the Results 61.4 Ranking Data 61.5 Ranking Data with Tied Values 71.6 Counts of Observations 81.7 Summary 91.8 Practice Questions 91.9 Solutions to Practice Questions 10Chapter 2 Testing Data for Normality 132.1 Objectives 132.2 Introduction 132.3 Describing Data and the Normal Distribution 142.4 Computing and Testing Kurtosis and Skewness for Sample Normality 172.4.1 Sample Problem for Examining Kurtosis 192.4.2 Sample Problem for Examining Skewness 222.4.3 Examining Skewness and Kurtosis for Normality Using SPSS 242.5 Computing the Kolmogorov–Smirnov One-Sample Test 272.5.1 Sample Kolmogorov–Smirnov One-Sample Test 292.5.2 Performing the Kolmogorov–Smirnov One-Sample Test Using SPSS 342.6 Summary 372.7 Practice Questions 372.8 Solutions to Practice Questions 38Chapter 3 Comparing Two Related Samples: The Wilcoxon Signed Rank and the Sign Test 393.1 Objectives 393.2 Introduction 393.3 Computing the Wilcoxon Signed Rank Test Statistic 403.3.1 Sample Wilcoxon Signed Rank Test (Small Data Samples) 413.3.2 Confidence Interval for the Wilcoxon Signed Rank Test 433.3.3 Sample Wilcoxon Signed Rank Test (Large Data Samples) 453.4 Computing the Sign Test 493.4.1 Sample Sign Test (Small Data Samples) 503.4.2 Sample Sign Test (Large Data Samples) 533.5 Performing the Wilcoxon Signed Rank Test and the Sign Test Using SPSS 573.5.1 Define Your Variables 573.5.2 Type in Your Values 573.5.3 Analyze Your Data 583.5.4 Interpret the Results from the SPSS Output Window 583.6 Statistical Power 603.7 Examples from the Literature 613.8 Summary 613.9 Practice Questions 623.10 Solutions to Practice Questions 65Chapter 4 Comparing Two Unrelated Samples: The Mann−Whitney U-Test and the Kolmogorov−Smirnov Two-Sample Test 694.1 Objectives 694.2 Introduction 694.3 Computing the Mann−Whitney U-Test Statistic 704.3.1 Sample Mann−Whitney U-Test (Small Data Samples) 714.3.2 Confidence Interval for the Difference between Two Location Parameters 744.3.3 Sample Mann−Whitney U-Test (Large Data Samples) 754.4 Computing the Kolmogorov–Smirnov Two-Sample Test Statistic 804.4.1 Sample Kolmogorov–Smirnov Two-Sample Test 814.5 Performing the Mann–Whitney U-Test and the Kolmogorov–Smirnov Two-Sample Test Using SPSS 844.5.1 Define Your Variables 844.5.2 Type in Your Values 854.5.3 Analyze Your Data 864.5.4 Interpret the Results from the SPSS Output Window 864.6 Examples from the Literature 884.7 Summary 894.8 Practice Questions 904.9 Solutions to Practice Questions 92Chapter 5 Comparing More Than Two Related Samples: The Friedman Test 975.1 Objectives 975.2 Introduction 975.3 Computing the Friedman Test Statistic 985.3.1 Sample Friedman’s Test (Small Data Samples without Ties) 995.3.2 Sample Friedman’s Test (Small Data Samples with Ties) 1015.3.3 Performing the Friedman Test Using SPSS 1055.3.4 Sample Friedman’s Test (Large Data Samples without Ties) 1085.4 Examples from the Literature 1115.5 Summary 1125.6 Practice Questions 1135.7 Solutions to Practice Questions 114Chapter 6 Comparing More Than Two Unrelated Samples: The Kruskal–Wallis H-Test 1176.1 Objectives 1176.2 Introduction 1176.3 Computing the Kruskal–Wallis H-Test Statistic 1186.3.1 Sample Kruskal–Wallis H-Test (Small Data Samples) 1196.3.2 Performing the Kruskal–Wallis H-Test Using SPSS 1246.3.3 Sample Kruskal–Wallis H-Test (Large Data Samples) 1286.4 Examples from the Literature 1346.5 Summary 1346.6 Practice Questions 1356.7 Solutions to Practice Questions 136Chapter 7 Comparing Variables of Ordinal or Dichotomous Scales: Spearman Rank Order, Point-Biserial, and Biserial Correlations 1397.1 Objectives 1397.2 Introduction 1397.3 The Correlation Coefficient 1407.4 Computing the Spearman Rank-Order Correlation Coefficient 1407.4.1 Sample Spearman Rank-Order Correlation (Small Data Samples without Ties) 1427.4.2 Sample Spearman Rank-Order Correlation (Small Data Samples with Ties) 1457.4.3 Performing the Spearman Rank-Order Correlation Using SPSS 1487.5 Computing the Point-Biserial and Biserial Correlation Coefficients 1507.5.1 Correlation of a Dichotomous Variable and an Interval Scale Variable 1507.5.2 Correlation of a Dichotomous Variable and a Rank-Order Variable 1527.5.3 Sample Point-Biserial Correlation (Small Data Samples) 1527.5.4 Performing the Point-Biserial Correlation Using SPSS 1567.5.5 Sample Point-Biserial Correlation (Large Data Samples) 1597.5.6 Sample Biserial Correlation (Small Data Samples) 1637.5.7 Performing the Biserial Correlation Using SPSS 1677.6 Examples from the Literature 1677.7 Summary 1677.8 Practice Questions 1687.9 Solutions to Practice Questions 170Chapter 8 Tests for Nominal Scale Data: Chi-Square and Fisher Exact Tests 1728.1 Objectives 1728.2 Introduction 1728.3 The χ2 Goodness-of-Fit Test 1728.3.1 Computing the χ2 Goodness-of-Fit Test Statistic 1738.3.2 Sample χ2 Goodness-of-Fit Test (Category Frequencies Equal) 1738.3.3 Sample χ2 Goodness-of-Fit Test (Category Frequencies Not Equal) 1768.3.4 Performing the χ2 Goodness-of-Fit Test Using SPSS 1808.4 The χ2 Test for Independence 1848.4.1 Computing the χ2 Test for Independence 1858.4.2 Sample χ2 Test for Independence 1868.4.3 Performing the χ2 Test for Independence Using SPSS 1908.5 The Fisher Exact Test 1968.5.1 Computing the Fisher Exact Test for 2 × 2 Tables 1978.5.2 Sample Fisher Exact Test 1978.5.3 Performing the Fisher Exact Test Using SPSS 2018.6 Examples from the Literature 2028.7 Summary 2038.8 Practice Questions 2048.9 Solutions to Practice Questions 206Chapter 9 Test for Randomness: The Runs Test 2109.1 Objectives 2109.2 Introduction 2109.3 The Runs Test for Randomness 2109.3.1 Sample Runs Test (Small Data Samples) 2129.3.2 Performing the Runs Test Using SPSS 2139.3.3 Sample Runs Test (Large Data Samples) 2179.3.4 Sample Runs Test Referencing a Custom Value 2199.3.5 Performing the Runs Test for a Custom Value Using SPSS 2219.4 Examples from the Literature 2259.5 Summary 2259.6 Practice Questions 2259.7 Solutions to Practice Questions 227Appendix A SPSS at a Glance 229Appendix B Critical Value Tables 235References 261Index 265