Nonparametric Statistics: A Step-by-Step Approach
[Book Description]
a very useful resource for courses in nonparametric statistics in which the emphasis is on applications rather than on theory. It also deserves a place in libraries of all institutions where introductory statistics courses are taught." CHOICE This Second Edition presents a practical and understandable approach that enhances and expands the statistical toolset for readers. This book includes: * New coverage of the sign test and the Kolmogorov-Smirnov two-sample test in an effort to offer a logical and natural progression to statistical power * SPSS(R) (Version 21) software and updated screen captures to demonstrate how to perform and recognize the steps in the various procedures * Data sets and odd-numbered solutions provided in an appendix, and tables of critical values * Supplementary material to aid in reader comprehension, which includes: narrated videos and screen animations with step-by-step instructions on how to follow the tests using SPSS; online decision trees to help users determine the needed type of statistical test; and additional solutions not found within the book.
[Table of Contents]
Preface ix
List Of Variables xiii
Chapter 1 Nonparametric Statistics: An 1 (12)
Introduction
1.1 Objectives 1 (1)
1.2 Introduction 1 (2)
1.3 The Nonparametric Statistical Procedures 3 (3)
Presented in This Book
1.3.1 State the Null and Research Hypotheses 4 (1)
1.3.2 Set the Level of Risk (or the Level 4 (1)
of Significance) Associated with the Null
Hypothesis
1.3.3 Choose the Appropriate Test Statistic 5 (1)
1.3.4 Compute the Test Statistic 5 (1)
1.3.5 Determine the Value Needed for 5 (1)
Rejection of the Null Hypothesis Using the
Appropriate Table of Critical Values for
the Particular Statistic
1.3.6 Compare the Obtained Value with the 6 (1)
Critical Value
1.3.7 Interpret the Results 6 (1)
1.3.8 Reporting the Results 6 (1)
1.4 Ranking Data 6 (1)
1.5 Ranking Data with Tied Values 7 (1)
1.6 Counts of Observations 8 (1)
1.7 Summary 9 (1)
1.8 Practice Questions 9 (1)
1.9 Solutions to Practice Questions 10 (3)
Chapter 2 Testing Data For Normality 13 (26)
2.1 Objectives 13 (1)
2.2 Introduction 13 (1)
2.3 Describing Data and the Normal 14 (3)
Distribution
2.4 Computing and Testing Kurtosis and 17 (10)
Skewness for Sample Normality
2.4.1 Sample Problem for Examining Kurtosis 19 (3)
2.4.2 Sample Problem for Examining Skewness 22 (2)
2.4.3 EXamining Skewness and Kurtosis for 24 (3)
Normality Using SPSS
2.5 Computing the Kolmogorov-Smirnov 27 (10)
One-Sample Test
2.5.1 Sample Kolmogorov-Smirnov One-Sample 29 (5)
Test
2.5.2 Performing the Kolmogorov-Smirnov 34 (3)
One-Sample Test Using SPSS
2.6 Summary 37 (1)
2.7 Practice Questions 37 (1)
2.8 Solutions to Practice Questions 38 (1)
Chapter 3 Comparing Two Related Samples: The 39 (30)
Wilcoxon Signed Rank And The Sign Test
3.1 Objectives 39 (1)
3.2 Introduction 39 (1)
3.3 Computing the Wilcoxon Signed Rank Test 40 (9)
Statistic
3.3.1 Sample Wilcoxon Signed Rank Test 41 (2)
(Small Data Samples)
3.3.2 Confidence Interval for the Wilcoxon 43 (2)
Signed Rank Test
3.3.3 Sample Wilcoxon Signed Rank Test 45 (4)
(Large Data Samples)
3.4 Computing the Sigh Test 49 (8)
3.4.1 Sample Sign Test (Small Data Samples) 50 (3)
3.4.2 Sample Sign Test (Large Data Samples) 53 (4)
3.5 Performing the Wilcoxon Signed Rank Test 57 (3)
and the Sign Test Using SPSS
3.5.1 Define Your Variables 57 (1)
3.5.2 Type in Your Values 57 (1)
3.5.3 Analyze Your Data 58 (1)
3.5.4 Interpret the Results from the SPSS 58 (2)
Output Window
3.6 Statistical Power 60 (1)
3.7 Examples from the Literature 61 (1)
3.8 Summary 61 (1)
3.9 Practice Questions 62 (3)
3.10 Solutions to Practice Questions 65 (4)
Chapter 4 Comparing Iwo Unrelated Samples: The 69 (28)
Mann-Whitney U-Test And The Kolmogorov-Smirnov
Two-Sample Test
4.1 Objectives 69 (1)
4.2 Introduction 69 (1)
4.3 Computing the Mann-Whitney U-Test 70 (10)
Statistic
4.3.1 Sample Mann-Whitney U-Test (Small 71 (3)
Data Samples)
4.3.2 Confidence Interval for the 74 (1)
Difference between Two Location Parameters
4.3.3 Sample Mann-Whitney U-Test (Large 75 (5)
Data Samples)
4.4 Computing the Kolmogorov-Smirnov 80 (4)
Two-Sample Test Statistic
4.4.1 Sample Kolmogorov-Smimov Two-Sample 81 (3)
Test
4.5 Performing the Mann-Whitney U-Test and 84 (4)
the Kolmogorov-Smirnov Two-Sample Test Using
SPSS
4.5.1 Define Your Variables 84 (1)
4.5.2 Type in Your Values 85 (1)
4.5.3 Analyze Your Data 86 (1)
4.5.4 Interpret the Results from the SPSS 86 (2)
Output Window
4.6 Examples from the Literature 88 (1)
4.7 Summary 89 (1)
4.8 Practice Questions 90 (2)
4.9 Solutions to Practice Questions 92 (5)
Chapter 5 Comparing More Than Two Related 97 (20)
Samples: The Friedman Test
5.1 Objectives 97 (1)
5.2 Introduction 97 (1)
5.3 Computing the Friedman Test Statistic 98 (13)
5.3.1 Sample Friedman's Test (Small Data 99 (2)
Samples without Ties)
5.3.2 Sample Friedman's Test (Small Data 101 (4)
Samples with Ties)
5.3.3 Performing the Friedman Test Using 105 (3)
SPSS
5.3.4 Sample Friedman's Test (Large Data 108 (3)
Samples without Ties)
5.4 Examples from the Literature 111 (1)
5.5 Summary 112 (1)
5.6 Practice Questions 113 (1)
5.7 Solutions to Practice Questions 114 (3)
Chapter 6 Comparing More Than Two Unrelated 117 (22)
Samples: The Kruskal-Wallis H-Test
6.1 Objectives 117 (1)
6.2 Introduction 117 (1)
6.3 Computing the Kruskal-Wallis H-Test 118 (16)
Statistic
6.3.1 Sample Kruskal-Wallis H-Test (Small 119 (5)
Data Samples)
6.3.2 Performing the Kruskal-Wallis H-Test 124 (4)
Using SPSS
6.3.3 Sample Kruskal-Wallis H-Test (Large 128 (6)
Data Samples)
6.4 Examples from the Literature 134 (1)
6.5 Summary 134 (1)
6.6 Practice Questions 135 (1)
6.7 Solutions to Practice Questions 136 (3)
Chapter 7 Comparing Variables Of Ordinal Or 139 (33)
Dichotomous Scales: Spearman Rank-Order,
Point-Biserial, And Biserial Correlations
7.1 Objectives 139 (1)
7.2 Introduction 139 (1)
7.3 The Correlation Coefficient 140 (1)
7.4 Computing the Spearman Rank-Order 140 (10)
Correlation Coefficient
7.4.1 Sample Spearman Rank-Order 142 (3)
Correlation (Small Data Samples without
Ties)
7.4.2 Sample Spearman Rank-Order 145 (3)
Correlation (Small Data Samples with Ties)
7.4.3 Performing the Spearman Rank-Order 148 (2)
Correlation Using SPSS
7.5 Computing the Point-Biserial and Biserial 150 (17)
Correlation Coefficients
7.5.1 Correlation of a Dichotomous Variable 150 (2)
and an IntervaLScale Variable
7.5.2 Correlation of a Dichotomous Variable 152 (1)
and a Rank-Order Variable
7.5.3 Sample Point-Biserial Correlation 152 (4)
(Small Data Samples)
7.5.4 Performing the Point-Biserial 156 (3)
Correlation Using SPSS
7.5.5 Sample Point-Biserial Correlation 159 (4)
(Large Data Samples)
7.5.6 Sample Biserial Correlation (Small 163 (4)
Data Samples)
7.5.7 Performing the Biserial Correlation 167 (1)
Using SPSS
7.6 Examples from the Literature 167 (1)
7.7 Summary 167 (1)
7.8 Practice Questions 168 (2)
7.9 Solutions to Practice Questions 170 (2)
Chapter 8 Tests For Nominal Scale Data: 172 (38)
Chi-Square And Fisher Exact Tests
8.1 Objectives 172 (1)
8.2 Introduction 172 (1)
8.3 The xｲ Goodness-of-Fit Test 172
8.3.1 Computing the xｲ Goodness-of-Fit Test 173 (1)
Statistic
8.3.2 Sample xｲ Goodness-of-Fit Test 173 (3)
(Category Frequencies Equal)
8.3.3 Sample xｲ Goodness-of-Fit Test 176 (4)
(Category Frequencies Not Equal)
8.3.4 Performing the xｲ Goodness-of-Fit 180 (4)
Test Using SPSS
8.4 The xｲ Test for Independence 184 (12)
8.4.1 Computing the xｲ Test for Independence 185 (1)
8.4.2 Sample xｲ Test for Independence 186 (4)
8.4.3 Performing the xｲ Test for 190 (6)
Independence Using SPSS
8.5 The Fisher Exact Test 196 (6)
8.5.1 Computing the Fisher Exact Test for 2 197 (1)
x 2 Tables
8.5.2 Sample Fisher Exact Test 197 (4)
8.5.3 Performing the Fisher Exact Test 201 (1)
Using SPSS
8.6 Examples from the Literature 202 (1)
8.7 Summary 203 (1)
8.8 Practice Questions 204 (2)
8.9 Solutions to Practice Questions 206 (4)
Chapter 9 Test For Randomness: The Runs Test 210 (19)
9.1 Objectives 210 (1)
9.2 Introduction 210 (1)
9.3 The Runs Test for Randomness 210 (15)
9.3.1 Sample Runs Test (Small Data Samples) 212 (1)
9.3.2 Performing the Runs Test Using SPSS 213 (4)
9.3.3 Sample Runs Test (Large Data Samples) 217 (2)
9.3.4 Sample Runs Test Referencing a Custom 219 (2)
Value
9.3.5 Performing the Runs Test for a Custom 221 (4)
Value Using SPSS
9.4 Examples from the Literature 225 (1)
9.5 Summary 225 (1)
9.6 Practice Questions 225 (2)
9.7 Solutions to Practice Questions 227 (2)
Appendix A SPSS At A Glance 229 (6)
Appendix B Critical Value Tables 235 (26)
References 261 (4)
Index 265
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