Nonparametric Statistical Inference

ISBN-10: 1420077619

ISBN-13: 9781420077612

Edition: 5th 2010 (Revised)

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Description:

The fifth edition of this classic text retains its original flavor, while providing a large collection of time tested commonly used nonparametric techniques, including both hypothesis tests and confidence intervals. It presents in-depth coverage of the theory and methods of the most widely used nonparametric procedures in statistical analysis and offers example applications appropriate for the social, behavioral, and life sciences. This new edition is thoroughly revised, rewritten, and reorganized as needed, with updated and revised examples and all essential user-friendly tables for easy implementation. No other nonparametric book does it this well at this level, or in a more accessible manner.
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Book details

List price: $112.95
Edition: 5th
Copyright year: 2010
Publisher: CRC Press LLC
Publication date: 7/26/2010
Binding: Hardcover
Pages: 650
Size: 6.50" wide x 9.75" long x 1.50" tall
Weight: 2.288
Language: English

Lokenath Debnath is Professor of the Department of Mathematics and Professor of Mechanical and Aerospace Engineering at the University of Central Florida in Orlando. He received his M.Sc. and Ph.D. degrees in pure mathematics from the University of Calcutta, and obtained D.I.C. and Ph.D. degrees in applied mathematics from the Imperial College of Science and Technology, University of London. He was a Senior Research Fellow at the University of Cambridge and has had visiting appointments to several universities in the United States and abroad. His many honors and awards include two Senior Fulbright Fellowships and an NSF Scientist award to visit India for lectures and research. Dr. Debnath is author or co-author of several books and research papers in pure and applied mathematics, and serves on several editorial boards for scientific journals. He is the current and founding Managing Editor of the International Journal of Mathematics and Mathematical Sciences.

Preface to the Fifth Edition
Introduction and Fundamentals
Introduction
Fundamental Statistical Concepts
Basic Definitions
Moments of Linear Combinations of Random Variables
Probability Functions
Distributions of Functions of Random Variables Using the Method of Jacobians
Chebyshev's Inequality
Central Limit Theorem
Point and Interval Estimation
Hypothesis Testing
P Value
Consistency
Pitman Efficiency
Randomized Tests
Continuity Correction
Order Statistics, Quantiles, and Coverages
Introduction
Quantile Function
Empirical Distribution Function
Empirical Quantile Function
Statistical Properties of Order Statistics
Cumulative Distribution Function of X<sub>(r)</sub>
Probability Density Function of X<sub>(r)</sub>
Probability-Integral Transformation
Joint Distribution of Order Statistics
Distributions of the Median and Range
Distribution of the Median
Distribution of the Range
Exact Moments of Order Statistics
kth Moment about the Origin
Covariance between X<sub>(r)</sub> and X<sub>(s)</sub>
Large-Sample Approximations to the Moments of Order Statistics
Asymptotic Distribution of Order Statistics
Tolerance Limits for Distributions and Coverages
One-Sample Coverages
Two-Sample Coverages
Ranks, Block Frequencies, and Placements
Summary
Problems
Tests of Randomness
Introduction
Tests Based on the Total Number of Runs
Exact Null Distribution of R
Moments of the Null Distribution of R
Asymptotic Null Distribution
Discussion
Applications
Tests Based on the Length of the Longest Run
Rims Up and Down
Applications
A Test Based on Ranks
Summary
Problems
Tests of Goodness of Fit
Introduction
The Chi-Square Goodness-of-Fit Test
The Kolmogorov-Smirnov (K-S) One-Sample Statistic
Applications of the Kolmogorov-Smirnov (K-S) One-Sample Statistics
One-Sided Tests
Confidence Bands
Determination of Sample Size
Lilliefors's Test for Normality
Lilliefors's Test for the Exponential Distribution
Anderson-Darling (A-D) Test
Visual Analysis of Goodness of Fit
Summary
Problems
One-Sample and Paired-Sample Procedures
Introduction
Confidence Interval for a Population Quantile
Hypothesis Testing for a Population Quantile
The Sign Test and Confidence Interval for the Median
P value
Normal Approximations
Zero Differences
Power Function
Simulated Power
Sample Size Determination
Confidence Interval for the Median
Problem of Zeros
Paired-Sample Procedures
Applications
Rank-Order Statistics
Treatment of Ties in Rank Tests
Randomization
Midranks
Average Statistic
Average Probability
Least Favorable Statistic
Range of Probability
Omission of Tied Observations
The Wilcoxon Signed-Rank Test and Confidence Interval
The Problem of Zero and Tied Differences
Power Function
Simulated Power
Sample Size Determination
Confidence-Interval Procedures
Paired-Sample Procedures
Use of Wilcoxon Statistics to Test for Symmetry
Applications
Summary
Problems
The General Two-Sample Problem
Introduction
The Wald-Wolfowitz Runs Test
The Problem of Ties
Discussion
The Kolmogorov-Smirnov (K-S) Two-Sample Test
One-Sided Alternatives
Ties
Discussion
Applications
The Median Test
Applications
Confidence-Interval Procedure
Power of the Median Test
The Control Median Test
Curtailed Sampling
Power of the Control Median Test
Discussion
Applications
The Mann-Whitney U Test and Confidence Interval
The Problem of Ties
Confidence-Interval Procedure
Sample Size Determination
Discussion
Summary
Problems
Linear Rank Statistics and the General Two-Sample Problem
Introduction
Definition of Linear Rank Statistics
Distribution Properties of Linear Rank Statistics
Usefulness in Inference
Problems
Linear Rank Tests for the Location Problem
Introduction
The Wilcoxon Rank-Sum Test and Confidence Interval
Applications
Other Location Tests
Terry-Hoeffding (Normal Scores) Test
van der Waerden Test
Percentile Modified Rank Tests
Summary
Problems
Linear Rank Tests for the Scale Problem
Introduction
The Mood Test
The Freund-Ansari-Bradley-David-Barton Tests
The Siegel-Tukey Test
The Klotz Normal-Scores Test
The Percentile Modified Rank Tests for Scale
The Sukhatme Test
Confidence Interval Procedures
Other Tests for the Scale Problem
Applications
Summary
Problems
Tests of the Equality of k Independent Samples
Introduction
Extension of the Median Test
Extension of the Control Median Test
The Kruskal-Wallis One-Way ANOVA Test and Multiple Comparisons
Applications
Other Rank-Test Statistics
Tests against Ordered Alternatives
Applications
Comparisons with a Control
Case I: �<sub>1</sub> Known
Case II: �<sub>1</sub> Unknown
Applications
Summary
Problems
Measures of Association for Bivariate Samples
Introduction: Definition of Measures of Association in a Bivariate Population
Kendall's Tau Coefficient
Null Distribution of T
The Large-Sample Nonnull Distribution of Kendall's Statistic
Tied Observations
A Related Measure of Association for Discrete Populations
Use of Kendall's Statistic to Test against Trend
Spearman's Coefficient of Rank Correlation
Exact Null Distribution of R
Asymptotic Null Distribution of R
Testing the Null Hypothesis
Tied Observations
Use of Spearman's R to Test against Trend
The Relations between R and T; E(R), T, and �
Another Measure of Association
Applications
Summary
Problems
Measures of Association in Multiple Classifications
Introduction
Friedman's Two-Way Analysis of Variance by Ranks in a k x n Table and Multiple Comparisons
Applications
Page's Test for Ordered Alternatives
The Coefficient of Concordance for k Sets of Rankings of n Objects
Relationship between W and Rank Correlation
Tests of Significance Based on W
Estimation of the True Preferential Order of Objects
Tied Observations
Applications
The Coefficient of Concordance for k Sets of Incomplete Rankings
Tests of Significance Based on W
Tied Observations
Applications
Kendall's Tau Coefficient for Partial Correlation
Applications
Summary
Problems
Asymptotic Relative Efficiency
Introduction
Theoretical Bases for Calculating the ARE
Examples of the Calculation of Efficacy and ARE
One-Sample and Paired-Sample Problems
Two-Sample location Problems
Two-Sample Scale Problems
Summary
Problems
Analysis of Count Data
Introduction
Contingency Tables
Contingency Coefficient
Some Special Results for k x 2 Contingency Tables
Fisher's Exact Test
McNemar's Test
Analysis of Multinomial Data
Ordered Categories
Summary
Problems
Summary
Appendix of Tables
Normal Distribution
Chi-Square Distribution
Cumulative Binomial Distribution
Total Number of Runs Distribution
Runs Up and Down Distribution
Kolmogorov-Smirnov One-Sample Statistic
Binomial Distribution for � = 0.5
Probabilities for the Wilcoxon Signed-Rank Statistic
Kolmogorov-Smirnov Two-Sample Statistic
Probabilities for the Wilcoxon Rank-Sum Statistic
Kruskal-Wallis Test Statistic
Kendall's Tau Statistic
Spearman's Coefficient of Rank Correlation
Friedman's Analysis-of-Variancc Statistic and Kendall's Coefficient of Concordance
Lilliefor's Test for Normal Distribution Critical Values
Significance Points of T<sub>XY.Z</sub> for Kendall's Partial Rank-Correlation Coefficient
Page's L Statistic
Critical Values and Associated Probabilities for the Jonckheere-Terpstra Test
Rank von Neumann Statistic
Lilliefors's Test for Exponential Distribution Critical Values
Answers to Selected Problems
References
Index
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