Nonparametric Statistical Inference

Name: Nonparametric Statistical Inference
Price: 87.0 USD
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ISBN: 9781420077612

ISBN-10: 1420077619

ISBN-13: 9781420077612

Edition: 5th 2010 (Revised)

Authors: Jean Dickinson Gibbons, Subhabrata Chakraborti

List price: $130.00

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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…

Book details

List price: $130.00
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…



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: ï¿½<sub>1</sub> Known



Case II: ï¿½<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 ï¿½



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 ï¿½ = 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