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Jean D. Gibbons

Bio: Jean D. Gibbons is an academic researcher from University of Alabama. The author has contributed to research in topics: Nonparametric statistics & Tourism. The author has an hindex of 18, co-authored 66 publications receiving 6144 citations.


Papers
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Book
01 Dec 1971
TL;DR: Theoretical Bases for Calculating the ARE Examples of the Calculations of Efficacy and ARE Analysis of Count Data.
Abstract: Introduction and Fundamentals Introduction Fundamental Statistical Concepts Order Statistics, Quantiles, and Coverages Introduction Quantile Function Empirical Distribution Function Statistical Properties of Order Statistics Probability-Integral Transformation Joint Distribution of Order Statistics Distributions of the Median and Range Exact Moments of Order Statistics Large-Sample Approximations to the Moments of Order Statistics Asymptotic Distribution of Order Statistics Tolerance Limits for Distributions and Coverages Tests of Randomness Introduction Tests Based on the Total Number of Runs Tests Based on the Length of the Longest Run Runs Up and Down A Test Based on Ranks Tests of Goodness of Fit Introduction The Chi-Square Goodness-of-Fit Test The Kolmogorov-Smirnov One-Sample Statistic Applications of the Kolmogorov-Smirnov One-Sample Statistics Lilliefors's Test for Normality Lilliefors's Test for the Exponential Distribution Anderson-Darling Test Visual Analysis of Goodness of Fit 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 Rank-Order Statistics Treatment of Ties in Rank Tests The Wilcoxon Signed-Rank Test and Confidence Interval The General Two-Sample Problem Introduction The Wald-Wolfowitz Runs Test The Kolmogorov-Smirnov Two-Sample Test The Median Test The Control Median Test The Mann-Whitney U Test and Confidence Interval Linear Rank Statistics and the General Two-Sample Problem Introduction Definition of Linear Rank Statistics Distribution Properties of Linear Rank Statistics Usefulness in Inference Linear Rank Tests for the Location Problem Introduction The Wilcoxon Rank-Sum Test and Confidence Interval Other Location Tests 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 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 Other Rank-Test Statistics Tests against Ordered Alternatives Comparisons with a Control Measures of Association for Bivariate Samples Introduction: Definition of Measures of Association in a Bivariate Population Kendall's Tau Coefficient Spearman's Coefficient of Rank Correlation The Relations between R and T E(R), tau, and rho Another Measure of Association Applications 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 Page's Test for Ordered Alternatives The Coefficient of Concordance for k Sets of Rankings of n Objects The Coefficient of Concordance for k Sets of Incomplete Rankings Kendall's Tau Coefficient for Partial Correlation Asymptotic Relative Efficiency Introduction Theoretical Bases for Calculating the ARE Examples of the Calculations of Efficacy and ARE Analysis of Count Data Introduction Contingency Tables Some Special Results for k x 2 Contingency Tables Fisher's Exact Test McNemar's Test Analysis of Multinomial Data Summary Appendix of Tables Answers to Problems References Index A Summary and Problems appear at the end of each chapter.

2,988 citations

Book
01 Jan 1977
TL;DR: In this article, the philosophy of selecting and ordering populations has been studied in the context of normal distribution models, and the main focus of this paper is on the following: 1. Selecting the one best population for Normal Distributions with Common Known Variance (CKV) 2.
Abstract: 1. The Philosophy of Selecting and Ordering Populations 2. Selecting the One Best Population for Normal Distributions with Common Known Variance 3. Selecting the One Best Population for Other Normal Distribution Models 4. Selecting the One Best Population Bionomial (or Bernoulli) Distributions 5. Selecting the One Normal Population with the Smallest Variance 6. Selecting the One Best Category for the Multinomial Distribution 7. Nonparametric Selection Procedures 8. Selection Procedures for a Design with Paired Comparisons 9. Selecting the Normal Population with the Best Regression Value 10. Selecting Normal Populations Better than a Control 11. Selecting the t Best Out of k Populations 12. Complete Ordering of k Populations 13. Subset Selection (or Elimination) Procedures 14. Selecting the Best Gamma Population 15. Selection Procedures for Multivariate Normal Distributions Appendix A. Tables for Normal Means Selection Problems Appendix B. Figures for Normal Means Selection Problems Appendix C. Table of the Cumulative Standard Normal Distribution F(z) Appendix D. Table of Critical Values for the Chi-Square Distribution Appendix E. Tables for Binomial Selection Problems Appendix F. Figures for Binomial Selection Problems Appendix G. Tables for Normal Variances Selection Problems Appendix H. Tables for Multinomial Selection Problems Appendix I. Curtailment Tables for the Multinomial Selection Problem Appendix J. Tables of the Incomplete Beta Function Appendix K. Tables for Nonparametric Selection Problems Appendix L. Tables for Paired-Comparison Selection Problems Appendix M. Tables for Selecting from k Normal Populations Those Better Than a Control Appendix N. Tables for Selecting the t Best Normal Populations Appendix O. Table of Critical Values of Fisher's F Distribution Appendix P. Tables for Complete Ordering Problems Appendix Q. Tables for Subset Selection Problems Appendix R. Tables for Gamma Distribution Problems Appendix S. Tables for Multivariate Selection Problems Appendix T. Excerpt of Table of Random Numbers Appendix U. Table of Squares and Square Roots Bibliography References for Applications Index for Data and Examples Name Index Subject Index.

357 citations


Cited by
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Journal ArticleDOI
TL;DR: The Gene Set Enrichment Analysis (GSEA) method as discussed by the authors focuses on gene sets, that is, groups of genes that share common biological function, chromosomal location, or regulation.
Abstract: Although genomewide RNA expression analysis has become a routine tool in biomedical research, extracting biological insight from such information remains a major challenge. Here, we describe a powerful analytical method called Gene Set Enrichment Analysis (GSEA) for interpreting gene expression data. The method derives its power by focusing on gene sets, that is, groups of genes that share common biological function, chromosomal location, or regulation. We demonstrate how GSEA yields insights into several cancer-related data sets, including leukemia and lung cancer. Notably, where single-gene analysis finds little similarity between two independent studies of patient survival in lung cancer, GSEA reveals many biological pathways in common. The GSEA method is embodied in a freely available software package, together with an initial database of 1,325 biologically defined gene sets.

34,830 citations

Journal ArticleDOI
TL;DR: The standard nonparametric randomization and permutation testing ideas are developed at an accessible level, using practical examples from functional neuroimaging, and the extensions for multiple comparisons described.
Abstract: Requiring only minimal assumptions for validity, nonparametric permutation testing provides a flexible and intuitive methodology for the statistical analysis of data from functional neuroimaging experiments, at some computational expense. Introduced into the functional neuroimaging literature by Holmes et al. ([1996]: J Cereb Blood Flow Metab 16:7-22), the permutation approach readily accounts for the multiple comparisons problem implicit in the standard voxel-by-voxel hypothesis testing framework. When the appropriate assumptions hold, the nonparametric permutation approach gives results similar to those obtained from a comparable Statistical Parametric Mapping approach using a general linear model with multiple comparisons corrections derived from random field theory. For analyses with low degrees of freedom, such as single subject PET/SPECT experiments or multi-subject PET/SPECT or fMRI designs assessed for population effects, the nonparametric approach employing a locally pooled (smoothed) variance estimate can outperform the comparable Statistical Parametric Mapping approach. Thus, these nonparametric techniques can be used to verify the validity of less computationally expensive parametric approaches. Although the theory and relative advantages of permutation approaches have been discussed by various authors, there has been no accessible explication of the method, and no freely distributed software implementing it. Consequently, there have been few practical applications of the technique. This article, and the accompanying MATLAB software, attempts to address these issues. The standard nonparametric randomization and permutation testing ideas are developed at an accessible level, using practical examples from functional neuroimaging, and the extensions for multiple comparisons described. Three worked examples from PET and fMRI are presented, with discussion, and comparisons with standard parametric approaches made where appropriate. Practical considerations are given throughout, and relevant statistical concepts are expounded in appendices.

5,777 citations

ReportDOI
TL;DR: The authors analyzes compensation schemes which pay according to an individual's ordinal rank in an organization rather than his output level and shows that wages based upon rank induce the same efficient allocation of resources as an incentive reward scheme based on individual output levels.
Abstract: This paper analyzes compensation schemes which pay according to an individual's ordinal rank in an organization rather than his output level. When workers are risk neutral, it is shown that wages based upon rank induce the same efficient allocation of resources as an incentive reward scheme based on individual output levels. Under some circumstances, risk-averse workers actually prefer to be paid on the basis of rank. In addition, if workers are heterogeneous inability, low-quality workers attempt to contaminate high-quality firms, resulting in adverse selection. However, if ability is known in advance, a competitive handicapping structure exists which allows all workers to compete efficiently in the same organization.

4,711 citations

Journal ArticleDOI
29 Sep 2006-Science
TL;DR: The first installment of a reference collection of gene-expression profiles from cultured human cells treated with bioactive small molecules is created, and it is demonstrated that this “Connectivity Map” resource can be used to find connections among small molecules sharing a mechanism of action, chemicals and physiological processes, and diseases and drugs.
Abstract: To pursue a systematic approach to the discovery of functional connections among diseases, genetic perturbation, and drug action, we have created the first installment of a reference collection of gene-expression profiles from cultured human cells treated with bioactive small molecules, together with pattern-matching software to mine these data. We demonstrate that this "Connectivity Map" resource can be used to find connections among small molecules sharing a mechanism of action, chemicals and physiological processes, and diseases and drugs. These results indicate the feasibility of the approach and suggest the value of a large-scale community Connectivity Map project.

4,429 citations

Journal ArticleDOI
TL;DR: The basics are discussed and a survey of a complete set of nonparametric procedures developed to perform both pairwise and multiple comparisons, for multi-problem analysis are given.
Abstract: a b s t r a c t The interest in nonparametric statistical analysis has grown recently in the field of computational intelligence. In many experimental studies, the lack of the required properties for a proper application of parametric procedures - independence, normality, and homoscedasticity - yields to nonparametric ones the task of performing a rigorous comparison among algorithms. In this paper, we will discuss the basics and give a survey of a complete set of nonparametric procedures developed to perform both pairwise and multiple comparisons, for multi-problem analysis. The test problems of the CEC'2005 special session on real parameter optimization will help to illustrate the use of the tests throughout this tutorial, analyzing the results of a set of well-known evolutionary and swarm intelligence algorithms. This tutorial is concluded with a compilation of considerations and recommendations, which will guide practitioners when using these tests to contrast their experimental results.

3,832 citations