Ebook: Introduction to Statistics: The Nonparametric Way

The introductory statistics course presents serious pedagogical problems to the instructor. For the great majority of students, the course represents the only formal contact with statistical thinking that he or she will have in college. Students come from many different fields of study, and a large number suffer from math anxiety. Thus, an instructor who is willing to settle for some limited objectives will have a much better chance of success than an instructor who aims for a broad exposure to statistics. Many statisticians agree that the primary objective of the introductory statistics course is to introduce students to variability and uncertainty and how to cope with them when drawing inferences from observed data. Addi­ tionally, the introductory COurse should enable students to handle a limited number of useful statistical techniques. The present text, which is the successor to the author's Introduction to Statistics: A Nonparametric Approach (Houghton Mifflin Company, Boston, 1976), tries to meet these objectives by introducing the student to the ba­ sic ideas of estimation and hypothesis testing early in the course after a rather brief introduction to data organization and some simple ideas about probability. Estimation and hypothesis testing are discussed in terms of the two-sample problem, which is both conceptually simpler and more realistic than the one-sample problem that customarily serves as the basis for the discussion of statistical inference.

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The present text introduces the student to the basic ideas of estimation and hypothesis testing early in the course after a rather brief introduction to data organization and some simple ideas about probability. Estimation and hypothesis testing are discussed in terms of the two-sample problem. The book exploits nonparametric ideas that rely on nothing more complicated than sample differences Y-X, referred to as elementary estimates, to define the Wilcoxon-Mann-Whitney test statistics and the related point and interval estimates. The ideas behind elementary estimates are then applied to the one-sample problem and to linear regression and rank correlation. Discussion of the Kruskal-Wallis and Friedman procedures for the k-sample problem rounds out the nonparametric coverage. The concluding chapters provide a discussion of Chi-square tests for the analysis of categorical data and introduce the student to the analysis of binomial data including the computation of power and sample size. Most chapters in the book have an appendix discussing relevant Minitab commands.

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The present text introduces the student to the basic ideas of estimation and hypothesis testing early in the course after a rather brief introduction to data organization and some simple ideas about probability. Estimation and hypothesis testing are discussed in terms of the two-sample problem. The book exploits nonparametric ideas that rely on nothing more complicated than sample differences Y-X, referred to as elementary estimates, to define the Wilcoxon-Mann-Whitney test statistics and the related point and interval estimates. The ideas behind elementary estimates are then applied to the one-sample problem and to linear regression and rank correlation. Discussion of the Kruskal-Wallis and Friedman procedures for the k-sample problem rounds out the nonparametric coverage. The concluding chapters provide a discussion of Chi-square tests for the analysis of categorical data and introduce the student to the analysis of binomial data including the computation of power and sample size. Most chapters in the book have an appendix discussing relevant Minitab commands.
Content:
Front Matter....Pages i-xii
Introduction: Why Study Statistics?....Pages 1-3
Organizing and Summarizing Data....Pages 5-28
Intuitive Inference....Pages 29-44
Probability....Pages 45-64
The Normal Distribution....Pages 65-85
Hypothesis Testing....Pages 87-101
The Wilcoxon Two-Sample Test....Pages 103-127
Nonparametric and Parametric Tests....Pages 129-142
Estimation: The Two-Sample Shift Model....Pages 143-163
Point Estimates, Confidence Intervals, and Tests of Hypotheses....Pages 165-172
The One-Sample Problem....Pages 173-199
The Two-Sample Problem: Paired Observations....Pages 201-219
The Analysis of Bivariate Data....Pages 221-249
Least Squares Regression and Correlation....Pages 251-271
Comparative Experiments:k-Samples....Pages 273-294
Analysis of Variance....Pages 295-301
The Analysis of Categorical Data....Pages 303-313
Chi-Square Tests for Two-Way Classifications....Pages 315-334
Binomial Probabilities....Pages 335-347
The Analysis of Binomial Experiments....Pages 349-370
Back Matter....Pages 371-415

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The present text introduces the student to the basic ideas of estimation and hypothesis testing early in the course after a rather brief introduction to data organization and some simple ideas about probability. Estimation and hypothesis testing are discussed in terms of the two-sample problem. The book exploits nonparametric ideas that rely on nothing more complicated than sample differences Y-X, referred to as elementary estimates, to define the Wilcoxon-Mann-Whitney test statistics and the related point and interval estimates. The ideas behind elementary estimates are then applied to the one-sample problem and to linear regression and rank correlation. Discussion of the Kruskal-Wallis and Friedman procedures for the k-sample problem rounds out the nonparametric coverage. The concluding chapters provide a discussion of Chi-square tests for the analysis of categorical data and introduce the student to the analysis of binomial data including the computation of power and sample size. Most chapters in the book have an appendix discussing relevant Minitab commands.
Content:
Front Matter....Pages i-xii
Introduction: Why Study Statistics?....Pages 1-3
Organizing and Summarizing Data....Pages 5-28
Intuitive Inference....Pages 29-44
Probability....Pages 45-64
The Normal Distribution....Pages 65-85
Hypothesis Testing....Pages 87-101
The Wilcoxon Two-Sample Test....Pages 103-127
Nonparametric and Parametric Tests....Pages 129-142
Estimation: The Two-Sample Shift Model....Pages 143-163
Point Estimates, Confidence Intervals, and Tests of Hypotheses....Pages 165-172
The One-Sample Problem....Pages 173-199
The Two-Sample Problem: Paired Observations....Pages 201-219
The Analysis of Bivariate Data....Pages 221-249
Least Squares Regression and Correlation....Pages 251-271
Comparative Experiments:k-Samples....Pages 273-294
Analysis of Variance....Pages 295-301
The Analysis of Categorical Data....Pages 303-313
Chi-Square Tests for Two-Way Classifications....Pages 315-334
Binomial Probabilities....Pages 335-347
The Analysis of Binomial Experiments....Pages 349-370
Back Matter....Pages 371-415
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