Statistical methods : the geometric approach
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Bibliographic Information
Statistical methods : the geometric approach
（Springer texts in statistics）
Springer-Verlag, c1991
- : us
- : gw
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Includes bibliographical references and index
Description and Table of Contents
- Volume
-
: us ISBN 9780387975177
Description
A novel exposition of the analysis of variance and regression. The key feature here is that these tools are viewed in their natural mathematical setting - the geometry of finite dimensions. This is because geometry clarifies the basic statistics and unifies the many aspects of analysing variance and regression.
Table of Contents
I Basic Ideas.- 1 Introduction.- 1.1 Why Use Geometry?.- 1.2 A Simple Illustration.- 1.3 Tradition and Practice.- 1.4 How to Read This Book.- Exercise.- 2 The Geometric Tool Kit.- 2.1 Introducing Vectors.- 2.2 Putting Vectors Together.- 2.3 Angles Between Vectors.- 2.4 Projections.- 2.5 Sums of Squares.- Exercises.- Solutions to the Reader Exercises.- 3 The Statistical Tool Kit.- 3.1 Basic Ideas.- 3.2 Combining Variables.- 3.3 Estimation.- 3.4 Reference Distributions.- Solutions to the Reader Exercises.- 4 Tool Kits At Work.- 4.1 The Scientific Method.- 4.2 Statistical Analysis.- Exercises.- II Introduction to Analysis of Variance.- 5 Single Population Questions.- 5.1 An Illustrative Example.- 5.2 General Case.- 5.3 Virtues of Our Estimates.- 5.4 Summary.- Class Exercise.- Exercises.- Solutions to the Reader Exercises.- 6 Questions About Two Populations.- 6.1 A Case Study.- 6.2 General Case.- 6.3 Computing.- 6.4 Summary.- Class Exercise.- Exercises.- Solution to the Reader Exercise.- 7 Questions About Several Populations.- 7.1 A Simple Example.- 7.2 Types of Contrast.- 7.3 The Overview.- 7.4 Summary.- Solutions to the Reader Exercises.- III Orthogonal Contrasts.- 8 Class Comparisons.- 8.1 Analyzing Example A.- 8.2 General Case.- 8.3 Summary.- Class Exercise.- Exercises.- 9 Factorial Contrasts.- 9.1 Introduction.- 9.2 Analyzing Example B.- 9.3 Analyzing Example C.- 9.4 Generating Factorial Contrasts.- 9.5 Summary.- Exercises.- 10 Polynomial Contrasts.- 10.1 Analyzing Example D.- 10.2 Consolidating the Ideas.- 10.3 A Case Study.- 10.4 Summary.- Exercises.- Solutions to the Reader Exercises.- 11 Pairwise Comparisons.- 11.1 Analyzing Example E.- 11.2 Least Significant Difference.- 11.3 Multiple Comparison Procedures.- 11.4 Summary.- Class Exercise.- Exercises.- IV Introducing Blocking.- 12 Randomized Block Design.- 12.1 Illustrative Example.- 12.2 General Discussion.- 12.3 A Realistic Case Study.- 12.4 Why and How to Block.- 12.5 Summary.- Class Exercise.- Exercises.- 13 Latin Square Design.- 13.1 Illustrative Example.- 13.2 General Discussion.- 13.3 Summary.- Exercise.- 14 Split Plot Design.- 14.1 Introduction.- 14.2 Analysis.- 14.3 Discussion.- 14.4 Summary.- Exercises.- Solutions to the Reader Exercises.- V Fundamentals of Regression.- 15 Simple Regression.- 15.1 Illustrative Example.- 15.2 General Case.- 15.3 Confidence Intervals.- 15.4 Correlation Coefficient.- 15.5 Pitfalls for the Unwary.- 15.6 Summary.- Class Exercise.- Exercises.- Solutions to the Reader Exercises.- 16 Polynomial Regression.- 16.1 No Pure Error Term.- 16.2 Pure Error Term.- 16.3 Summary.- Exercises.- 17 Analysis of Covariance.- 17.1 Illustrative Example.- 17.2 Independent Lines.- 17.3 Use of ANCOVA.- 17.4 Summary.- Exercises.- Solutions to the Reader Exercises.- 18 General Summary.- 18.1 Review.- 18.2 Where to from Here?.- 18.3 Summary.- Appendices.- A Unequal Replications: Two Populations.- A.1 Illustrative Example.- A.2 General Case.- Exercises.- B Unequal Replications: Several Populations.- B.1 Class Comparisons.- B.2 Factorial Contrasts.- B.3 Other Cases.- B.4 Summary.- Exercises.- C Alternative Factorial Notation.- Solution to the Reader Exercise.- D Regression Through the Origin.- E Confidence Intervals.- E.1 General Theory.- T Statistical Tables.- References.
- Volume
-
: gw ISBN 9783540975175
Description
This exposition of analysis of variance and regression uses diagrams and graphs to illustrate these aspects of statistics for students of any discipline who need some familiarity with the subject area. The approach is based on the geometric methods used by the founder of modern statistics, Sir Ronald Fisher. Using geometry, therefore, the text links the statistical methods of the underlying mathematics described, while real-life case studies link theory and practice. Each new situation is introduced by a detailed analysis of a case study, including assumption checking and result presentation. The computing aspect of the book is in Minitab and there are class exercises and numerous practical exercises. This undergraduate textbook is intended for students and researchers in the fields of statistics, mathematics, and biostatistics/agriculture.
Table of Contents
Basic Ideas: Introduction: The Geometric Tool Kit. The Statistical Tool Kit. Tool Kits At Work.- Introduction to Analysis of Variance: Single Population Questions. Questions About Two Populations. Questions About Several Populations. Orthogonal Contrasts: Class Comparisons. Factorial Contrasts. Polynomial Contrasts. Pairwise Comparisons.- Introducing Blocking: Randomized Block Design. Latin Square Design. Split Plot Design.- Fundamentals of Regression: Simple Regression.- Polynomial Regression.- Analysis of Covariance.- General Summary. Appendices: A: Unequal Replications. Two Populations. B: Unequal Replications. Several Populations. C: Alternative Factorial Notation. D: Regression Through the Origin. E: Confidence Intervals. T: Statistical Tables. References. Index.
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