Statistical Methods: The Geometric Approach

ISBN-13: 9781461269656 / Angielski / Miękka / 2012 / 561 str.

David J. Saville; Graham R. Wood; David J. Saville

Opis

This book is a novel exposition of the traditional workhorses of statistics: analysis of variance and regression. The key feature is that these tools are viewed in their natural mathematical setting, the geometry of finite dimensions. The Authors To introduce ourselves, Dave Saville is a practicing statistician working in agricultural research; Graham Wood is a university lecturer involved in the teaching of statistical methods. Each of us has worked for sixteen years in our current field. Features of the Book People like pictures. One picture can present a set of ideas at a glance, while a series of pictures, each building on the last, can unify a wealth of ideas. Such a series we present in this text by means of a systematic geometric approach to the presentation of the theory of basic statistical methods. This approach fills the void between the traditional extremes of the "cookbook" approach and the "matrix algebra" approach, providing an elementary but at the same time rigorous view of the subject. It combines the virtues of the traditional methods, while avoiding their vices.

Recenzje

"This is an interesting attempt to present analysis of variance and related topics in an informative way."
(Biometrics)

Spis treści

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.