Statistical Methods: The Geometric Approach

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.

I Basic Ideas.- 1 Introduction.- 2 The Geometric Tool Kit.- 3 The Statistical Tool Kit.- 4 Tool Kits At Work.- II Introduction to Analysis of Variance.- 5 Single Population Questions.- 6 Questions About Two Populations.- 7 Questions About Several Populations.- III Orthogonal Contrasts.- 8 Class Comparisons.- 9 Factorial Contrasts.- 10 Polynomial Contrasts.- 11 Pairwise Comparisons.- IV Introducing Blocking.- 12 Randomized Block Design.- 13 Latin Square Design.- 14 Split Plot Design.- V Fundamentals of Regression.- 15 Simple Regression.- 16 Polynomial Regression.- 17 Analysis of Covariance.- 18 General 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.