Statistical Methods: The Geometric Approach

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.