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Statistical Methods: The Geometric Approach

  • Fester Einband
  • 584 Seiten
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A novel exposition of the analysis of variance and regression. The key feature here is that these tools are viewed in their natura... Weiterlesen
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Beschreibung

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.

Klappentext

This book presents a novel exposition of the subjects of analysis of variance and regression. The key feature is that these tools are viewed in their natural mathematical setting, the geometry of finite dimensions. Geometry clarifies the basic statistics and unifies the many aspects of analysis of variance and regression.



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

Inhalt

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.

Produktinformationen

Titel: Statistical Methods: The Geometric Approach
Autor:
EAN: 9780387975177
ISBN: 0387975179
Format: Fester Einband
Herausgeber: Springer New York
Genre: Mathematik
Anzahl Seiten: 584
Gewicht: 1033g
Größe: H241mm x B160mm x T36mm
Jahr: 1997
Auflage: 1st ed. 1991. Corr. 3rd printing 1997

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