The aim of this book is to present the mathematics underlying elementary statistical methods in as simple a manner as possible. These methods include independent and paired sample t-tests, analysis of variance, regression, and the analysis of covariance. The author's principle tool is the use of geometric ideas to provide more visual insight and to make the theory accessible to a wider audience than is usually possible. TOC:From the contents: Introduction.- Paired Samples.- Independent Samples.- Several Independent Samples (Analysis of Variance).- Simple Regression.- Overview.- Appendices:…mehr
The aim of this book is to present the mathematics underlying elementary statistical methods in as simple a manner as possible. These methods include independent and paired sample t-tests, analysis of variance, regression, and the analysis of covariance. The author's principle tool is the use of geometric ideas to provide more visual insight and to make the theory accessible to a wider audience than is usually possible. TOC:From the contents: Introduction.- Paired Samples.- Independent Samples.- Several Independent Samples (Analysis of Variance).- Simple Regression.- Overview.- Appendices: Geometric Tool Kit; Statistical Tool Kit; Computing; Alternative Test Statistic; Solutions to Exercises; Statistical Tables.
1 Introduction.- 1.1 Aim of This Book.- 1.2 The Basic Idea.- 1.3 The General Method.- 1.4 An Alternative Test Statistic.- 1.5 Estimation.- 1.6 Layout of the Book.- 1.7 Word to Teachers.- 1.8 References.- 2 Paired Samples.- 2.1 Mixed-Sex Twins.- 2.2 Sample Size of Two.- 2.3 Sample Size of Three.- 2.4 General Case.- 2.5 Summary.- Class Exercise.- Exercises.- 3 Independent Samples.- 3.1 Heights of Students.- 3.2 Samples of Size Two.- 3.3 General Case.- 3.4 Summary.- Class Exercise.- Exercises.- 4 Several Independent Samples (Analysis of Variance).- 4.1 Selenium Levels.- 4.2 Samples of Size Two.- 4.3 Full Data Set.- 4.4 General Case.- 4.5 Summary.- Class Exercise.- Exercises.- 5 Simple Regression.- 5.1 Air Pollution.- 5.2 Sample of Size Five.- 5.3 General Case.- 5.4 Summary.- Class Exercise.- Exercises.- 6 Overview.- 6.1 Statistical Triangle.- 6.2 Conclusion.- Exercises.- Appendices.- A Geometric Tool Kit.- Exercises.- B Statistical Tool Kit.- C Computing.- C.1 Computing Using a Simple Spreadsheet.- C.2 Computing Using a Regression Routine.- C.3 Summary.- Exercises.- D Alternative Test Statistic.- D.1 Basic Idea.- D.2 Paired Samples.- D.3 General Method.- D.4 Independent Samples.- D.5 Several Independent Samples.- D.6 Simple Regression.- D.7 Equivalence of Test Statistics.- D.8 Summary.- Class Exercise.- Exercises.- E Solutions to Exercises.- E.1 Solutions for Chapter 2 Exercises.- E.2 Solutions for Chapter 3 Exercises.- E.3 Solutions for Chapter 4 Exercises.- E.4 Solutions for Chapter 5 Exercises.- E.5 Solutions for Chapter 6 Exercises.- E.6 Solutions for Appendix A Exercises.- E.7 Solutions for Appendix C Exercises.- E.8 Solutions for Appendix D Exercises.- T Statistical Tables.- References.
1 Introduction.- 1.1 Aim of This Book.- 1.2 The Basic Idea.- 1.3 The General Method.- 1.4 An Alternative Test Statistic.- 1.5 Estimation.- 1.6 Layout of the Book.- 1.7 Word to Teachers.- 1.8 References.- 2 Paired Samples.- 2.1 Mixed-Sex Twins.- 2.2 Sample Size of Two.- 2.3 Sample Size of Three.- 2.4 General Case.- 2.5 Summary.- Class Exercise.- Exercises.- 3 Independent Samples.- 3.1 Heights of Students.- 3.2 Samples of Size Two.- 3.3 General Case.- 3.4 Summary.- Class Exercise.- Exercises.- 4 Several Independent Samples (Analysis of Variance).- 4.1 Selenium Levels.- 4.2 Samples of Size Two.- 4.3 Full Data Set.- 4.4 General Case.- 4.5 Summary.- Class Exercise.- Exercises.- 5 Simple Regression.- 5.1 Air Pollution.- 5.2 Sample of Size Five.- 5.3 General Case.- 5.4 Summary.- Class Exercise.- Exercises.- 6 Overview.- 6.1 Statistical Triangle.- 6.2 Conclusion.- Exercises.- Appendices.- A Geometric Tool Kit.- Exercises.- B Statistical Tool Kit.- C Computing.- C.1 Computing Using a Simple Spreadsheet.- C.2 Computing Using a Regression Routine.- C.3 Summary.- Exercises.- D Alternative Test Statistic.- D.1 Basic Idea.- D.2 Paired Samples.- D.3 General Method.- D.4 Independent Samples.- D.5 Several Independent Samples.- D.6 Simple Regression.- D.7 Equivalence of Test Statistics.- D.8 Summary.- Class Exercise.- Exercises.- E Solutions to Exercises.- E.1 Solutions for Chapter 2 Exercises.- E.2 Solutions for Chapter 3 Exercises.- E.3 Solutions for Chapter 4 Exercises.- E.4 Solutions for Chapter 5 Exercises.- E.5 Solutions for Chapter 6 Exercises.- E.6 Solutions for Appendix A Exercises.- E.7 Solutions for Appendix C Exercises.- E.8 Solutions for Appendix D Exercises.- T Statistical Tables.- References.
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