Fixed Effects Analysis of Variance covers the mathematical theory of the fixed effects analysis of variance. The book discusses the theoretical ideas and some applications of the analysis of variance. The text then describes topics such as the t-test; two-sample t-test; the k-sample comparison of means (one-way analysis of variance); the balanced two-way factorial design without interaction; estimation and factorial designs; and the Latin square. Confidence sets, simultaneous confidence intervals, and multiple comparisons; orthogonal and nonorthologonal designs; and multiple regression analysis and related matters are also encompassed. Mathematicians, statisticians, and students taking related courses will find the book useful.
Inhalt
Preface
Acknowledgments
1 Introduction
2 The T-Test
Summary
Problems
3 Two-Sample T-Test
Summary
Problems
4 The K-Sample Comparison Of Means (One-Way Analysis Of Variance)
Summary and Generalization
Problems
5 The Balanced Two-Way Factorial Design Without Interaction
Summary
Problems
6 Estimation And More On Factorial Designs
Summary
Problems
7 The Latin Square
Problems
8 Confidence Sets, Simultaneous Confidence Intervals, and Multiple Comparisons One-Dimensional Case
Multidimensional Case
Simultaneous Confidence Intervals Using
Bonferroni's Inequality
The S-Method of Simultaneous Confidence Intervals
T-Type Simultaneous Confidence Intervals
Summary
Problems
9 Orthogonal And Nonorthogonal Designs, Efficiency
Summary
Problems
10 Multiple Regression Analysis And Related Matters
Regression Analysis
Multiple Regression
Partial Correlation
Problems
Appendixes
1 Review Of Linear Algebra And Vector Space Theory
2 Tables Of Statistical Distributions
Table 1 Critical Values for the t- and Normal Distributions
Table 2 Critical Values for the F-Distribution
Table 3 Critical Values for the Studentized Range from a Normal Distribution
Index