Confidence Intervals

Using lots of easy to understand examples from different disciplines, the author introduces the basis of the confidence interval framework and provides the criteria for 'best' confidence intervals, along with the trade-offs between confidence and precision.The book covers such pertinent topics as: the transformation principle whereby a confidence interval for a parameter may be used to construct an interval for any monotonic transformation of that parameter; confidence intervals on distributions whose shape changes with the value of the parameter being estimated; and, the relationship between confidence interval and significance testing frameworks, particularly regarding power.

Michael Smithson is a Reader in the School of Psychology at The Australian National University of Canberra.

Series Editor's Introduction

v

Introduction and Overview

1

(2)

Confidence Statements and Interval Estimates

3

(15)

Decisions and Criteria for Confidence Intervals

9

(3)

Why Confidence Intervals?

12

(6)

Central Confidence Intervals

18

(14)

Central and Standardizable Versus Noncentral Distributions

18

(1)

Confidence Intervals Using the Central t and Normal Distributions

19

(5)

Confidence Intervals Using the Central Chi-Square and F Distributions

24

(3)

The Transformation Principle

27

(5)

Noncentral Confidence Intervals for Standardized Effect Sizes

32

(9)

Noncentral Distributions

32

(2)

Computing Noncentral Confidence Intervals

34

(7)

Applications in ANOVA and Regression

41

(25)

Fixed-Effects Versus Random-Effects Models

42

(1)

Fixed-Effects ANOVA

43

(3)

Random-Effects ANOVA

46

(2)

A Priori and Post Hoc Contrasts

48

(4)

Regression: Multiple, Partial, and Semi-Partial Correlations

52

(7)

Effect-Size Statistics for MANOVA and Setwise Regression

59

(2)

Confidence Interval for a Regression Coefficient

61

(3)

Goodness-of-Fit Indices in Structural Equations Model

64

(2)

Applications in Categorical Data Analysis

66

(11)

Odds Ratio, Difference Between Proportions, and Relative Risk

66

(3)

Chi-Square Confidence Intervals for One Variable

69

(3)

Two-Way Contingency Tables

72

(1)

Effects in Log-Linear and Logistic Regression Models

73

(4)

Significance Tests and Power Analysis

77

(9)

Significance Tests and Model Comparison

77

(2)

Power and Precision

79

(2)

Designing Studies Using Power Analysis and Confidence Intervals

81

(5)

Confidence Intervals for Power

86

(1)

Concluding Remarks

86

(4)

References

90

(3)

About the Author

93

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Summary

Author Biography

Table of Contents

Supplemental Materials