Introduction

CHAPTER 1

The Item Characteristic Curve 5

Computer Session for Chapter 1 12

Procedures for an Example Case 12

Exercises 15

Things To Notice 19

CHAPTER 2

Item Characteristic Curve Models 21

The Logistic Function 21

Computational Example 23

The Rash, or One-Parameter, Logistic Model 25

Computational Example 26

The Three-Parameter Model 28

Computational Example 29

Negative Discrimination 31

Guidelines for Interpreting Item Parameter Values 33

Computer Session for Chapter 2 35

Procedures for an Example Case 35

Exercises 38

Things To Notice 45

CHAPTER 3

Estimating Item Parameters 47

The Group Invariance of Item Parameters 51

Computer Session for Chapter 3 55

Procedures for an Example of Fitting an
Item Characteristic Curve to Response Data 56

Exercises 57

Procedures for an Example Case
Illustrating Group Invariance 58

Exercises 60

Things To Notice 62

CHAPTER 4

The Test Characteristic Curve 65

Item 1 66

Item 2 66

Item 3 67

Item 4 67

Computer Session for Chapter 4 71

Procedures for an Example Case 71

Exercises 73

Things To Notice 82

CHAPTER 5

Estimating an Examinee’s Ability 85

Ability Estimation Procedures 85

Item Invariance of an Examinee’s Ability Estimate 90

Computer Session for Chapter 5 92

Procedure for Investigating the

Sampling Variability of Estimated Ability 93

Exercises 95

Procedures for Investigating the
Item Invariance of an Examinee’s Ability 98

Exercises 100

Things To Notice 103

CHAPTER 6

The Information Function 106

Item Information Function 108

Test Information Function 109

Definition of Item Information 111

Computing a Test Information Function 115

Interpreting the Test Information Function 117

Computer Session for Chapter 6 118

Procedures for an Example Case 118

Exercises 121

Things To Notice 130

CHAPTER 7

Test Calibration 133

The Test Calibration Process 133

The Metric Problem 134

Test Calibration Under the Rasch Model 135

Summary of the Test Calibration Process 141

Computer Session for Chapter 7 142

Procedures for the test calibration session 143

Things To Notice 148

Putting the Three Tests on a
Common Ability Scale (Test Equating) 150

Easy Test 151

Hard Test 152

CHAPTER 8

Specifying the Characteristics of a Test 156

Developing a Test From a Precalibrated Item Pool 157

Some Typical Testing Goals 158

Computer Session for Chapter 8 158

Some Ground Rules 159

Procedures for an Example Case 159

Exercises 164

Things To Notice 166

References 169

Selected Resources on Item Response Theory 170

Index 174