Baker, Frank (2001). The Basics of Item Response Theory. ERIC Clearinghouse on Assessment and Evaluation, University of Maryland, College Park, MD.

Chapter 1 - The Item Characteristic Curve

Chapter 2 - Models

Chapter 3 - Estimation of item parameters

Chapter 4 - Test Characteristic Curve

Chapter 5 - Ability Estimation

Chapter 6 - Information function

Chapter 7 - Test Calibration

Chapter 8 - Test Characteristics

References & Resources


Table of contents

Complete book
(800K) pdf IRT page


Update - you really should buy the second edition of this book.


When this book was first published in 1985, the fields of educational measurement and psychometrics were in a transitional period. The majority of practice was based upon the classical test theory classical test theory developed during the 1920s. However, a new test theory had been developing over the past forty years that was conceptually more powerful than classical test theory. Based upon items rather than test scores, the new approach was known as item response theory. While the basic concepts of item response theory were, and are, straightforward, the underlying mathematics was somewhat advanced compared to that of classical test theory. It was difficult to examine some of these concepts without performing a large number of calculations to obtain usable information. The first edition of this book was designed to provide the reader access to the basic concepts of item response theory freed of the tedious underlying calculations through an APPLE II computer program. Readers of this book may now find a new version of the program, written in Visual Basic 5.0). Readers accustomed to sophisticated statistical and graphics packages will find it utilitarian, but nevertheless helpful in understanding various facets of the theory.

This book is organized in a building block fashion. It proceeds from the simple to the complex, with each new topic building on the preceding topics. Within each of the eight chapters, a basic concept is presented, the corresponding computer session is explained, and a set of exploratory exercises is defined. Readers are then strongly encouraged to use the computer session to explore the concept through a series of exercises. A final section of each chapter, called "Things To Notice," lists some of the characteristics of the concept that you should have noticed and some of the conclusions you should have reached. If you do not understand the logic underlying something in this chapter, you can return to the computer session and try new variations and explorations until clarity is achieved.

When finished with the book and the computer sessions, the reader should have a good working knowledge of the fundamentals of item response theory. This book emphasizes the basics, minimizes the amount of mathematics, and does not pursue technical details that are of interest only to the specialist. In some sense, you will be shown only "what you need to know," rather than all the glorious details of the theory. Upon completion of this book, the reader should be able to interpret test results that have been analyzed under item response theory by means of programs such as BICAL (Wright and Mead, 1976; Mislevy and Bock, 1986). In order to employ the theory in a practical setting, the reader should study more advanced books on the application of the theory. Additional print and online resources listed in the back of this new edition now supplement my original recommendations of Lord (1980), Hambleton and Swaminathan (1984), Wright and Stone (1979), or Hulin, Drasgow and Parsons (1983).

Getting Started

a. Go to Download and install the accompanying software.

b. A title page will be shown on the screen. Click to get the main menu.

c. Use the mouse to highlight the INTRODUCTION TO SYSTEM session and press [SELECT].

d. The following menu will appear:






The author recommends that you spend a few minutes with this session, even if you are an experienced computer user, to become familiar with the way the system handles the interactive procedures.

e. With the main menu on the screen, other sessions can be selected by using the mouse to highlight the session of interest, then clicking on [SELECT].

f. Once in a session, it is best to proceed through it sequentially. You may notice that the various screens you’ve worked through stay open on the bottom of your computer screen until you reach the closing screen for a session, which will allow you to return to the main menu. This is simply a function of the way the original software for the first edition of the book was updated.


Over the past century, many people have contributed to the development of item response theory. Three persons deserve special recognition. D.N. Lawley of the University of Edinburgh published a paper in 1943 showing that many of the constructs of classical test theory classical test theory could be expressed in terms of parameters of the item characteristic curve. This paper marks the beginning of item response theory as a measurement theory. The work of Dr. F.M. Lord of the Educational Testing Service has been the driving force behind both the development of the theory and its application for the past 50 years. Dr. Lord systematically defined, expanded and explored the theory as well as developed computer programs needed to put the theory into practice. This effort culminated in his classic books (with Dr. Melvin Novick, 1968; 1980) on the practical applications of item response theory. In the late 1960s, Dr. B.D. Wright of the University of Chicago recognized the importance of the measurement work by the Danish mathematician Georg Rasch. Since that time he has played a key role in bringing item response theory, the Rasch model in particular, to the attention of practitioners. Without the work of these three individuals, the level of development of item response theory would not be where it is today.

The author is indebted to Mr. T. Seavey of Heinemann Educational Books for first suggesting that I do a small book on item response theory, which resulted in the first edition of this book in 1985. This suggestion allowed me to fulfill a long-standing desire to develop an instructional software package dealing with item response theory for the then-state-of-the-art APPLE II and IBM PC computers. An upgraded version of this software has now been made available on the World Wide Web (

Frank B. Baker
Madison Wisconsin