[...]... classical test theory, is perhaps not essential for XI Xii PREFACE the reader Chapter 2, an introduction to item response theory, is easy to read Some of Chapter 3 is important only for those who need to understand the relation of item response theory to classical item analysis Chapter 4 is essential to any real understanding of item response theory and applications The reader who takes the trouble to master...Preface The purpose of this book is to make it possible for measurement specialists to solve practical testing problems by use of item response theory This theory expresses all the properties of the test, as a measuring instrument, in terms of the properties of the test items Practical applications include 1 2 3 4 5 6 7 8 9 10 The estimation of invariant parameters describing each test item; item banking... skill In order to do this, we must know something about how his ability or skill determines his response to an item Thus item response theory starts with a mathematical statement as to how response depends on level of ability or skill This relationship is given by the item response function (trace line, item charac­ teristic curve) This book deals chiefly with dichotomously scored items Responses will... classical item theory (which is only a part of classical test theory) consists of such algebraic tautologies Such a theory makes no assumptions about matters that are beyond the control of the psychometrician It cannot predict how individuals will respond to items unless the items have previously been administered to similar individuals In practical test development work, we need to be able to predict... understanding of the applications under discussion provided he has previously understood Chapter 4 The basic ideas of Chapters 16 and 17, on estimated true-score distributions, are important for the future development of mental test theory These chapters are not a basic part of item response theory and may be omitted by the general reader Reviewers will urge the need for a book on item response theory that... approximately, we must be able to estimate the 11 12 2 ITEM RESPONSE THEORY INTRODUCTION AND PREVIEW examinee's ability from any set of items that may be given to him We must also know how effective each item in the pool is for measuring at each ability level Neither of these things can be done by means of classical mental test theory In most testing work, our main task is to infer the examinee's ability... primer of item response theory Technical Report 941078 Oklahoma City, Okla.: U.S Coast Guard Institute, 1978 FREDERIC M LORD I INTRODUCTION TO ITEM RESPONSE THEORY 1 Classical Test Theory Summary and Perspective 1.1 INTRODUCTION This chapter is not a substitute for a course in classical test theory On the contrary, some knowledge of classical theory is presumed The purpose of this chapter is to provide... study of 150 five-choice 0 100 80 60 30 SCORE 60 90 100 80 60 40 % 6 30 SCORE 60 FIG 2.3.2 Proportion of correct answers to an item as a function of number-right test score The two items shown are the two worst examples of nonmonotonicity among the 150 items studied 20 0 RIGHT % RIGHT 40 20 0 18 90 2.4 UNIDIMENSIONAL TESTS 19 items was made to determine proportion of correct answers as a function of number-right... illustration of the need for such a theory, consider the basic problem of tailored testing: Given an individual's response to a few items already administered, choose from an available pool one item to be administered to him next This choice must be made so that after repeated similar choices the examinee's ability or skill can be estimated as accurately as possible from his responses To do this even... 863-872 2 Item Response Theory Introduction and Preview 2.1 INTRODUCTION Commonly, a test consists of separate items and the test score is a (possibly weighted) sum of item scores In this case, statistics describing the test scores of a certain group of examinees can be expressed algebraically in terms of statistics describing the individual item scores for the same group [see Eq (1-21) to (1-25)] . practical testing problems by use of item response theory. This theory expresses all the properties of the test, as a measuring instrument, in terms of the properties of the test items. Practical applications. for those who need to understand the relation of item response theory to classical item analysis. Chapter 4 is essential to any real understanding of item response theory and applications. The. NY 10016 Milton Park, Abingdon Oxon OX14 4RN Library of Congress Cataloging in Publication Data Lord, Frederic M 1912- Applications of item response theory to practical testing problems. Bibliography: