Test Theory: A Unified Treatment

by McDonald; Roderick P.

• ISBN13: 9780805830750
• ISBN10: 0805830758
• Format: Hardcover
• Copyright: 1999-07-01
• Publisher: Psychology Pres

Summary

This book introduces the reader to the main quantitative concepts, methods, and computational techniques needed for the development, evaluation, and application of tests in the behavioral/social sciences, including educational tests. Two empirical examples are carried throughout to illustrate alternative methods. Other data sets are used for special illustrations. Self-contained programs for confirmatory and exploratory factor analysis are available on the Web. Intended for students of psychology, particularly educational psychology, as well as social science students interested in how tests are constructed and used, prerequisites include a course on statistics. The programs and data files for this book can be downloaded from www.psypress.com/test-theory/

Table of Contents

Preface	ix
1 General Introduction	1	(16)
Contextual and Historical	4	(5)
How to Use This Text	9	(3)
Preview of Remaining Chapters	12	(3)
Review Guide	15	(1)
End Notes	16	(1)
2 Items and Item Scores	17	(15)
Item Types	18	(8)
Item Scores and Test Scores	26	(3)
Some Philosophical Considerations	29	(1)
Review Guide	30	(1)
End Notes	31	(1)
3 Item and Test Statistics	32	(23)
Binary Item Statistics	32	(13)
Quantitative Item Statistics	45	(4)
Test Scores	49	(4)
Review Guide	53	(1)
End Notes	54	(1)
4 The Concept of a Scale	55	(7)
Review Guide	61	(1)
End Notes	61	(1)
5 Reliability Theory for Total Test Scores	62	(14)
The True-Score Model for Test Scores	64	(4)
Applications of the Model	68	(7)
Review Guide	75	(1)
End Notes	75	(1)
6 Test Homogeneity, Reliability, and Generalizability	76	(45)
Homogeneity and the Single-Factor Model	77	(10)
The Reliability of a Homogeneous Test	87	(3)
Coefficient Alpha and the Spearman-Brown Formula	90	(7)
Binary Data	97	(6)
Some Principles of Generalizability	103	(15)
Review Guide	118	(1)
End Notes	119	(2)
7 Reliability--Applications	121	(20)
Test Length and Reliability	121	(5)
Scale and Reliability	126	(2)
Estimating and Bounding a True Score	128	(5)
Problems of Attenuation	133	(3)
Error in Difference Scores	136	(3)
Review Guide	139	(1)
End Notes	140	(1)
8 Prediction and Multiple Regression	141	(26)
Bivariate Regression	142	(3)
Multiple Regression	145	(9)
Some Properties of Estimates	154	(2)
Selection of Predictor Variables	156	(1)
Partial Covariance and Correlation	157	(2)
An Empirical Example	159	(6)
Review Guide	165	(1)
End Notes	165	(2)
9 The Common Factor Model	167	(30)
The Multiple-Factor Model--By Example	168	(9)
The Multiple-Factor Model--General	177	(11)
Higher Order and Hierarchical Factors	188	(3)
The Rotation Problem	191	(2)
The Analysis of Correlation Matrices	193	(2)
Review Guide	195	(1)
End Notes	195	(2)
10 Validity	197	(34)
Item Content and Test Score Validation	200	(6)
Internal Psychometric Analysis	206	(5)
Convergent and Discriminant Validity	211	(2)
Multitrait-Multimethod Matrices	213	(9)
Concurrent Validity and Predictive Utility	222	(6)
Review Guide	228	(1)
End Notes	228	(3)
11 Classical Item Analysis	231	(17)
Item-Test Relations	231	(8)
Test Statistics	239	(4)
Item Correlations	243	(4)
Review Guide	247	(1)
End Notes	247	(1)
12 Item Response Models	248	(22)
Item Response Functions	249	(6)
The Principle of Local Independence	255	(2)
Item Factor Analysis	257	(3)
Estimating Item Parameters	260	(8)
Review Guide	268	(1)
End Notes	269	(1)
13 Properties of Item Response Models	270	(39)
The Concept of a Score	271	(3)
Information and the Linear Item Response Model	274	(6)
Information and Measurement Error in Item Response Models	280	(8)
The One-, Two-, and Three-Parameter Logistic Models	288	(10)
Formula Scores and Transformations	298	(9)
Review Guide	307	(1)
End Notes	308	(1)
14 Multidimensional Item Response Models	309	(16)
A Multidimensional Item Response Model	310	(5)
Information Functions and Measurement Error	315	(6)
Measuring Validity of Binary Items	321	(2)
Review Guide	323	(1)
End Notes	324	(1)
15 Comparing Populations	325	(22)
Quantitative Responses	329	(10)
Binary Items	339	(5)
Review Guide	344	(1)
End Notes	345	(2)
16 Alternate Forms and the Problem of Equating	347	(20)
Equivalence of Test Forms	349	(2)
Matching Test Forms	351	(5)
The Problem of Test Equating	356	(9)
Review Guide	365	(1)
End Notes	366	(1)
17 An Introduction to Structural Equation Modeling	367	(41)
Measuring Cause-Effect Relations	368	(3)
The Conventions of Structural Equation Modeling	371	(6)
Path Analysis Without Common Factors	377	(21)
Path Analysis With Common Factors	398	(8)
Review Guide	406	(1)
End Notes	406	(2)
18 Some Scaling theory	408	(35)
Fundamental Properties of Measurements	409	(10)
Coombs's Theory of Data	419	(3)
Some Scaling Models and Methods	422	(19)
Review Guide	441	(1)
End Notes	441	(2)
19 Retrospective	443	(10)
Appendix A. Some Rules for Expected Values	453	(2)
Glossary	455	(14)
References	469	(8)
Author Index	477	(4)
Subject Index	481