Hawking in these lectures roger penrose and i will put forward our related but rather di. Comparisons between classical test theory and item. Basics of classical test theory theory and assumptions types of reliability example classical test theory classical test theory ctt often called the true score model called classic relative to item response theory irt which is a more modern approach ctt describes a set of psychometric procedures used to test items and scales. Despite theoretical differences between item response theory irt and classical test theory ctt, there is a lack of empirical knowledge about how, and to what extent, the irt and cttbased item and person statistics behave differently. Introduction to measurement theory what is test theory. These include item and scale characteristics that derive from ctt as well as types of reliability and validity. Comparisons between classical test theory and item response theory in automated assembly of parallel test forms the journal of technology, learning, and assessment volume 6, number 8 april 2008 a publication of the technology and assessment study collaborative caroline a. Item response theory was an upstart whose popular acceptance lagged in part because the.
Overview of classical test theory and item response theory. Introduction to classical and modern test theory ebook. An alternative scaling approach, and reduction procedure, is a methodology based on the concept proposed by the danish mathematician, georg rasch 5. Classical test theory is rarely considered by individuals taking psychometric tests or the companies using them, but is essential in its uses, as there is no point in a test that has to be highly scrutinized for errors before the candidates responses are even measured. Item response theory requires several items so that there is adequate opportunity to have a sufficient range for levels of item difficulty and person attribute. What it is and how you can use the irt procedure to apply it xinming an and yiufai yung, sas institute inc. Influences on and limitations of classical test theory. Variance in the dependent variable is the crux of all statistical analyses, hence, it is the focus of all statistical analyses. Classical test theory ctt for assessing reliability and validity psyc 948. Most of the assessment systems are now using the classical test theory ctt, the real ability of students is not exactly revealed because they rely only on counting the number of true responses. Classical test theory ctt is an historical predecessor to g theory. The goal is to circumvent the semantic and syntactic deficiencies and criticisms associated with classical test theory. Handwaving at cttbased assessments of validity cttbased assessments of reliability why alpha doesnt really matter. The techniques of ctt are applied in assessment situations to improve test analysis and test refinement procedures.
The variance of true score more closely approximates that of observed score when the error variances are small and the reliability is greater. For the love of physics walter lewin may 16, 2011 duration. Classical psychometric test theory ctt aims at studying the reliability of a realvalued test score variable measurement, test that maps a crucial aspect of qualitative or quantitative observations into the set of real numbers. Pdf test theory, classical test theory researchgate. Classical test theory and anova can be viewed as the parents of generalizability theory, but the child is both more and less than the simple conjunction of its parents. The goal of this project is to help students and researchers run ctt analysis as easily as possible. Abstract item response theory irt is concerned with accurate test scoring and development of test items. The purpose of this chapter is to locate item response theory. The most prominent testtheoretical frameworks are classical test theory ctt and item response theory irt including the rasch model. Despite its brevity, it has proved its value in classical test theory and item response theory assessments, the three traits have different correlates, and the measures appear to cover the range of subtraits e. As its name indicates, irt primarily focuses on the itemlevel information in contrast to the ctts. When frank baker wrote his classic the basics of item response theory in 1985, the field of educational assessment was dominated by classical test theory based on test scores. With test theories, the term test or assessment is applied widely. The practice of testing has become increasingly common and the reliance on information gained from test scores to make decision has made an indelible mark on our culture.
If youre having problems with irtshiny feel free to refer to our github wiki or the documentation available on cran. Classical test theory and the measurement of reliability. Classical test theory ctt often called the true score model called classic relative to item response theory irt which is a more modern approach ctt describes a set of psychometric procedures used to test items and scales reliability, difficulty, discrimination, etc. Classical test theory versus rasch analysis for quality of. But as will be discussed in chapter 11, this will lead to almost the same conclusion. Classical test theory ctt has been the foundation for measurement theory for over 80 years. Aside from determining the reliability of a test score variable itself ctt allows answering questions such as. Thirtythree of the items in the test were answered correctly by all five students while one of the items was answered incorrectly by all five students. Classical test theory an overview sciencedirect topics. Our discussion of classical test theory is, by design, an elementary one. In addition, the following assumptions are often made by classical test.
You design test items to measure various kinds of abilities such as math ability, traits such as. We also identify computer packages for performing gtheory analyses, most of which can be obtained free of charge, and describe how they compare with regard to data input requirements, ease of use, complexity of designs supported, and output produced. Relating variance partitioning in substantive analyses to the same process in measurement analyses. The present paper explains how different factors affect classical reliability estimates such as test retest, interrater, internal consistency, and equivalent forms coefficients. The techniques of ctt are applied in assessment situations to improve test analysis and. Classical test theory assumptions, equations, limitations, and item analyses c lassical test theory ctt has been the foundation for measurement theory for over 80 years. Introduction to classical and modern test theory crocker, linda, algina, james on. The theory starts from the assumption that systematic effects between responses of examinees are due only to variation in ability of interest. Reliability reliability and the classical true score model procedures for estimating reliability introduction to generalizability theory. The additive model may be considered as the best exponent of classical test theory ctt in test development and construction 3,4.
The figure shows the 16 items by sequence number in the test. This linearity assumption underlies the practice of creating tests from the linear combination of items or subtests. Surveys, achievement tests, intelligence tests, psychological assessments, writing. Psychometric theory offers two approaches in analyzing test data. This approach to testing based on item analysis considers the chance of getting particular items right or wrong. The new psychometrics item response theory classical test theory is concerned with the reliability of a test and assumes that the items within the test are sampled at random from a domain of relevant items. The code for this application is available at this github. Classical test theory and item response theory provide useful methods for assessing content validity during the early development of a pro measure. The assumptions and concepts underlying ctt are discussed. These limitations are the random sampling theory and item response detailed in item, person and. This model is referred to as classical test score theory, classical test theory, or simply test theory. Within the ctt framework influential quality criteria like objectivity, reliability, and validity as well as methods for assessing them have been developed. Pdf the practice of testing has become increasingly common and the reliance on information gained from test scores to make decision has. Test theory is essentially the collection of mathematical concepts that formalize and clarify certain questions about constructing and using tests, and then provide methods for answering them mcdonald, 1999, p.
Irt, on the other hand, is more theory grounded and models the probabilistic distribution of examinees success at the item level. C lassical test theory ctt has been the foundation for measurement theory for over 80 years. Educational and psychological measurem june 1998 v58 n3. An example of the power of correcting for attenuation may be seen in table 7. Statistical concepts for test theory introduction to scaling process of test construction test scores as composites unit 2.
The statistics produced under ctt include measures of item difficulty. Classical test theory ctt comprises a set of concepts and methods that provide a basis for many of the measurement tools currently used in health research. Classical test theory assumes linearitythat is, the regression of the observed score on the true score is linear. We shall speak alternately and shall give three lectures each, followed by a discussion on our di. In theory of measurement in education and psychology, classical test theory ctt is a popular framework. Classical test theory ctt, also known as the true score theory, refers to the analysis of test results based on test scores. Classical test theory ctt for assessing reliability and. Classical test theory ctt and item response theory irt. Demonstrating the difference between classical test theory. Classical testtheoryin historical perspective ross e. G theory enables an investigator to quantify and distinguish the sources of inconsistencies in observed scores that arise, or could arise, over replications of a measurement procedure. The conceptual foundations, assumptions, and extensions of the basic premises of ctt have allowed for the development of some excellent psychometrically sound scales.
Introduction to classical test theory ji zeng and adam wyse psychometricians michigan department of education office of educational assessment and accountability. Traub the ontario instituteforstudies in educationof the university oftoronto whatwere the historic origins ofclassical test theory. The data shown are 16 items included in a 50item test administered to five students. I should emphasize that these will be technical lectures. The entire educational system is today highly concerned with the design and. For example, although generalizability theory liberalizes classical test theory, not all aspects of classical theory are incorporated in generalizability theory.