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. This is a modern test theory as opposed to classical test theory. This suggestion allowed me to fulfill a longstanding desire to develop an instructional software package dealing with item response theory for the. The mathematics required to calculate the asymptotic standard errors of the parameters of three commonly used logistic item response models is described and used to generate values for some common situations. Item response theory, reliability and standard error brent culligan 2 0 1 f. In psychometrics, the theory has been superseded by the more sophisticated models in item response theory irt and generalizability theory gtheory.
It is intended to consider the broad measurement problems that arise in these areas and is written for a reader who needs only a. Some standard errors in item response theory springerlink. These theories all involve measurement models, sometimes referred to as latent variable models, which are. Item response theory models student ability using question level performance instead of aggregate test level performance. Using python, i was able to successfully program most of the algorithms in the book with the exception of marginal maximum likelihood, which somehow yields biased estimates of a parameters. Irt provides a foundation for statistical methods that are utilized in contexts such as test development, item analysis, equating, item banking, and computerized adaptive testing. Chapter 8 the new psychometrics item response theory. Presents an item response theory irt method for estimating standard errors of measurement of scale scores for the situation in which scale scores are nonlinear transformations of numbercorrect scores.
In chapter 7, well learn about reliability within the item response theory model. This suggestion allowed me to fulfill a longstanding desire to develop an instructional software package dealing with item response theory for the thenstateoftheart apple ii and ibm pc computers. Item response theory irt has grown from its roots in postwar mentaltesting problems, through intensive use in educational measurements in the 1970s, 1980s, and 1990s, to become a mature statistical toolkit for modeling of multivariate discrete response data using subjectlevel latent variables. Internal consistency reliability in item response theory.
In order to obtain the many advantages of item response theory, tests should be designed, constructed, analyzed, and. On the relationship between classical test theory and item response theory. A reliable test may or may not be valid, but an unreliable test can never be valid. These are a the use of personfit statistics in the assessment of how item response theory measurement models differ across manifest groups e.
Pugh this study investigated the utility of confirmatory factor analysis cfa and item response theory irt models for testing the comparability of psychological measurements. This chapter presents an overview of classical test theory ctt, strong true. Using a meaningbased approach that emphasizes the why over the how to, psychometrics. Item response theory irt is arguably one of the most in. This lack of congruence between the construction and analysis procedures has kept the full power of item response theory from being exploited. Instead of assuming all questions contribute equivalently to our understanding of a students abilities, irt provides a mo.
In psychometrics, item response theory irt also known as latent trait theory, strong true score theory, or modern mental test theory, is a paradigm for the design, analysis, and scoring of tests, questionnaires, and similar instruments measuring abilities, attitudes, or other variables. If participant wealth item cost, we should see a positive item response level of positive item response tells us about where on the scale the participant lies, e. Allison ames provide an overview of monte carlo simulation studies mcss in item response theory irt. The goal of this set of notes is explore issues of reliability and validity as they apply to psychological measurement. The report is intended for use as a reference by researchers and test developers working in the. The reliability estimates and sems for the computerdelivered verbal reasoning and quantitative reasoning measures of the general test are based on item response theory irt. Michael furr discusses traditional psychometric perspectives and issues including reliability, validity, dimensionality, test bias, and response bias as well as advanced procedures and.
Each is an attempt to explain the process by which individuals respond to items. This chapter introduces reliability within the framework of the classical test theory ctt model, which is then extended to generalizability g theory. The theory and practice of item response theory rafael. English language arts and mathematics grades 38 \ technical report pearson 2014. Understanding item analyses item analysis is a process which examines student responses to individual test items questions in order to assess the quality of those items and of the test as a whole.
Sep 03, 2016 item response theory item response theory irt refers to a family of latent trait models used to establish psychometric properties of items and scales sometimes referred to as modern psychometrics because in largescale education assessment, testing programs and professional testing firms irt has almost completely replaced ctt as method of. Item response theory is a newer theory with a focus on test items that adds more tools for solving measurement problems in psychology test bias adaptive testing item selection ctt focuses more on the total score of a scale or subscale. In psychometrics, the theory has been superseded by the more sophisticated models in item response theory irt and generalizability theory g theory. Item response theory aka irt is also sometimes called latent trait theory. However, irt is not included in standard statistical packages like spss, but sas can estimate irt models via proc irt and proc mcmc and there are irt packages for the open source statistical. It is shown that the maximum likelihood estimation of a lower asymptote can wreak havoc with the accuracy of estimation of a location parameter, indicating that if one needs to. Understanding item analyses office of educational assessment.
Introduction to educational and psychological measurement. Item response theory columbia university mailman school of. I know i can resort to classical test theory, cronbachs alpha, and other measures, but is there a way to characterize reliability within irt. An introduction to item response theory and rasch analysis. However, the indices are not constant as they are entirely dependent on the sample of examinees from whom they are obtained. Reliability is seen as a characteristic of the test and of the variance of the trait it measures. Reliability and validity, part i effect size calculators.
Item response theory is used to describe the application of mathematical models to data from questionnaires and tests as a basis for measuring abilities, attitudes, or other variables. All irt models are built to measure subjective phenomena, and the basic one is the rasch model. This study was designed to address issues related to the extent to which itembased estimation methods overestimate the reliability of test scores composed of testlets and to compare several estimation methods for different measurement. Item response theory irt has its roots in thurstones work to scale tests of mental development in the 1920s. Alternative methods of measuring reliability based on other psychometric methods, such as generalisability theory or itemresponse theory, can be used for monitoring and improving the quality of osce examinations 610, but will not be discussed here. However, the indices are not constant as they are entirely dependent on the sample of. Irt describes the relationship between a latent trait e. Introduction to educational and psychological measurement using r. Although demars irt can be considered to be an introductory book and requires almost no mathstats background it covers a variety of topics about item response theory. For further details on gt, see generalizability theory.
Eric ej598338 conditional standard errors of measurement. The reported values are an average of all the estimates obtained for all the multistage tests delivered between july 1, 2015, and june 30, 2018. As a result of a comprehensive survey of the related literature, the author provides nuggets of information about a wide range of rules of thumb and analysis alternatives. It is a theory of testing based on the relationship between individuals performances on a test item and. In psychometrics, item response theory irt also known as latent trait theory, strong true score theory, or modern mental test theory is a paradigm for the design, analysis, and scoring of tests, questionnaires, and similar instruments measuring abilities, attitudes, or other variables. The contents of chapters cover almost all important topics. An introduction provides thorough coverage of fundamental issues in psychological measurement. Lords book, applications of item response theory to practical testing problems, presented much of the current irt theory in language easily understood by many practitioners. 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. Item response theory irt and other advanced techniques for determining reliability are more frequently used with highstakes and standardized testing. As discussed by bock, thurstone envisioned a measurement model in which the probability of success on a given intelligence test item was a function of the chronological age of the respondent. Applying item response theory modeling in educational research.
In its simplest form, item response theory posits that the probability of a random person j with ability. A really great book that provides detailed and step by step derivations and programmings of item response theory parameter estimation techniques. An introduction to item response theory and rasch analysis of. It is not the only modern test theory, but it is the most popular one and is currently an area of active research. Classical test theory is an influential theory of test scores in the social sciences. Two approaches for exploring measurement invariance steven p. Mar 10, 2016 item response theory models student ability using question level performance instead of aggregate test level performance. Measurement precision varies across ranges of item difficulty and person ability. Despite the name, item response theory irt is not really a theory but rather a collection of measurement models. Designed for researchers, psychometric professionals, and advanced students, this book clearly presents both the howto and the why of irt. Item response theory irt is a latent variable modeling approach used to minimize bias and optimize the measurement power of educational and psychological tests and other psychometric applications. It is based on the application of related mathematical models to testing data. Item response theory advances the concept of item and test information to replace reliability.
These standard errors are very useful in understanding the reliability of your scale, as estimated by an item response model. Previous assessments of the reliability of test scores for testletcomposed tests have indicated that itembased estimation methods overestimate reliability. The classic source on gt is the book by cronbach et al. Item response theory irt is an important method of assessing the validity of measurement scales that is underutilized in the field of psychiatry. It covered basic concepts, comparison to ctt methods, relative efficiency, optimal number of choices per item, flexilevel tests, multistage tests, tailored testing. Jan 01, 2009 item response theory irt is a latent variable modeling approach used to minimize bias and optimize the measurement power of educational and psychological tests and other psychometric applications. Classical test theory and item response theory the wiley. Conditional standard errors of measurement for scale. Reliability is seen as a characteristic of the test and of.
Implications of cognitive psychology for educational measurement and the use of test in specific areas are also addressed. Item response theory item response theory irt refers to a family of latent trait models used to establish psychometric properties of items and scales sometimes referred to as modern psychometrics because in largescale education assessment, testing programs and professional testing firms irt has almost completely replaced ctt as method of. Doc item response theory, reliability and standard error. Item response theory provides a way to model the probability that a person with x ability will be able to perform at a level of y. Item response theory, reliability and standard error. Classical test theory an overview sciencedirect topics. Like the previous edition, this text is designed as a comprehensive text in measurement for researchers and for use in graduate courses in psychology, education and areas of business such as management and marketing. Information is also a function of the model parameters. Reliability and error in measurement instruments developed.
Item response theory an overview sciencedirect topics. It is used for statistical analysis and development of assessments, often for high stakes tests such as the graduate record examination. These indices are measured by the items proportion, p, of examinees who answer the question correctly and the itemtotal correlation, r. Krabbe, in the measurement of health and health status, 2017. Confirmatory factor analysis and item response theory. The approach will be to look these issues by examining a particular scale, the ptsdinterview ptsdi. Internal consistency reliability in item response theory models. Then, the entry discusses how the standard errors of estimates are derived, with an emphasis on the differences between standard errors and standard deviations. How can internal consistency reliability of a test and of individual test items be quantified in item response theory models. For example, according to fisher information theory, the item information supplied in the case of the 1pl for dichotomous response data is simply the probability of a correct response multiplied. Like classical test theory, gt is primarily concerned with the behavior of the test as a whole, rather than the performance of components, such as subscores or items. Two examples are used to illustrate the calculation of standard errors of a parameter estimate and. It is shown that the maximum likelihood estimation of a lower asymptote can wreak havoc with the accuracy of estimation of a location parameter, indicating that if one needs to have. Item analysis is especially valuable in improving items which will be used again in later tests, but it can also be used to eliminate ambiguous or.
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