Classical Test Theory (CTT) and Item Response Theory (IRT) are among the most popular frameworks for assessing measurement problems. In both perspectives, the critical issues explored include the characteristics of a person, and an analysis of the abilities which influence the results of educational and psychological tests through identification of item parameters including item difficulty, discrimination, and the examinees’ potential. While CTT has been frequently used in the past for psychological and educational measurement, IRT is steadily becoming a favorite measurement framework.
Classic Test Theory
For more than 80 years, CTT has been the foundation for measurement theory (Kline, 2005). The primary assumption commences from the idea that the difference in the ability of interest influences systematic impacts between various responses of examinees. CTT’s model assumes that test scores (TO) comprise of a true score (T) and an error score (E) which are both independent (Magno, 2009). CTT also assumes that a person has a true score which can be obtained if there are no measurement errors. Notably, the critical difference between the true score and the observed test score is a result of an error in measurement.
When measuring self-esteem, some of the aspects which respondents may be prompted to respond to include: I believe I have good qualities; I am a person of worth (compared to others). A person who has high self-esteem will certainly answer “often true”, but one with low self-esteem will respond with “seldom true” to the above statements. But this is not the case for random fluctuations which is definitely the point. On the condition that the response to items differs only on consideration of random fluctuations, then the items are perceived to be parallel which are functions of the same true score. The differences between these fluctuations is a result of random error.
Item Response Theory
IRT is a true score theory which portrays stronger assumptions compared to CTT. It considers the chance of being right or wrong and the Rasch model is the most convenient example of this theory. IRT models are “mathematical equations that define the estimated probability of a given response to a given item” (Cook, 2013). One of the vital characteristics of IRT is that item performance relates to the amount of latent trait of a respondent’s which is a statistical construct. Latent traits refer to the ability measurable by a test and the total score, therefore, is an estimate of the latent trait.
When measuring self-esteem, there are several parameters which may be used including the one parameter (item difficulty), two parameter models (item difficulty and item discrimination), and three parameter models (item difficulty, item discrimination, and guessing). The one parameter analysis, Rasch model, measures the logits which is the mean f the item difficulty and is a representation of the likelihood that a person will engage in a challenge. The logit establishes a link between an individual’s expression of self-esteem to the measure of difficulty. The connection makes it possible for measures on a scale to be transformed into an explanatory description which produces the measurements. IRT indicates the number of items endorsed and the difficulty level. A person who has low-self esteem will probably endorse natural items like “feel worthy” while a person with high self-esteem will endorse challenging items like “do things well”.
Conclusion
Reliability is a ration of the true score to the observed variance. CTT presents that the more true variance, the greater the reliability of the self-esteem measure. IRT analysis results in meaningful measures of self-esteem as it identifies items which depict the various levels of the constructs to be measured and link the values derived to qualitative content.
References
Cook, K. F. (2013, January 17). A Conceptual Introduction to Item Response Theory: Part 2. IRT Is a Probability Model. Retrieved from https://www.youtube.com/watch?v=b6FKYV1-mEU
Kline, T. J. B. (2005). Psychological testing: A practical approach to design and evaluation. Thousand Oaks, CA: Sage Publications
Magno, C. (2009). Demonstrating the Difference between Classical Test Theory and Item Response Theory. The International Journal of Educational and Psychological Assessment, 1(1), 1-11.
