The last video of 10 videos in this SPOC on "Writing test items for measuring student progress" presents the differences between the two main theoretical models in testing, classical test theory and modern test theory, with a focus on the Rasch model, including the connection between the ability of students and the difficulty of the test items.

The speaker begins with defining what a test model is and describing its data elements. An example of a classical simple item analysis i giving.

Next, the video describes the basic difference between the classical test theory, which focus on explaining the total test score, and the Rasch model, which is a probabilistic model with two variables, the ability of the student and the difficulty of the item. Item response analysis (IRT) is described, including explanation of the item characteristic curve (ICC) and how it indicates the probability for correct response given the student's ability. The video then give examples of distractor analysis of both well-functioning and not so well functioning test items.

The video ends with a summary of the precondition for the Rasch model, and it highlights the importance of ensuring that the data fits the model to ensure that the test measures the same construct as the other items.

Further reading

Rasch, G. (1960). Studies in mathematical psychology: I. Probabilistic models for some intelligence and attainment tests. Danmarks Pædagogiske Institut. ISBN 0598554513, 9780598554512
Wright, B. & Stone, M. (1979). Best test design. MESA Press: Chicago, IL, 240 pages. ISBN: 094193800X, 978-0941938006 (link to pdf)
Haladyna, Thomas & Rodriguez, Michael. (2021). Using Full-information Item Analysis to Improve Item Quality. Educational Assessment. Vol. 26. pp. 198-211. DOI:10.1080/10627197.2021.1946390
Thissen, D., Steinberg, L., & Fitzpatrick, A. R. (1989). Multiple-choice models: The distractors are also part of the item. Journal of Educational Measurement, 26(2), 161–176. https://doi.org/10.1111/j.1745-3984.1989.tb00326.x