Ability and Difficulty Measurements

Basic Concepts

In the context of Rasch Analysis, ability measures a single concept, i.e. the subjects’ skill in one area.  Elsewhere on this website, we have been using Rasch analysis for tests where there is a single correct answer. Rasch analysis can also be used in other contexts, although in all cases we still want ability to measure a single concept or attribute.

Rasch analysis can also be used with questionnaires using a Likert scale. E.g. suppose that we ask high school students to rate certain school subjects (e.g. English, History, Science, etc.) on a scale of 0 (don’t like), 1 (neutral), and 2 (like), then Rasch analysis can be used where “ability” measures how much students (the “subjects” in this context) like a wider range of school subjects) and “difficulty” measures the likability of school subjects (the “items”) with the least difficult being the school subjects that are most liked.

Since we are using measurements of 0, 1, and 2, we can’t use the UCON method, described Building a Rasch Model, at least as presented on that webpage (although extensions to this approach are described elsewhere), but we can use the PROX method as described in PROX Model for Rasch Analysis.

Other Likert scales

Note that we can use other rating approaches; e.g. extremely dislike, dislike, neutral, like, and really like. In this case, we can use ratings of 0, 1, 2, 3, and 4. Note that ratings must start with 0. When we use the Rasch data analysis tool, in this case, we must enter 4 in the Highest score field of the dialog box shown in Figure 1 of Real Statistics Support for Rasch Analysis.

As mentioned above, we can only measure one concept or attribute at a time, and so we don’t want to combine items where the students are say rating both a school subject’s likability as well as how easy it is to get a good grade in that subject.

References

Wright, B. D. and Stone, M. H. (1979) Best test design. MESA Press: Chicago, IL
https://research.acer.edu.au/measurement/1/

Wright, B. D. and Masters, J. N. (1982) Rating scale analysis. MESA Press: Chicago, IL
https://research.acer.edu.au/measurement/2/

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