Standard Setting, Cut-Scores, and Incorrect Decisions

Anthony James asks:

Is there a term in the testing literature to refer to the stability, accuracy or consistency of pass/fail decisions in high-stakes tests when we compare candidates scores with a cut-score?

I have come up with some terms such as 'false positives', 'false negatives' and 'decision validity'. Is there a more precise term?

Gregory Stone answers:

There are several concepts we must consider when setting standards.

First, standard setting is an evaluative decision. Measurement assists us (extremely well if justifiable, valid models are used) but ultimately it is an evaluative decision. We cannot be slaves to calculations. Instead, assuming you have a construct, and can therefore describe what a person who passes has mastered, changes to the derived cut score should be considered in terms of content, and realistically, political reality. "If I reduce the score to X, I am giving up mastery of Y sort of content," for example. If such a loss is OK, then proceed. If not, consider more than just your standard - consider your expectations, development of the content, task analysis, etc. We cannot put the weight of these qualitative decisions on the back of the quantification.

Second, "stability" and "consistency," and to a lesser extent accuracy are really parameters of validity (or validation). Reasoned standard setting models provide error terms. Reasoned standard setting models demonstrate the description of a meaningful, content-based standard. Reasoned standard setting excludes iterative processes that simply introduce external norming, and, like IRT (2-3PL) introduce sample/item specific information that negating the possibility of generalization, equating, etc. All such conversations revolve around "Construct Validity" but construct validity in Messick's holistic expression, not simply a collection of pieces. Whether epistemological (Messick) or ontological (Borsboom) the idea of construct validity is the same. Therefore, assuming a reasonable model is used, there is no "false," because the standard is defined as a particular set of content. It is what it is. If we disagree, it doesn't mean the process has produced a false result.

Third, you ask about fairness. That's an excellent point. Reasonable models include an accounting of error as said. However, more importantly why are we giving or denying a person a job on the basis of one test score, whatever the cut score? Why do we hold back children, or prevent them from graduating on the basis of one score? The premise is that a single test score (a measure of mastery) is equivalent to "competency." It is not. Competency involves much more than a single score, regardless of how fair the cut score and well-developed the test may be. We too often consider mastery and competency as interchangeable. This is a problem. So if you deny a person a job or reject an applicant from college, it does not mean the standard on the exam is problematic; rather, it reflects a process of hiring/admission that produces results that fail the tests of validity and validation. Would we, for example, involuntarily hospitalize an individual on the basis of one psychological assessment tool? Of course not. We would review their overall case file. We would talk with them at length during a session. Why then do we believe one exam should wield so much power in achievement or employment or certification?

Construct Validity (and Validation) are the only terms we really need I would suggest. This isn't a statistical problem (with false x's) but an evaluative one.

(Excerpted from a conversation on the Rasch Listserv)

Standard Setting, Cut-Scores, and Incorrect Decisions, G. Stone ... Rasch Measurement Transactions, 2011, 24:4, 1311

Rasch Publications
Rasch Measurement Transactions (free, online) Rasch Measurement research papers (free, online) Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch Applying the Rasch Model 3rd. Ed., Bond & Fox Best Test Design, Wright & Stone
Rating Scale Analysis, Wright & Masters Introduction to Rasch Measurement, E. Smith & R. Smith Introduction to Many-Facet Rasch Measurement, Thomas Eckes Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr. Statistical Analyses for Language Testers, Rita Green
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Journal of Applied Measurement Rasch models for measurement, David Andrich Constructing Measures, Mark Wilson Rasch Analysis in the Human Sciences, Boone, Stave, Yale
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