Abstract:

Almost always the assessment tests success is determined by a passing threshold, that is the limit value meant to define if a performance is bad or good.

But how to identify the threshold value and the criteria to establish the number of correct answers a candidate must give to show the competencies attainment? Is there a method to define it also in case of semi-structured and complex tests? Which factors affect the border point identification and help us to distinguish a positive result by an unsuccessful test?

Many trainers conceive their assessment strategies inspired by school and university traditional criteria (as the “18/30” minimum score currently in use in Italian universities). Most frequently instructional designers can hardly describe how they make their assessment choices, why they opt for a certain passing threshold or which is their reference theoretical frame. In fact trainers commonly neglect such matter. And everything looks pre-established, like a rule of nature: the “passing score criterion”. As if debating about it was a useless rhetorical exercise.

The point is nothing can be a priori established and the assumed “passing score criterion” is not only unfounded but in some cases false and meaningless. Why? Because there’s not a rule of nature able to determine a reliable and sharable “passing score” value.

What’s hidden behind the concept of “passing score” but a prejudice? How can a hypothetical 60% of the maximum score be undoubtedly equivalent to the fact students actually got the required knowledge/competencies?
Identifying a passing threshold essentially means determining a balance point where above probabilistic values about students getting the required competencies can be formally certified.

How can we determine such balance point leaving aside all the factors potentially altering the “passing score criterion” objectivity? Students could randomly answer, tests be unreliable or the attended passing threshold inadequate and so on. All these variables affect the test validity and can’t be ignored.

The present paper aims to describe a “passing thresholds” calculation model based on the conditional probabilities Bayes theorem. In fact, according to Bayes the balance value of the passing threshold must combine some conditions in order to effectively check the chances a student actually attained the required competencies.
Such balance point has to be related to the test typology and calculated at every turn, depending on the factors virtually perturbing the assessment phase.

Finally, after introducing the theoretical calculation model and confuting all the persistent prejudices about the matter, the author shows some application cases and ideal experiments to demonstrate how the “passing score criterion” actually is against all common and shared assessment logics.

Keywords:

Achievement threshold, Assessment, Bayes theorem.