The Problem of Assessment
Even directly observed work-place assessment is not completely valid. The fact of being observed can make a difference to performance, for example. Anyone whose teaching has been observed can testify to this—even if you do nothing differently, the students may be inhibited, or "play up", or try to be "good". And the further one goes from the practical situation, the more problematic assessment becomes.
Let us assume that out of a given group of students, it is possible to tell who is competent in a given area and who is not. This is an entirely idealistic construction, of course, because whatever basis we construct for making the judgement, it will itself be a form of assessment. (Note, too, that "competence" as used here, is merely a general term covering knowledge as well as practice, and has no necessary implications of a competence-based assessment scheme.)
In practice, when setting an examination in a "hard" subject (as opposed to a "soft" one—the STEM disciplines, for example, are hard in this sense, and indeed in others, too), we decide in advance how difficult to make it, often with a view to how many "ought" to pass, or norm-referencing, discussed here and here. When we set a coursework essay, of course, we often make up our minds how strictly to mark only when we sit down actually to do it. It has been argued that such an norm-referenced approach underlies "grade inflation" in school examinations in the UK, and the discrediting of GCSE and A level qualifications. (News story here.)
Such an idealistic construction is known as a "gold standard". In the case in the diagram, about 80% are competent (or "deserve to pass") and about 20% aren't.
Let us further assume that we have an assessment scheme which is highly valid. It comes to the "right" answer about 80% of the time. Again, this is idealistic, because we rarely have a clue as to the quantifiable validity of such a scheme
What happens when we use this scheme with our group of students?
We end up with:
- 64% "True Positives": they are competent, and the assessment scheme agrees that they are. In other words, they passed and so they ought to have done.
- 16% "True Negatives", who failed and deserved to do so.
- 4% "False Positives": they passed, but they did not deserve to do so, and
- 16% "False Negatives", who failed, but should have passed.
False Positives are also known as "Type l" errors—finding something when it is not really there; contrasted with "Type ll" errors—failing to find something which is there. The most extensive literature on this comes from the field of medical testing and diagnosis; there is plenty of formal explanation on the web, but it can be very confusing. See here for an accessible explanation for non-mathematicians.
This is both unfair, and a potentially serious technical problem. I would not be happy if I felt that my doctor, or the pilot flying my airliner, had qualified as a False Positive!
There is of course a solution: raise the "pass" threshold. Unfortunately it's wrong. Whichever way you look at it, the validity of the scheme remains at 80% — you haven't made it any higher. And because the number of inaccurate judgements was a relatively small proportion to begin, a large shift in the proportion of overall passes and fails has only a tiny effect on the "false" outcomes. And raising the threshold in practice often means taking into account factors which are not strictly relevant or valid, such as the quality of presentation of assignments, or whether the views expressed accord with those of the assessor: there is a high probability that this may operate selectively to the disadvantage of "non-standard" students, and violate equal opportunities.
What's the answer?
There isn't a complete one. We have to live with it, and make strenuous efforts to improve validity. In particular, do not rely on a single assessment exercise: use a range of approaches emphasising different components of the taught material. Bloom's taxonomy is a useful tool to help you analyse your taught material and to match up potential assessment approaches. You can then undertake a more detailed evaluation of the strengths and weaknesses of your repertoire of techniques, and uncover where your errors are tending to occur.
The business of false negatives and false positives goes much further than this, of course. It is at the root of Bayes' (or Laplace's) theorem about making predictions on the basis of imperfect knowledge, and the uncertainties of, for example, diagnostic tests in medicine as well as educational assessment.
- There is more about it here (including a handy calculator).
- And here, using Venn diagrams.
- And a surprisingly readable book; McGrayne S B (2011) The Theory that would not Die: how Bayes' rule cracked the enigma code, hunted down Russian submarines and emerged triumphant from two centuries of controversy London; Yale University Press
This is an archived copy of Atherton J S (2013) Learning and Teaching [On-line: UK] Original material by James Atherton: last up-dated overall 10 February 2013
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 Unported License.
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