Adjusting Marks
Introduction
The official University position is that Module Examiners are responsible to the Examination Board for returning marks which reflect the performance of students in relation to the Learning Outcomes of the module. Examiners should feel free to adjust marks if they believe that the raw marks do not correctly reflect students' performance. The Examination Board should be informed of any adjustment.
Adjustment ('scaling') should not be carried out merely to achieve a particular distribution of marks. There is no fixed proportion of marks which should be in a particular degree class, for example.
The School endeavours to produce scatterplots before Examination Boards, showing for a given module, the actual mark for each student against his or her average mark overall. Such plots can show up modules which apparently have too high or too low marks overall, as well as those in which the discrimination between strong and weak students is too high or too low. The Preliminary Examination Board ('Module Board') may then recommend mark adjustment to the Module Examiner.
Methods of Adjusting Marks
Two time-honoured methods are to add a fixed number of marks or to multiply marks by a fixed factor. Both have disadvantages.
Adding a fixed number of marks is hard to justify: why give all students the same additional marks? One problem is that the adjusted mark may go over 100% for some students. Another is that unless great care is taken to separate out such cases, students who obtained 0 through absence or by not answering any questions may unjustifiably receive marks. Considerable confusion is caused later when absent students appear to have marks.
Multiplying marks by a fixed factor can be justified if it appears that in effect the work was marked out of less than 100%, perhaps because of an error in a question or a mark scheme or because some part of the assessment was just too difficult. It is still necessary to ensure that the adjusted mark does not go over 100%, but the problem with students with 0 disappears.
Although these methods are commonly used, there is no real reason to keep to linear adjustments, since the relationship between marks obtained and achievement in the subject is unlikely to be linear.
A strong case can be made that any adjustment method should keep 0% and 100% fixed. The simplest formula which does this is:
Adjusted = Raw + K*Raw*(Max - Raw)
K is determined by choosing a particular pair (Actual, Desired) where the Actual mark is to be adjusted to the Desired mark. Then:
K = (Desired - Actual) / (Actual * (Max - Actual))
Thus, for example, to adjust marks so that an Actual mark of 35% becomes a Desired mark of 40% (i.e. to adjust the pass mark to be the original 35%):
K = (40-35) / (35 * (100 - 35)) = 0.002197802
So that:
Adjusted = Raw + 0.002197802 * Raw * (100 - Raw)
I've set up an Excel spreadsheet to do this calculation (it should work in Open Office, etc.).
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