A-GRADES AND PERCENTAGE MARKS

Note for COGSAS, 5 November 1997

The University is probably committed to a general marking scale which in terms of degree classes looks like this:

fail < 30 <= pass < 40 <= 3rd < 50 <= 2ii < 60 <= 2i < 70 <= 1st

One problem with this is that 30 percentage points are allocated to first class marks, which in a literal system are given A grades. There is no obvious way to map from A-, A and A+ to percentages.

One way to get a feel for what such mappings imply is to take account of the fact that degree classification depends largely on an overall mean. The effects of different choices on the final result can be clarified by looking at hypothetical cases.

A simple case to illustrate the point is to imagine a programme with two equally weighted courses in which a student gets A+ on one course and C+ on another (assuming that examiners somehow know what they mean by these letter grades). Possible mappings from letter to numerical grades give different outcomes for the student:

    Course 1        Course 2            Average         Overall result
                                                        based on average

    C+ -> 58        A+ -> 90            74              1st
    C+ -> 58        A+ -> 85            72              1st
    C+ -> 58        A+ -> 80            69              2i

All the above mappings for an A+ have been mentioned as possibilities. In the third example, the rules for pulling up a student might be important, so there is an interaction between use of the marking scale and the classification rules.

Another example of such a boundary effect occurs with an equally weighted average of 4 courses, where a student gets, say, 3 C-'s and an A:

    Courses 1,2,3   Course 4            Average         Overall result
                                                        based on average

    C- -> 52        A  -> 85            60.25           2i
    C- -> 52        A  -> 75            57.75           2ii

What is needed is consensus on the extent to which excellence in one course counterbalances average performance in others.

David Young

[Note: a fuller paper is available here.]