The moderating algorithm calculates a conversion curve to convert the raw assessment marks into moderated assessment marks.

The curve is a simple parabola of the form:

[maths]y = ax^2 + bx + c[/maths]

where 'x' is the raw assessment mark, 'y' is the moderated assessment mark, and the constants 'a', 'b' and 'c' are calculated from the distributions of raw assessment marks and exam marks.

However, it's important that the parabola doesn't have a turning point anywhere within the range of marks that are being moderated, because if it does you can't guarantee that a higher raw mark will always result in a higher moderated mark and vice versa.

If the curve is concave down, raw marks (x-values) beyond the turning point will result in lower moderated marks (y-values) than at or before the turning point, and if the curve is concave up, raw marks (x-values) beyond the turning point will result in higher moderated marks (y-values) than at or before the turning point.

In these situations the rank order of students is changed by the moderating process.

If the algorithm calculates a curve which has that problem, the curve can't be used, so the bottom moderated mark is adjusted to a value which moves the turning point outside the range of marks. Thus within the range of marks for the group being moderated, the curve can be said to be monotonically increasing, as a higher x-value will always produce a higher y-value.

See also:

Monotonic function - Wikipedia, the free encyclopedia
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