Talk:Ofqual exam results algorithm

The algorithm

This is very clearly written, subscripts would be nice. I wonder how many people would understand that CAG and k both depend on student, that is, if the students are numbered in rank order 1,2,3,...,n then CAG(1), CAG(2),..., CAG(n) are the corresponding centre assessment grades, but also k(1),k(2),...,k(n) in increasing order would be values of the random variable with distribution given by the formula on the right (for each fixed value of j).

A question is, how are the values k(1),k(2),..,k(n) meant to be chosen? If we know that the desired distribution (the averaged and corrected distribution on the right side of the equation for each j) gives a particlar proportion of each grade A*, A, B, .... then we can allocate the k(i) in order to those grades. I suppose in general as the area under the curve is 1, we would choose k(1),k(2),... so that vertical lines drawn on the graph with those horizontal coordinates divide the area into n+1 parts each with equal area 1/(n+1). So k(n+1-i) is the inverse image of i/(n+1) under the function which is the integral of the distribution. In other words, the k(i) chosen so that the cumulative distribution function evaluated at k(1),k(2),...,k(n) would be each of n/(n+1), (n-1)/(n+1),..., 1/(n+1). So 0<k(n)<k(n-1)<...<k(2)<k(1)<1.

I guess the unfairness was that grade inflation is controlled *for each individual student* and in *each individual course*. While the method of controlling grade inflation doesn't matter much for the final statistics, from the standpoint of fairness for individual students, it isn't right to say 'Here's the maximum grade you could ever have received based on previous performance of your school'.