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Why the Belfast Telegraph and Irish News must set the record straight on grammar school league tables.

Dr Hugh Morrison

Immediately below is a short letter  sent to the editor of the Belfast Telegraph approximately one year ago.  It concerned a conceptual error in the paper’s A-Level league tables.  Despite repeated requests to make the public aware of their  error in the rank order, the letter never appeared in print.  On May 22, 2017 the Irish News published a league table generated by precisely the same flawed algorithm.


To be assigned a low rank in the Belfast Telegraph’s recently published league tables is likely to do little for the reputation of a school.  Given the potential reputational damage, it is vital to ensure that the numerical rank assigned to each school is meaningful.  Examination grades are reported on what is known as an ordinal scale.  There is an ordering of standards associated with the various grades: An A* grade represents a higher standard than an A grade, which in turn represents a higher standard than a B grade, and so on.  In the Belfast Telegraph’s league tables, ranks are computed by adding grades.  Alas, this produces meaningless numbers because arithmetic in general, and addition in particular, is impermissible for ordinal scales.  The Belfast Telegraph must make this error clear to its readers.


The Belfast Telegraph clearly believes that its league tables measure academic excellence.   It refers to the likely impact of cuts on “excellence,” schools which are “top of the class,” and “top performing” schools.  Rebecca Black writes: “Whether you believe the highest priority for a school should be academic excellence or not, it is impossible not to be impressed at the consistently high performance of our top Catholic schools.”  But are such inferences justified?  Are these league tables capable of even identifying excellent schools?


The Belfast Telegraph eschews the orthodox method used throughout the world by newspapers when publishing school league tables, the so-called “Grade Point Average” procedure.  This attempts to respect the fact that the scale of standards implicit in the various grades is ordinal by assigning a weight to each grade.  For example, with regard to the A-level league table, 12 points might be assigned to an A* grade, 10 to an A grade, 8 to a B grade, and 6 to a C grade.  However, in the Belfast Telegraph’s methodology, all four grades are assigned exactly the same value.  Unfortunately, a league table which treats a CCC profile as indistinguishable from a profile of A*A*A* cannot lay claim to distinguish schools on the basis of their academic excellence.