Nineteen Point One
Internal assessment carries 20 marks in one Intermediate subject at a school with 42 candidates in a single section. The teacher's award sheet reads: mean 19.1, standard deviation 0.42, lowest award 18, and 31 candidates at 19 or 20. The evidence behind the marks exists in principle - three unit tests of 25 marks each, one project of 20 marks, and an attendance register - but what the teacher submitted to the principal is a single column of final totals with no test-wise or project-wise breakup. Six candidates carry project marks although no project file has been located. The principal must forward the marks in four days. A parent has written that the marks look uniform and unearned. A re-test for the six is possible in two days.
1. Separate the statistical problem from the procedural problem in this file. Which one should a moderator act on first, and why is the order not arbitrary?
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The statistical signal is the compression: a standard deviation of 0.42 on a 20-mark scale, with 31 of 42 candidates within two marks of the maximum and nobody below 18. An assessment component is supposed to discriminate, and this one barely does.
But a compressed distribution is not by itself evidence of wrongdoing. A well-taught class assessed against generous criteria will compress, and the spread alone cannot distinguish that from careless or inflated awarding.
The procedural defect is different in kind. Totals without a breakup cannot be audited, reproduced or defended. There is no path from a test paper to a mark, so neither the principal nor an external moderator can test whether the compression is legitimate.
That is why procedure comes first and the order is not arbitrary: it is the only route to a finding on the statistics. Request the item-wise marks, recompute five candidates by hand from the test scripts, and compare. If the recomputation reproduces the totals, the problem is assessment design - criteria too easy - and the remedy is different from the remedy for inflated awarding.
2. Set out a four-day course of action that deals with the six missing files, the 38 candidates clustered at 19 and 20, and the parent's complaint, without inventing marks.
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Day one: reconstruct a component-wise sheet for all 42 from the test and project registers. Anything that cannot be traced to a script, a register entry or a dated file is recorded as not evidenced. This is done before any decision about marks, because the decision depends on what survives.
Day two: re-test the six whose files are missing, since they have two days of notice available. If a candidate cannot produce the file and the teacher cannot evidence the work, the project component is reduced to what is evidenced, under a rule written down and applied to all six alike. The other 36 are not touched by this step.
Day three: check whether the clustering follows from the criteria. If the unit tests were out of 25 and most candidates scored above 22, the compression is a design fault. Report the raw marks and say so in the forwarding note.
Day four: forward the marks with a short note explaining the reconstruction. Reply to the parent in writing with the criteria and the method, never with another child's marks, and direct any further grievance to the principal in writing.
3. The teacher proposes to solve the problem by subtracting 3 marks from every candidate. Explain why this is not a remedy, using validity and rank order rather than a general appeal to fairness.
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It treats a documentation failure as though it were a finding of inflation. No evidence has been examined at the point the subtraction is applied, so the remedy is disconnected from any diagnosis; if the totals later turn out to be reproducible, the school has permanently falsified a valid record.
It also fails on its own terms. Subtracting a constant from everyone shifts the mean and leaves the standard deviation at 0.42 and the rank order unchanged. Since the complaint is precisely that the marks do not discriminate, a uniform deduction changes nothing that was objected to, while making the file less accurate than before.
The candidates who are actually penalised are the ones whose evidence is complete, and the ones who benefit are those whose files are missing, since their unverifiable marks are now laundered into a defensible-looking total.
If there is a real finding, the remedy is to re-mark a sample against the stated criteria and, if warranted, re-mark all 42, which changes individual totals in different directions and restores discrimination. A constant is a way of appearing to act.