There is a huge uproar in the land of the lions about the Advanced Level results being completely unreliable. So, I thought I’d add my 2 cents on the subject.

Disclaimer: I did study math at uni, but I’ve forgotten ~~all~~ most of it and I took only one stat class. So, I will keep it simple – that is not by choice, I am forced to.

The problem has arisen due to two different sets of exams taking place due to two different syllabi being employed. There are repeaters from 2009 and 2010 doing the old syllabus and then there are the 2011 kids doing the new syllabus. So, the outcome is that there were two sets of results.

But for university entry there needs to be a result set from which the top few can be selected. From what I understand, they took the two means of the Z-score distributions and polled it to get an adjusted mean. From this the adjusted Z-score was calculated.

There are 2 main errors in this process.

First, the Z-score calculation is not a linear function. Results from non-linear functions cannot be treated with linear functions. A simple example is to take the square function.

10+3=13 but 10^{2}+3^{2} ≠ 13^{2}

Similarly, linear manipulation (polling the mean) of results from non-linear functions (Z-score) gives erroneous outcomes.

Second, how can 2 different exams be matched up properly? Two people who got the exact same result on two different exams cannot be deemed as equals. Furthermore, taking the mean, median etc are all flawed methods.Since the population taking the exams are varied there is no way to match one to the other.

So, the bottom line is that there is no correct (or should I say justifiable) way of doing this. 2 different exams – 1 result. One way or the other, some people will get the short end of the stick. But, I guess that’s life people – it’s not fair. You just have to live with it.

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Even worse (I think), the group taking the exam based on the new syllabus differs systematically from the group taking the exam based on the old syllabus who are repeating for the second or third time. The newbies will be a broader group, including everyone in that cohort, from the cream of the crop that’ll get the scores needed for uni entrance to the stragglers who’ll give up. Picture a nice, wide bell curve of scores. The older crew includes only those that didn’t make it into uni their first or second time (so no top scorers) but are close enough to possibly passing that it’s worth trying again (so fewer bottom scorers). Picture a skinny bell curve. If they combine the two groups in a way that assumes a similar distribution of scores it’ll foul things up entirely.

I don’t know the data well, but I would guess a fairer way of doing this would be to look at past years and calculate typically what percent of the kids granted uni entrance are first-timers, and what percent are second- or third-timers. Assuming it’s a relatively stable proportion over the years, you could then use those number to determine the cut scores for the two different exams.

Hit the nail on the head sis. The way you’ve suggested is reasonable.

As usual no one thinks ahead in SL. The new syllabus has been in effect for about 6 years and no one thought of this before? And as usual there is no transperancy in anything, so no one will trust the system even if they do give the correct result.

It’s pretty pathetic when the authorities mess with the most important for some of these kids. I mean most kids peg their hopes on getting thru ALs and into uni.