Infernal Ramblings
A Malaysian Perspective on Politics, Society and Economics

False Negatives and False Positives

Written by johnleemk on 3:00:46 pm Jun 2, 2007.

When testing a particular hypothesis, statisticians isolate possible errors into two types: type I and type II errors. A type I error occurs when we reject the hypothesis when in reality the hypothesis is true; a type II error occurs when we accept the hypothesis, when in reality we should have rejected it.

What does this statistical trivia have to do with Malaysian education? Well, every time we evaluate or assess our students, we are basically testing the hypothesis that the student is "smart".

In our exam-oriented system, our assessment of this hypothesis hinges mainly on students' performance in standardised examinations. We accept the hypothesis of "smartness" if the student scores an A; we reject it if the student, say, scores a C.

Generally speaking, it is difficult to avoid one type of error without falling prey to the other. If we want to reduce the rate of false positives, we could make the examinations very difficult, but this would have the unintended side-effect of increasing the chance of false negatives.

Likewise, if we want to identify as many "smart" students as possible, we would want to avoid false negatives — but making the exams too easy would in turn lead to many more false positives, students identified as smart when in reality they are not.

Another thing to bear in mind is that although this inverse correlation between false negatives and false positives generally holds true, it is by no means an ironclad law.

For example, our education system probably has a remarkably high rate of false positives. Every year, the number of straight A scorers goes up — and unless our examiners are inhumanly perfect, odds are that this is due to a growing probability of false positives.

The result is that there is a lot of pressure on students to score well in their exams — because if you don't score well, you clearly are at the bottom of the intellectual heap.

However, this is not always true. I do not think the false negative rate is very high, but I think it is definitely nonzero. I would classify myself as a false negative — my Malaysian examination results have been largely mediocre, but under a different examination system (the Cambridge GCE O and A Levels), I have done quite well.

An interesting question to ask ourselves would be why the false positive rate is so high. (If you doubt this assertion, just assess the intellectual calibre of the top students in any secondary school, and ask yourself if they are intelligent enough to get the marks they have been getting.)

I suggest that this is because our examination system is incredibly easy to game. Our examination system tests students on only one variable — how well they can memorise data.

Now, if there were no attempts to work around this, this would be probably a reasonable judge of intelligence. Intelligent people, by and large, do tend to be better at retaining information than others. (There would be a significant rate of false negatives, though — people like me who can't be motivated to memorise things for no reason would not do well in this system, regardless of actual intelligence.)

However, the fact is, people do try to work around this evaluation system. The proliferation of the intellectually deficient tuition industry is testament to this.

When you can coach people to memorise things, the examination system loses its predictive value — the false positive rate increases significantly. The government may be lowering the examination standards, but at the same time, we are also artificially increasing the proportion of students who can perform in the exams.

A better examination system would be one that cannot be gamed so easily. An ideal examination system would assess students based not just on their command of the material, but how well they can apply it — how well they can think about it, and draw conclusions from it.

This is obviously still a gameable system. The ease with which students perform in the O and A Level exams without needing to think about the material they have mastered is proof of this.

But at the very least, it reduces both the rate of false negatives and false positives. It is easier for an intelligent person who thinks to do well in this system, and it is harder for a person who does not think.

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Infernal Ramblings is a Malaysian website focusing on current events and sociopolitical issues. Its articles run the gamut from economics to society to education.

Infernal Ramblings is run by John Lee. For more, see the About section. If you have any questions or comments, do drop him a line.

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