Dec 19, 2007

PSLE Results and the Colour of Your Skin

If you've been reading the newspapers lately, you might have noticed that this year's top PSLE student was Malay. Natasha Nabila not only topped the 2007 exams, but also set a record for the highest results ever attained in the PSLE exams.

This would have surprised many people, because historically Malays in Singapore have done badly in school (relative to the other racial groups). Initially I thought that Natasha's success might be a positive sign of a trend that the Malays are finally catching up.

However, the statistics don't bear this out. This MOE chart breaks down PSLE pass rates by race, over a 10-year period. We see that as a group, Malays still lag behind, and the gap isn't closing. So Natasha is an exception to the rule, rather than an indicator of a trend.

The blogger over here (Both Sides of the Johor Straits) notes, however, that in recent years, the minority races (Malays and Indians) seem to be statistically overrepresented among the very top PSLE performers. For example, the top PSLE student in 2005 was Malay. The top performer in 2006 was Indian. The top performer in 2007 was Malay.

This is interesting, because statistically, even if Malays, Indians and Chinese were academically equal (and they're not - as a group, the Chinese do better than the rest), the probability is that the top performer would be Chinese (as the Chinese are numerically, and by far, the biggest group).

So the blogger has a conspiracy theory. He thinks that the MOE is "cheating" to ensure that the top student is non-Chinese. MOE's rationale would be to raise the morale of the minority races and to provide a positive role model (bearing in mind that each year, the top PSLE student receives abundant publicity in the media):
All credits due to our top non-Chinese PSLE students, but I think that the recent trend in top non-Chinese PSLE students may indicate some backroom number-shuffling at MOE. Even though statistics & probability year-on-year predict that non-Chinese students do not fare as well at PSLE, I’ll not be surprised that the people at MOE have ways of ensuring a feel-good factor for all ethnic groups in Singapore (keeping in mind that PSLE exams scripts are marked in secret, the papers are not returned to students, the grades are not contestable and even the full-marks for each exam-topic are not revealed).

Assuming that the top students in 2007 scored full-marks for the Maths and Science papers (which is possible), Natasha must have scored nearly full-marks for English language and Malay language (full-marks in these papers are impossible), as she stood clear above her peers in terms of total marks for all papers. Having said that, a top Malay PSLE student as announced by MOE can do much to lift the spirits of the Malay community in terms of ethnic pride and reinforcing MOE’s ‘educational meritocracy’ policy.

Well, who knows. It's a possible theory, I suppose. However, I have a simpler alternative explanation.

In each year, all the PSLE students take exactly the same exams (English, Maths and Science) - except for the 2nd language paper. Here the Chinese take the Chinese Language paper; the Malays take the Malay Language paper; and the Indians take Tamil Language).

At the top end of the curve, the very best students are all striving to achieve marks as close to perfect as possible. For English, Maths, Science, they all take the same paper, so the same ultimate obstacles to a perfect or almost-perfect score apply to all.

However, if the Chinese Language paper is marked more rigorously than the other Language papers, then there would be a good probability that non-Chinese students would be statistically overrepresented at the very top end of the curve (where everyone is striving for perfect or almost-perfect marks).

It's not necessarily a deliberate attempt by the Education Ministry to engineer a non-Chinese top PSLE student. It may simply be that the Chinese Language exam is marked more rigorously, because that's the way the Chinese Language markers are. The glass ceiling would emerge in those sections of the paper which require the marker's subjective assessment.

For example, if there is an essay section worth 40 marks, and if in practice the Chinese marker is willing to give a maximum 35 marks for an absolutely brilliant Chinese essay, well, there's your glass ceiling.

On the other hand, If the Malay/Tamil marker has no qualms about giving 39 or 40 out of 40 marks for an absolutely brilliant Malay/Tamil essay, then simple probability tells us that there's a good chance that the overall top PSLE student could be non-Chinese.

This differential is too small to have any measurable effect of the respective PSLE performance of the racial groups, when we view them as a group. But this differential matters, when it comes to identifying the very best few students (eg the top 10) in the entire nation.

It's like Matt Biondi in the 1992 Olympics commenting that if he had grown his fingernails a little longer, he could have won the 100m men's butterfly gold medal. With short fingernails, he touched home one hundredth of a second slower than the winner, and had to settle for the silver medal.

By analogy, Singaporeans taking the PSLE Chinese paper could be swimming with short fingernails. Of course, for the vast majority of students, this is a non-issue. They don't swim fast enough for the length of their fingernails to matter.

"My fingernails are too short.
That must be why I coudn't qualify for the Olympics."


Blackjack said...

I have a much simpler explanation, which is related to yours. The PSLE score is normalised per subject. Hence, the PSLE score is based on how many standard deviations above the mean a student scores in each subject. The distributions for the English, Math and Science are similar but for second language the mean and standard deviation is different.

It may just be that the highest score achievable in 2nd language is higher in Malay or Tamil because of that. Nothing sinister, just a quirk of the scoring system. Not even much to do with whether people mark more leniently.

Anonymous said...

It would be intersting if MOH could reveal the top scorers for just the common subjects taken by all students ie English, Maths and Science.

mk said...

I had an ex-teacher cab driver who had a similar theory. His reasoning, however, was that Malay was just an "easier" language to learn (rather than a grading convention), relatively speaking.

Not sure how rigorous that is, esp. considering the languages are not distributed randomly.

Either ways, he too suspected that if you just look at English, Math and Science, the toppers would show a hugely different profile. If true, no wonder we get so few data points on PSLE. Think of the controversy.

I'm still new enough here to not understand why, when they announced the results, we segregated the top students by race anyways.

Lau Min-tsek said...

General population for Singapore is (Wikipedia, 2007):
Chinese - 75.2%
Malay - 13.6%
Indian - 8.8%
Others - 2.2%

From the blog "both sides of the johor straits" (, the breakdown in race for the overall top students are (from 1999 to 2007):

Chinese - 8 (67%)
Malay - 3 (25%)
Indian - 1 (8%)

Just one additional student change at any of the race group will swing the % score by 8.3%. In other words, the sample size is too small to have any meaningful stats and conclusion. The variation is too wide for this small sample size.

Also, the discussion that minority races are over-represented as the top students is based on the past 3 years results, where no Chinese got the top honours. This is too short a time scale. When we look back to 1999 (9 years), we see the numbers start to even out. If we go back even further, I suspect the numbers will come close to the population distribution (or maybe not..... *shrug* :P).

I won't be surprised if for the next few years, we have a few Chinese who are the overall top students and none from the minority races. Increase in no of years = increase in sample size = less variation (assuming all else being equal -- which it may not, but let's not discuss this).

However, looking at the % representation of the overall top students, it is fairly representative of the overall population, taking into account the large variation.

There is also another way to look at the numbers.

If you look at the distribution of race of all the top students (not the overall top students), the breakdown from 1999 to 2007 is:

Chinese - 99 (89%) vs pop size of 75.2% (or about 18% higher than the population demographic)
Malay - 10 (9%) vs pop size of 13.6% (or about 34% lower than the population demographic)
Indian - 2 (2%) vs pop size of 8.8% (or about 77% lower than the population demographic)

Now this seems to tell me something. Like what the article suggest, the Malays are under represented. But it also showed that the Indians are under-represented too -- in fact, MORE so than the Malays.

But does this mean anything?

Let us all remember what the numbers measure -- they measure top students.

The results of top students may be considered the exception, rather than the rule. So the racial break down of top students may not correlate to the average results of the entire student population.

Again, from "Both Sides of the Johor Straits", the breakdown for PSLE passes (as opposed to top students), are (in 2007):

"In 2007, 99% of Chinese who sat the PSLE passed, with Indians at 95.9% and Malays at 93.5%"

The Malays used to be worse, having a pass rate of 88.6% in year 2000.

I don't have the numbers to proof it, but I recall that historically, Indians have higher pass rates than Malays in every year since we have PSLE. (and also by wider margins in the past).

Common sense would suggest that Indians would than have a higher representation in % in top students in relation to their population size, when compared to Malays, since more Indians pass PSLE.

This is not borne out by the result from 1999 to 2007. In fact the reverse is seen, as we can see in the above. Despite Indians having higher pass rates compared to Malays, Indians are under-represented at the top students category by 77% in relation to their population size compared to Malays, who are under-represented by 34%.

In other words, as far as top performers are concerned, Indians do worse than Malays. BUT, on the AVERAGE, Indians do better than the Malays.

This means there is no correlation between the racial breakdown of the top students and that of the general population who passes the PSLE exams.

The numbers for top students are the exceptions, and not the rule to any meaningful interpretation of race in academic results.

random said...

Why settle for a simple explanation when we can have conspiracy theories? :)

"I'm still new enough here to not understand why, when they announced the results, we segregated the top students by race anyways."

Well, here's my conspiracy theory:

Because when you present the data that way, you steer people into concluding that any pattern in the difference is necessarily due to the race of the children, which no one can do anything about, rather than socio-economic differences, which we can and should be doing something about?

Anonymous said...

>Well, who knows. It's a possible theory, I suppose.

I don't think so. Yes, while I think the MOE is much happier to see a non-Chinese take the top spot, I think it would be too risky to manage the results. Because if it leaks out, a lot of heads will roll.

So your theory is more probable.

Anonymous said...

The conspiracy theory you presented sounds great, except that it's overly kind towards the government. I doubt the people in MOE have actually rationalized and came to the conclusion that they had to encourage the minority races, but rather it seems more to me that this is a cover up for the poor results of minority races. By doing so, these Singaporeans from minority races will not realise the actual truth of the matter - which is that their results are seriously lagging far behind. This ensures that they do not then question the government and blame it for their poor socio-economic plight like what's happening in Malaysia. I think, this is a really exciting posisibility that should be further explored.

mk said...

"Because when you present the data that way, you steer people into concluding that any pattern in the difference is necessarily due to the race of the children, which no one can do anything about, rather than socio-economic differences, which we can and should be doing something about?"

thanks random, talk about clever framing. we have a lot of buzz on race but not on the poverty-education link.

aside: i hear some charities/grassroots here organize drives for school supplies/books for our local kids.

from the literature i can recall, education performance differences are primarily linked to socioeconomic variation (race might simply show up because it might correlate with socioeconomics but is not a IV/cause).

i think you shouldn't call that a conspiracy theory though, that's just how politics works. :)

ps: its like 3 AM so i'm not being rigorous but i hope the gist comes across...

Henry Leong said...

Hilarious shot!

Anonymous said...

First point
Fact: For the past 20 years, the Chinese language exam standard has been lowered and lowered and lowered (and then lowered yet again!) to suit the fake ang mohs among use.

Proof: MOE statistics say 81% of each cohort get A or A* in PSLE Chinese.

Implication: You can't distinguish yourself even if you get A/A* in PSLE Chinese. No big deal - among your 100 Chinese classmates, 80 others would have done just as well as you did (provided you are not from ACS Junior. Ha!).

Fact: Malay and Indian exam papers have higher standard

Proof: MOE says 75% of the pupils get A* or A for Malay. Corresponding figure for Tamil is 78%

Fact: PSLE T-score is a statistical way of scoring, which measures how well a candidate perform *relative* to his fellow candidates. Therefore, if you score 100 in Malay, you will get a higher T-score compared to scoring 100 in Chinese.

Second point
Ever since a few years ago when pupils can apply for direct admission to some secondary schools (RI and RGS and all other independent schools, for eg) *before* even taking their psle, the gifted stream student are no longer working as hard as they used to - why should they? their place at RI is already confirmed *before* psle. Thus, a raw score of X 10 years ago will give you a lower T-score, compared to the same raw score of X today. Remember: T-score is all over relative performance - relative to your peers.

Third point
Fact: Contrary to what reader mk said, the more difficult a subject is, the easier it is for you to get super high T-score if you do well in it. Because that's the definition of T-score!

Eg: pecentage of pupils getting A* and A in English language is only 44%. If you got an A*, you would have beaten at least 60% of your fellow candidates. Your high T-score will enable you to apply to RI, whereas someone who is equally as good as you are in Math and Science and Chinese, may not get in. Now if you are bad in English, then that's the end of you - you cannot get into top schools and hence garner a scholarship post-PSLE. Period. This is how we ended up with all the elites coming from English speaking background - an intentional political policy desiged to make sure that those "communists" Chinese students in the 1970s will not become elites. (It is for this same reason that until recently, only those who are good in English are allowed to take Chinese at first language - the govt does not want to end up with a group of "communists" who do not think in "English-style")

Anonymous said...

It's interesting to me that smart Chinese people would gather together and speculate on how a Malay can triumph in an examination, as if it's not known to happen. Is it so hard to simply believe that a Malay girl has done well in her exams and be happy for her?

She is, after all, a Gifted Education Programme student, which means that she has done well early in her life to gain a place in such an elite stream.

It's pretty typical of the majority to always assume their superiority of all spheres of Singaporean life, and feel insecure when a minority does well.

Actually, it's kind of sad, and it points to a streak of racism that still exists in Singaporeans.

Ahmad Raju DeSouza

Anonymous said...

I think its just being racist. Seriously, why do we care which RACE tops the PSLE?

Bringing this up just undermines the minority students' results and makes the majority students resentment increase.

Yes Malay is a simple language to pass; but go and try to ACE it. Are those implying that Malay is a simple language trying to say that the Malays are a simple lot who use a simple language as opposed to the Chinese who are a more "cultured" lot and thus have a much harder language?

Does it smell a tinge of racism to you? I think this discussion begins to STINK of racism.

Probability does NOT mean that the the if I have an even sided coin, I WOULD have 50 heads and 50 tails when I do 100 coin tosses. It does not even mean I would have 90 heads or 10 tails. It just means that for EACH TOSS the result would be a head or a tail. Do NOT use your rudimentary and A-level understanding of statistics here.

Its appalling to see that we are discussing such a matter, even amongst so called intellects.

Anonymous said...

I think it is part of a govt strategy to try to make minorities look good or be represented, even as a token, wherever possible especially in an area of not much significance. PSLE is one. What's the big deal? There are many more hurdles to go eg 'O', 'A'levels and univ. And also some positions in govt. Why are there some Malay ministers and MPs but none as perm sec or head of stat boards or the SAF? And why most of our Presidents are non Chinese?

Mr Wang Says So said...

"She is, after all, a Gifted Education Programme student, which means that she has done well early in her life to gain a place in such an elite stream."

I think you're mistaken about where I'm coming from. I'm just talking about probabilities.

I have no doubt that Natasha is a very, very bright student, just like all her other GEP classmates.

And if the majority of GEP students are male, probability tells us that the top GEP student is likely to be male.

If the majority of GEP students are female, probability tells us that the top GEP student is likely to be female.

If the majority of GEP students were Spanish or Indian, probability tells us that the top GEP student is likely to be Spanish or Indian.

If the majority of GEP students were Chinese, probability tells that the top GEP student is likely to be Chinese.

None of the above is sexist or or racist, but simply mathematical.

The actual outcome, however, went against probability for three straight years in a row, and so the question is whether this is just a statistical quirk, or whether there is some other factor like what I, or the other blogger, or some readers here, have mentioned.

moomooman said...

12 years ago, in 1995... More and more Singapore Chinese Families use English as the main language at home.

This has led to a deterioration of the proficiency of the Chinese Language in most of the chinese students.

This is exactly the reasons why Government has tried to make chinese much easier to pass now than before.

Face it... I'm sure all the commentors here would not have done any better in a PSLE chinese paper.

It's a fact that Chinese is a difficult language.

Mr Wang Says So said...

In the present context, I don't actually think that it's particularly meaningful to talk about whether any language is inherently more difficult than any other language (or more generally, whether any subject is more difficult than any other subject).

Fact is, we could jolly well teach "Quantum Physics" or "Political Science" at PSLE level. The topic will just have to greatly simplified, that's all. And the actual grades which the students score will depend on the standards that the exam-setters set, and the marking methodology. Which is inherently arbitrary.

Among the students who choose "Quantum Physics", there is no inherent unfairness because they all take the same Quantum Physics paper.

Among the students who choose "Political Science" there is no inherent unfairness because they all take the same Political Science paper.

Of course, if a minority of students choose "Political Science" and a majority of students choose "Rocket Science",

and year after year, the overall top students turn out to be those who chose "Political Science" -

then we would justififiably start wondering whether the differences in the marking methodologies / standards of these two subjects which is causing the overall top students to be those who choose "Political Science".

This, I emphasise, is not necessarily the case. It could be the case. An alternative explanation could simply be that the highest achievers, for some reason (including random quirk), are all just opting to take "Political Science".


On another note:

A reader left a comment alluding, among other things, to different racial groups and their relative penis/breast size etc. There's a valid point somewhere, but I've chosen not to publish the comment.

If that reader will resend the comment and substitute the examples given, or otherwise rephrase the language more delicately, I may publish the comment.

月下影子 said...

"It's a fact that Chinese is a difficult language."

I could have also easily said that English had been a difficult language for me to master (since I spoke nor wrote any English at home until I went to primary school), same for Mathematics or Science or any other subject for that matter.

(In fact, Chinese was the only subject that I had done really well in all my student life, but I went on to score well enough in other subjects to see myself through university.)

But what do I do about it? Continue to whine about how difficult a subject to learn it is, or simply step up on my efforts to try to ace it?

Or expect the government to lower the standard just so the majority of us could pass the examination? Surely, I cannot expect the same for English. I am not even talking about which of the two has a greater importance in terms of socio-economic value (by the way, the government's stance on learning Chinese in order to do business with China really stinks of pseudo-pragmatism, as with many of its other policies particularly in education - think of how the education policies have changed over the years starting 1970s)

Basically, it is about how you view each subject. Is it not about trying to do your best in each subject, whichever age you are at?

Really, which subject is not difficult to learn?

Statistics, scores, grades. Has education gone the "wrong" way? Is garnering good grades at the PSLE, or other examinations, the one and only definitive measure of how well you compare to others? Is that the one ultimate goal of getting an education - to beat others at examinations? Of course we cannot deny the fact that these examinations are there for a purpose, but really, is that all there is to being educated?

Anonymous said...

Chinese as a language(write and speak) has never been difficult to Chinese in China for more than 5000 years.

If the International Varsity Debates jointly organised by China and Singapore Broadcasters were(are) of any proof, then even non Chinese are capable of good command of it. PM Ruud of Australia is a very fine example.

Anyone thinking this piece by Mr Wang is racist,should read deeper into the Article. The manipulations of statistics had resulted in minds(mainly Singaporeans) bended and washed.

When it comes to languages and other cultural traits such as clothings and foods, I do wish that indigenous, originality and authenticity be maintained. They should not be compromised or worse bastardised .

Denzuko1 said...

Dear Mr Wang,

I am very fond of reading your posts as most of the time it gives a lot of insight to alternate opinions. Although I contribute less here than Molly Meek, I no doubt visit your site regularly.

While I enjoy your latest posting on the PSLE result, I do need to point out to you regarding the difference in standard between the Malay and Mandarin subject.

I have studied both Mandarin and Malay during my school time, I took Mandarin as first language in my PSLE while Malay for GCE 'O' Level.

You might not find this much of a comparison and I would just like to share with you that the Malay papers is actually much more dificult than Mandarin, not because of me having more problem in Malay than Mandarin. Even as a second language, the level of difficulty is close to taking a first language and the format follows the English paper.

I have got a marginal pass for my Malay GCE 'O' Level, partially because of its difficulties and my problem in adjusting to the language.

However, the gag is this, I converted back to Mandarin as second language by the time of JC and you know what, the paper is still a breeze after 4 years of absence.

For one thing, the Chinese paper adopted Multiple Choise, a far cry from the Malay paper which still insisted on sentence writing throughout. Further more, the Malay syllabus emphasised on studying the Malay culture and its way of live, which I find absence in the Chinese syllabus.

In fact I see the Chinese paper as very diluted in nature and it does not worth learning at all. I was even more shock with recent revelation that there are people even complaint of its level of difficulties and proposed to water it down further.

If you have used other subject for discussion, I would support you, but not Malay. In fact I hold the highest regard to those who tempt and triump over the Malay language.

Anonymous said...

Basically, Mr Wang has a hypothesis - that scores in all other subjects being equal, taking Malay as the examined language is 'likely' to result in an overall higher score because it is 'easier' to score better marks.

This is analogous to another popular hypothesis among JC students - that it is better to avoid subjects where it is relatively 'harder' to score A's e.g. Literature or History.

The only reason race entered the equation is because rather uniquely, in the Singapore education system, a student is required to take his/her 'mother' tongue as the language to be tested.

Now even that is not straight forward. While Chinese students have to take Chinese as their tested language, Malay or Indian students could opt to learn Chinese instead and their language tested is Chinese. In old days, Chinese students could actually have Malay as their tested language but no longer.

Mr Wang's hypothesis can be tested. Compare the scores of the top percentile of Chinese and Malay students but exclude their language scores. (Would MOE release the data?)

Now my own hypothesis is that the language score doesn't make a statistical difference, that the top Malay student did just as well as the top Chinese student in Science and Maths. Anyway, three years is too short a period to arrive at a statistical conclusion. If over 50% of the time over ten years and with the language score removed, the top student is a Malay or Indian student, that would indeed be interesting, not so much because the top student is a non-Chinese but for the underlying social or cultural factors that made the top student perform well.

Mr Wang Says So said...

I also studied Malay previously. I took it as a 3rd language (even though the more "fashionable" choices then were Japanese, French, German etc).

I dropped the subject after Sec 2, as I felt somewhat overloaded with other subjects and CCA (or ECA, as they were known in those days).

In terms of inherent "easy-ness", I think one "easy" aspect is that wherever it doesn't have an indigeneous word of its own, it seems to just borrow from the English language.

For example, "orange" is "oren"; "apple" is "epal"; "bus" is "bas", English is "Inggeris".

But my earlier point still stands. The key factors are still not the inherent "difficulty" of any subject, but the level at which the exam is set and how the markers mark it.

Mr Wang Says So said...

More examples:

Doctor is "doktor"
Book is "buku"
Computer is "komputer"
Class is "kelas"
System is "sistem"
Encyclopaedia is "ensiklopedia"
Music is "musik"

Shamino said...

My personal favourite is still "teknologi" =)

Just wanted to point out that sometimes runs do appear more likely than we intuitively think they should be. Say you got a coin that has 80% probability of heads and flip it 20 times. A run of at least 3 tails would have about a 10% chance of coming out.

Of course if we increased it to 90% heads then the probability of at least 3 tails drops to 1%. But like blackjack said, it's probably due to a per subject curving that grants exceptional Malay/Indian students to pull ahead of their fellows, especially when the cohort is much smaller than those taking Chinese.

For me, the whole PSLE results vs skin colour doesn't make much sense, since by ignoring all other factors it seems to be trying to find a genetic factor to PSLE results. It would probably be more useful for MOE to categorize by income group / family background etc. Is Natasha from a well to do family background?

For the probability computations I couldn't find an exact formula, but this page has Excel code to do the computations.

jonathan said...

Despite Mr Wang's explanation, Natasha is still a statistical anomaly compared to her Malay peers. That's all there is - she's way ahead. She may well have got 40/40 for her essay while the second best essay got 35/40 - STILL just an anomaly. Let's just leave it at that she's just an exceptionally bright student, ahead of everyone else, regardless of race. Everyone here makes it sound like it's not right that it happened.

Denzuko1 said...

I am not too sure what Mr Wang mean by the level which it is set. To me it still link to the level of difficulty because Malay as second language is set close to the level of a first language. While Mandarin on the other hand is moved down the slide to the level of multiple choice, I would say that this is worse than second language.

If we include the race factor into the language exam, I would say the Malay excel better than the Chinese, the level of difficulty is not the factor, but rather individual roots to their own culture. No matter what, the Malays here are very staunch in retaining their own culture and those parents I know are still very traditional. Their main language at home is Malay.

What do Chinese speak at home, Manarin ocassionally, English, and dilect. Even for my kids, I have trouble getting them to speak my own dilect because my wife emphasised so much on English. My daughter is English speaking and I am putting in a lot of effort to convert her back to Cantonese.

I have a newphew who only spoke English, his father went to work in Hong Kong. When he went visiting, he tried to join with the local kids, he could not speak their language. The worst thing is that both parents can speak Cantonese, the father is even of Cantonese blood. Comments from the other kid, " are you a mute?"

Let's go back to the syllabus, I was fortunate enough to attend Malay for a week before I change the language back to Mandarin during JC. Do you know what they are teaching? The subject was the marriage process, what people do during a wedding. As far as I know, Mandarin lesson never touch on this kind of stuff.

yh said...

this is quite fun.
i've another hypothesis.
There are now many PRC children in our primary school system.
They do better at chinese even when compared to smart singaporean chinese who may otherwise have a chance at becoming the top student.
Smart chinese singaporean score is dragged down (slightly) by his chinese score.
Malay or indian child become top student.

Anonymous said...

My goodness. Despite Mr Wang's insistent that there's nothing racist nor sexist about his post, I can't help but wonder why he's singling out this girl's outstanding performance. Would Mr Wang be writing this post if the girl was Chinese or Indian?

Give her a break. She did well amongst her peers, and she would've done well even if her skin were white, black, blue or purple with polka dots since colour of skin has no corelation to the brain.

Don't rob that credit away from her by trying to justify it will all these theories.

Mr Wang Says So said...

Why am I singling out this for discussion? Very simple. My post is just a response to the other blogger (Both Sides of the Johor Straits).

He suggested that the Ministry of Education could be DELIBERATELY engineering the PSLE results, through "backroom number-shuffling", with the intention of producing a non-Chinese top PSLE student,

among other things, to lift the morale of the minority community, and to reinforce the public perception of "educational meritocracy" in the system.

I am saying that I do not think the MOE would deliberately do such a thing. In other words, I do not think that MOE deliberately searched for ways to make Natasha the top student, on account of her race.

jl said...


that's like saying because there are many children who come from english speaking backgrounds taking the english paper, they steepen the curve for non-native english speakers and thus it's unfair. it's a truism that the cohort's makeup will ultimately affect the performance of each student, but this is not unique to the chinese language.

my malay class was full of asean scholars (mostly chinese malaysians and indonesians) who were way ahead of everyone else in terms of language proficiency. And there are Indian nationals who ace their Tamil et al language exams too.

so unless you're talking about the sheer volume of prc students inundating the system, then i fail to see your point. the other reason's that you believe prc students are setting the glass ceiling for local chinese paper candidates, which betrays your inherent belief in the superiority of chinese people (i'm part chinese and no part malay myself, as it were) - which explains the entire hue and cry about natasha. It seems there's no convincing some people that it's entirely fathomable that one of *them* can beat the chinese at their own game, as anomalous as it is.

that said, i do agree that she's a statistical rarity, but 2 malays and 1 indian top pupil's not big enough a sample size for a conspiracy theory to have traction. i do think the MOE should be more transparent, but the whole releasing the results of 3 common subject business reeks of sore loser-ness and a need for vindication.

yh said...

you are suggesting that i'm racist and i'm rather offended.

As Mr Wang has mentioned, even if all three races were academically on par, it is less probable that a child of a minority race emerges as the top student. The chances are even smaller if you take the relative performance of each race into consideration.

For a event of such small probability to happen three years in the role may suggest that there is a systematic bias and, in my opinion, cannot be explain away as a 'statistical rarity'.

NOTHING to do with which race is superior. Any logical person, Indian, Malay or Chinese should be able to arrive at the same conclusion.

jl said...

i'm not trying to be adversarial, but some things are plain to see. Take your logic: "Smart chinese singaporean score is dragged down (slightly) by his chinese score. Malay or indian child become top student"

You're essentially saying a Singaporean Chinese (a "smart" chinese no less, as opposed to malay or indian "child") is poised for a top position but for the PRC Chinese who swooped in and stole his mantle.

There are similar variants in the other language papers as well, one being the Asean scholars, but that did not preclude Natasha from topping her batch. i'm not saying you're a racist. The phraseology just betrays a bit of bias.

Mr Wang Says So said...

Ok, let's do a few quick calculations. Assuming that:

1. no race is inherently academically superior to any other ;

2. 75% of the students are Chinese; and

3. it is equally difficult in all Language subjects to achieve a very high score (say, 98%),

then the probability of a non-Chinese student topping PSLE in three straight years is

(1 - 0.75) x ( 1 - 0.75) x (1 -0.75)

that is, around 1.6 per cent,

or abut 31 times worse than the probability of getting a heads, if you toss a coin.

Essentially, my main post refuses to bet on such odds, and prefers another explanation (which is that Assumption 3 is wrong).

hunguptodry said...

so many conjectures .... so little time.

It's like Matt Biondi in the 1992 Olympics commenting that if he had grown his fingernails a little longer ....

well, the longer fingernails would make him fractionally heavier and perhaps slower.

and why rain on the poor girl's parade? let her have her time in the sun. we all deserve it.

Anonymous said...

I may be wrong but I think her mother is a Chinese. I thought so when I saw the news reported on TV. Then a couple of days later, my friends and I happened to be talking about this subject. He appeared to be quite certain that her mother is a Chinese.

angry doc said...

"Ok, let's do a few quick calculations..."

Mr Wang,

Your calculations are only valid if the selection of the top student is a random event.

If assumption 1. is true, then the top student in a year can come from any of the races, regardless of the mix of the candidates in that cohort, and it doesn't matter if the percentage of Chinese is 75%, 99%, or 50%.

Shamino said...

Hi Mr Wang,

Regarding your probability calculation, it is only valid when you are considering a fixed 3 year period. As in my previous post, what we should calculate is the probability that in a span of say, 10 years, a non-Chinese tops the cohort for 3 (or more) straight years. Using your parameters, that probability would be 10%.

Translating into coin tosses, it is equivalent to the probability that in 10 tosses we get a run of at least 3 consecutive tails.

Mr Wang Says So said...

angry doc: no, you're wrong. We'll use extreme numbers to illustrate. Suppose there are 100,000 students of.Race X and only 100 students of Race Y. Assume that race is no predictor of academic superiority. The top student, out of the 100,100 students, is still much more likely to be of Race X than Race Y.

Mr Wang Says So said...

Shamino: the possible problem with your analysis is that the current marking methods may not have lasted for the past ten years.

Of course, whichever way we look at it, we're grappling with the lack of data, and the only organisation that has it probably won't be revealing it (especially if my theory or BSJS's theory is true).

angry doc said...

"Suppose there are 100,000 students of.Race X and only 100 students of Race Y. Assume that race is no predictor of academic superiority. The top student, out of the 100,100 students, is still much more likely to be of Race X than Race Y."

Assuming that race is no predictor, all we can say is that each child has a 1 in 100,100 chance of being the top student.

If all 100,100 children are identically smart, then the selection of the top student will be truly random and then what you say will be true.

However, if we assume that one kid is smarter than all the rest, and that what determines who this kid is is not his or her race, then any of the 100,100 kids can be this smartest kid, and that is not a random selection.

angry doc said...

Let me use another example to illustrate my point.

Assume we have a truly random die.

The chance of a '1' being rolled is 1 in 6.

Therefore the probabilty of 3 consecutive die-rolls all coming up with a '1' is 1/6 x 1/6 x 1/6 = 1/216, and the chance of 4 consecutive rolls being '1' wil be 1/1296, right?

Now if I have made 3 rolls, and each of the roll came up with '1', will you bet at 1 to 1296 odds that the next roll will not be a '1'?

Mr Wang Says So said...

"Assume we have a truly random die."

In our case, it is more accurate to think of it like this:

the die is equally likely to fall on any one of its six sides. However, five of those sides are marked "Chinese" and only one side is marked "non-Chinese".

"If all 100,100 children are identically smart, then the selection of the top student will be truly random ....."

Not that all children are IDENTICALLY smart - in the sense that all 100,100 children have the same exact IQ score of, say, 105 (which would be an astronomically unlikely event);

but that race is not a predictor of IQ; that is, a randomly selected individual of Race X is as likley as not to be smarter than a randomly selected individual of Race Y.

Shamino said...

Hi Mr Wang,

I'm merely using the same assumptions as you, which I thought would include that ignoring all other factors (marking scheme, economic background etc), the probability that for any year a Chinese would come out top is 75%. If the marking scheme could change in the past 10 years then it could also change in the past 3 years or even every year.

I guess given the (lack of) information available it is entirely possible that there is a group of men in black (or otherwise) that meet after the marking to tweak the results. But I'd rather just look for an easier explanation =)

It seems to me that you and angry doc aren't quite talking about the same thing. Using coin tosses with heads at 90%, with each toss being independent, angry doc says that after 2 flips of tails, the probability of tails on the 3rd flip is still 10%, which is correct. But Mr Wang is equally right in saying that if we looked at a group of 3 tosses (each toss still independent), the probability that all 3 tosses coming out tails would be 0.001, ie unlikely.

yh said...


Mr Wang's calculation shows that for an improbable event to occur three years in a row is even more improbable. This is correct.

I've some problem with your argument.

Suppose I buy a lottery ticket every year and I strike three years in a row. Improbable right? However, if I live to infinity years old and i buy a ticket for every year i live. the probability of the event (of me striking three years in a row) is 1!

You are right in saying that an event, however unlikely, will occur if you observe for long enough. But it doesn't make it less unlikely!

Shamino said...

Hi yh,

What you said is true, and I don't think I ever said an unlikely event becomes "less unlikely". I was only pointing out that it is not enough to consider the probability that the event occurs three years in a row, but rather the correct probability to calculate is that the event occurs at least three years in a row in a period of (for example) 10 years.

That is, assuming probability that a non-Chinese tops (assuming all other factors are ignored) is 0.25, we get the following:

Prob (non-Chinese tops the next 3 years) = 0.25 * 0.25 * 0.25 = 0.016

Prob (non-Chinese tops for at least 3 years in a row in a period of 10 years) = 0.1

The second probability is calculated using the method at

What I'm saying is that we should be using the second probability instead of the first.

As you said, if we observe long enough we would probably see the event occur, how long have we had PSLE already?

Shamino said...

If it makes it clearer, the main idea here is that our "sample space" should be the past N years of PSLE toppers rather than just a particular 3 years when we are trying to calculate how likely it is for a non-Chinese to top for 3 consecutive years.

Anon of December 20, 2007 2:56 PM said...

Mr. Wang,
Do you really know what is a T-score and how it is computed? Go to any of the more internet resourceful primary schools' website and check their powerpoint presentation for parents of primary 6 pupils.

Without going into the mathematical formula, T-score is a measure of how well a person score relative to his/her peers.

The opposite of what you said is happening. That is: the chinese paper is too easy and marked too leniently. As a result, a RAW score of say, 100/100, will not translate into a high T-score, because there are many other pupils also getting 100/100.

Again, opposite to what you said, the Malay paper is much harder and more stricter. So, a RAW score of 100/100 in Malay will translate into a much higher T-score because there are lesser pupils getting 100/100, compared to the Chinese exam paper.

And all these are already bored out by statistics because MOE's official statistics said that 80++% of pupils get A or A* in Chinese, but only 70++% of pupils get A or A* in Malay/Tamil.

Your hypothesis does not hold water at all, when view against the mathematical formula of T-score! To be long winded, it is the OPPOSITE of your hypothesis that is true, if one view this T-score formula mathematically instead of being clouded by non-mathematical personal prejudice/bias/whim and fancy.

Anyway, I am repeating myself. Ha!

Mr Wang Says So said...

You may be right. It doesn't really matter to me. Your theory is ultimately consistent with the essential point of my theory -

that there is SOMETHING in the way that the Language papers are being marked, which results in the best non-Chinese students having a small edge over the top Chinese students;

and not that, as BSJS has suggested, the MOE is deliberately engineering a non-Chinese top student for the sake of raising morale or providing a positive role model.

You seem very eager to make your point that the Chinese language is very easy; Chinese standards in Singapore have slipped drastically etc etc. Well, whatever lah, that is not the topic of my post. Maybe another day.

Mom-o'-Success said...

Dear Mr Wang

This is the first time I'm accessing your blog, which I came across by chance.

I happened to be in Singapore when the news about the top scorer for PSLE frontlined the republic's print media. After having left the system for close to three decades, it amazes me to know that there are still Singaporeans (and obviously highly-educated ones) indulging in discussions along the line of race, the way it's happening in this entry.

It's unthinkable by me seeing educated Singaporeans...

Thinking that there's a conspiracy to doctor the results of a common exam taken by minors (just because the child in question is a minority non-Chinese)...

Going into the rigmarole of statistical evidence to back one's argument (just to prove that it's improbable for a minority, non-Chinese to top the score chart)...

Insisting that there is a Chinese factor in the family lineage (and thus implying that a superb grey matter is the privilege of a Chinese)... (By the way, based on news report, the parents are both Malays; the mum is a housewife and the father is a technical staff at the airport - very ordinary parents indeed.)

Convinced that the outcome of last year's PSLE is a ploy by the authorities to create a 'feel-good' atmosphere for non-Chinese minorities...(thus implying that these minorities are in reality nowhere near that of the Chinese population in terms of capability and intelligence)...

It's very sad that after decades of efforts at nation-building and embracing the idea of ONE Singapore, there are still members of the citizenry who think of themselves more superior than their counterparts among the non-Chinese communities.

In wanting to rationalise the reasons behind the academic success of a non-Chinese child, what is forgotten is the element of divine intervention, assuming that there are among the blog participants who believe in God. "If God wills it, things will happen..."

There were times in the past when a mortal in Singapore tried to play god: he insisted we stopped at two; and later went on with the theory that highly educated parents would bear intelligent children (thus introduced measures that translated his thoughts into policies).In no time, Singapore will have an aging population, so now the younger mortal has decided that more is better.

How can one become a nation when deep in one's heart, one still thinks of oneself as the Superior US and one's fellow dark-skinned citizens as the Inferior THEM who cannot triumph over the Superior US.

What a shame and what a sham to think that highly-educated citizens of a first-world nation are fossilised in mindset, in believing that there is such a thing as a superior race.


Anonymous said...

Hi.Im currently in P6GEP this year.Im from the same pri sch as Nay(SHPS).FOR CA1 this year,i topped the class.Also,Nats a frens cousin of mine.And,for the past 5 years,i am in the top 10 position.Do u think i can top PSLE this year?PLS reply.ANY INTELLIGENT ANSWER.Tks.

Surendra said...

Why dont we all now request the MOE not to include the second language.
This is infact disadvantage for people who are taking Hindi as their 2nd language.
The Hindi paper is very very hard and getting 70% is also difficult and moreover there are many children whose MT is non-hindi but still they prefer to take this as they cannot take Chinese/Malay/Tamil.

Let us all now request MOE not to consider the 2nd language marks for ranking.

Anonymous said...

At the end of the day, after all of the logical assumptions and explanations the fact remains that there is still a possibility that the top scorer can infant be a Malay and I honestly don't understand what point the author is trying to prove by writing this whole long mess of an article just because the top scorer isn't a Chinese. You can do the math and conclude that there is indeed a higher possibility that the top scorer will be a Chinese student. But this does not cancel out the fact that the top scorer can still be a person of a different race despite the very low possibility and at the end of the day, the factors that will determine how high you score are your brains and hardwork, not your race. Stop trying to prove something that shouldn't even need an explanation to begin with.

Source: I scored 277 for my psle and graduated from primary school in the year 2010.