Bell Curve - To remove or not to remove?

[AWSP]

slmkhoo:

kamom:

Interesting, very interesting indeed. I wonder if the scholar/s sitting in a cushy office coming up with all kinds of policies can see the way you all see.


The best way is to do away with T-score and follow the \"O\" levels way...

A* - 1
A - 2
B - 3
C - 4
D - 5
E - 6

Easy and completely transparent.

Not really, because where they draw the lines between the grades is still unknown. They could still use a bell curve or other method to decide how many get each grade. I would prefer the US system of percentiles. That very clearly shows ranking within the cohort, and is not dependent on the difficulty of the exams.

I take a middle path, a percentile ranking within the subject and scoring system on the grades as by karmom would be better than the current T-score which distorts the weights.

[AWSP]

atutor2001:

all day happy day:

Hi All,

Please find the below links to have better understanding about T-score.......
http://www.edgefieldpri.moe.edu.sg/wbn/slot/u2208/Parents_Link/Understanding%20PSLE%20T-scores.pdf

Very good slides on basic understanding of T-score. Unfortunately there is nothing on the difference in Aggregate T-score for 2 candidates with the same Total Raw Score.

For example,
Candidate A has 100 for Math, 100 for Chinese, 50 for English, 50 for Science and the total raw score is 300
Candidate A has 50 for Math, 50 for Chinese, 100 for English and 100 for Science with the same total raw score is also 300.

Based on current trend for mean scores, I dare confirm that the Aggregate T-score of candidate A will definitely be way higher than B. It is this subtle in-built \"weightage\" system in the \"Aggregate T-score\" (dependent on the mean score) that nobody would like to comment.

Why is this not ok? Subject like Math can get very high marks for most but there are some who just can't - so they will be penalised more because of the high mean (average) in math.

Let say A very good in English but not so in Math and is lower by 10 marks in math than B but got 10 higher in English than B. The additional T-score gained by A from English will be lesser compared to the T-score lost for the 10 marks in math. So there is this in-built weightage in the computation whereby the fairness is questionable for ranking 2 students with the same total raw score. It is equivalent to putting higher weightage to a subject with higher mean score.

I absolutely agree with what you're saying. Especially when the standard deviation is not moving in the right direction ie the main cohort is clustered downwards for reasons like for example Chinese, since for most of us, our mother tongue has become Singlish rather than Chinese

[wonderm]

atutor2001:

all day happy day:

Hi All,

Please find the below links to have better understanding about T-score.......
http://www.edgefieldpri.moe.edu.sg/wbn/slot/u2208/Parents_Link/Understanding%20PSLE%20T-scores.pdf

Very good slides on basic understanding of T-score. Unfortunately there is nothing on the difference in Aggregate T-score for 2 candidates with the same Total Raw Score.

For example,
Candidate A has 100 for Math, 100 for Chinese, 50 for English, 50 for Science and the total raw score is 300
Candidate A has 50 for Math, 50 for Chinese, 100 for English and 100 for Science with the same total raw score is also 300.

Based on current trend for mean scores, I dare confirm that the Aggregate T-score of candidate A will definitely be way higher than B. It is this subtle in-built \"weightage\" system in the \"Aggregate T-score\" (dependent on the mean score) that nobody would like to comment.

Why is this not ok? Subject like Math can get very high marks for most but there are some who just can't - so they will be penalised more because of the high mean (average) in math.

Let say A very good in English but not so in Math and is lower by 10 marks in math than B but got 10 higher in English than B. The additional T-score gained by A from English will be lesser compared to the T-score lost for the 10 marks in math. So there is this in-built weightage in the computation whereby the fairness is questionable for ranking 2 students with the same total raw score. It is equivalent to putting higher weightage to a subject with higher mean score.

Agree with your analysis but not sure that I agree with your conclusion.

I am not so sure comparison by raw scores only is fairer than using the T-score. If I score 70% for subject A and B. But A is a subject which MOST other students can score well, whereas B is a subject where most other students don't do as well. Should the two 70% be \"viewed\" the same? or that 70% for subject B should be \"viewed\" more valuable if the purpose is to do relative ranking? I don't have the answer, just think it is not a simple case of which way is definitely more fair.

[VALyap]

AWSP:

The Bell Curve's evil is in the distortion in weighting. Mother Tongue becomes the heaviest weighted apparently because of the 'profile' of the cohort. A very apparent symptom from past years observation is that is that the top scorers have typically very strong command of second language. You do not see top scorers who demonstrate strong maths or science or english skills over the rest of the subjects. You may also try to guess the profile of last years top scorers which coincidentally has a \"significant\" number of Malay students. The distribution in Mother tongue is most logically not a bell curve but a hump shaped curve or a very left skewed distribution. A skewed distribution will create a lot of distortion. I think this part is totally unforeseen by the folks in MOE and they are not willing to admit the problem.

Based on immigration trend, I would place a bet that this years top 10 scorers will have a good representation by Tamil students. (Another skewing effect).
To the more statistically trained people, I am saying that 3rd moment effect is quite logically present given our children's profile in mother tongue. The disortionary effect is worse and more drastic than the 2nd moment effect(standard deviation).
The pressure in PSLE is not due to T-score but the competitive entry into the top IP school with limited placing. It doesnt matter which way you design your scoring as long as demand exceed supply by a huge mile.

I have the same analysis as you on the skewed bell-curve… Mother tongue seems to influence and heavier emphasis which may benefits some students especially of late past 5 years or more! Just a wild guess, I suspects that it may be deliberately to create some level playing field among certain demographic! Especially the the 3rd moment effect on 2nd lang or mother T! So that in IP schools, diversity in demographic can be done in this matter! Give others a chance to be in top IP schools! social scientist calls it social engineering! some of us studied this in Uni….

[atutor2001]

wonderm:

Agree with your analysis but not sure that I agree with your conclusion.

I am not so sure comparison by raw scores only is fairer than using the T-score. If I score 70% for subject A and B. But A is a subject which MOST other students can score well, whereas B is a subject where most other students don't do as well. Should the two 70% be \"viewed\" the same? or that 70% for subject B should be \"viewed\" more valuable if the purpose is to do relative ranking? I don't have the answer, just think it is not a simple case of which way is definitely more fair.

Generally most people exhibit academic ability in either language or math. The lucky ones have both. To me both language and math are of equal importance. However, currently, those good in math (high mean) are enjoying greater advantage in the aggregate T-score ranking system.

For improvement, I was toying with the idea of a 2-tier ranking system.

1st Level ranking
Students should be ranked by their total raw score first. (This will put all subjects on equal weightage). There will be many ties i.e. students with the same total raw score will be considered to be in the same \"band\". So the students are grouped and ranked by \"bands\" first.

2nd Level ranking
Within each \"band\", the current \"Aggregate T-score\" shall be applied to rank the students within the band. This will help take into consideration their relative ability with regard to the mean and sd.

The confusion that may arise will be a student in a higher band may have lower \"Aggregate T-score\" than another one in a lower band.

Just throwing some idea that I hope may make sense.

[PiggyLalala]

atutor2001:

PiggyLalala:

When the paper is easy, the mean will be higher but the SD will be smaller, isnt it?

When the paper is difficult, mean will be low but SD will be bigger, am I right?
So it is hard to say how the t-score will be affected? Yes or no?

I remembered that the trend is still the same. Lets see these new situations :

Situation 1
Mean = 75 higher average means EASY paper and SD = 11 (smaller DS)
For raw score of 100, T score = 73 pts
For raw score of 50, T score = 27.5pts (it is MUCH LESSER than half of 73 - the T score for 100 marks)

Situation 2
Mean = 60 lower average means DIFFICULT paper and SD = 14 (bigger SD)
For raw score of 100, T score = 79 pts
For raw score of 50, T score = 43 pts (it is MUCH MORE than half of 79 pts - the T score for 100 marks)

The SD can change. But the trend on how the mean will affect the T-score of those people with marks below the mean score remains the same. That is, when the mean is low, those below the average will suffer a bigger lost in T-score while if the mean is high, those below the average suffer a smaller lost in T-score.

Lets create this hypothetical case study for 2 subjects using the above set of data :

Math
Mean = 75 higher average means EASY paper and SD = 11 (smaller DS)
Candidate Ah Kow gets 100 marks, T score = 73 pts
Candidate Bob gets 50 marks, T score = 27.5pts

English
Mean = 60 lower average means DIFFICULT paper and SD = 14 (bigger SD)
Candidate Bob gets 100 marks, T score = 79 pts
Candidate Ah Kow gets 50 marks, T score = 43 pts

Aggregate T-score of Ah Kow = 73 + 43 = 116 pts
Aggregate T-score of Bob = 27.5 + 79 = 106.5 pts

Note that both Ah Kow and Bob have the same total raw score of 150 marks. However, due to the use of aggregate T-score, Bob lost to Ah Kow because he did badly in an easy paper.

Moral of the story : The marks of a paper where everyone does well i.e. high average (e.g. math and Chinese) are much more precious than those of English and Science.

Just want to clarify. In yr post, you mentioned that when the mean is low, those below the average will suffer a bigger lost in T-score while if the mean is high, those below the average suffer a smaller lost in T-score. However, in the example of bob and ah kow, bob lost to ah kow because he did badly in an easy paper(higher mean). I don't quite understand because high mean, smaller lost in t score?

[atutor2001]

Thank you PiggyLalala for hgihlighting the mistake. I have made the correction in blue below :

atutor2001:

PiggyLalala:

When the paper is easy, the mean will be higher but the SD will be smaller, isnt it?
When the paper is difficult, mean will be low but SD will be bigger, am I right?
So it is hard to say how the t-score will be affected? Yes or no?

I remembered that the trend is still the same. Lets see these new situations :

Situation 1
Mean = 75 higher average means EASY paper and SD = 11 (smaller DS)
For raw score of 100, T score = 73 pts
For raw score of 50, T score = 27.5pts (it is MUCH LESSER than half of 73 - the T score for 100 marks)

Situation 2
Mean = 60 lower average means DIFFICULT paper and SD = 14 (bigger SD)
For raw score of 100, T score = 79 pts
For raw score of 50, T score = 43 pts (it is MUCH MORE than half of 79 pts - the T score for 100 marks)

The SD can change. But the trend on how the mean will affect the T-score of those people with marks below the mean score remains the same. That is, when the mean is low, those below the average will suffer a bigger (sorry error should be smaller)lost in T-score while if the mean is high, those below the average suffer a smaller (sorry error should be bigger)lost in T-score.

Lets create this hypothetical case study for 2 subjects using the above set of data :

Math
Mean = 75 higher average means EASY paper and SD = 11 (smaller DS)
Candidate Ah Kow gets 100 marks, T score = 73 pts
Candidate Bob gets 50 marks, T score = 27.5pts

English
Mean = 60 lower average means DIFFICULT paper and SD = 14 (bigger SD)
Candidate Bob gets 100 marks, T score = 79 pts
Candidate Ah Kow gets 50 marks, T score = 43 pts

Aggregate T-score of Ah Kow = 73 + 43 = 116 pts
Aggregate T-score of Bob = 27.5 + 79 = 106.5 pts

Note that both Ah Kow and Bob have the same total raw score of 150 marks. However, due to the use of aggregate T-score, Bob lost to Ah Kow because he did badly in an easy paper.

Moral of the story : The marks of a paper where everyone does well i.e. high average (e.g. math and Chinese) are much more precious than those of English and Science.

[oldies]

atutor2001:

Generally most people exhibit academic ability in either language or math. The lucky ones have both. To me both language and math are of equal importance. However, currently, those good in math (high mean) are enjoying greater advantage in the aggregate T-score ranking system.

Hi atutor2001,
Any idea which group of kids will perform better in secondary? The ones who are strong in maths or language ?

Thanks!

[atutor2001]

oldies:

atutor2001:

Generally most people exhibit academic ability in either language or math. The lucky ones have both. To me both language and math are of equal importance. However, currently, those good in math (high mean) are enjoying greater advantage in the aggregate T-score ranking system.

Hi atutor2001,
Any idea which group of kids will perform better in secondary? The ones who are strong in maths or language ?

Thanks!

Based on my personal kay pohing, I find that the one stronger in language tends to be more successful. Subjects such as philosophy, public administration, law, economic... needs good ability in language. It is more difficult to understand, analyse and apply such knowledge as compared to science and math. Philosophy, economics... provides the main framework for success - vision e.g. the Apple guy. Although he is also good technically, without the \"vision\", technical know-how can only help to improve or refine an existing knowledge. There will be no grand new invention or break through like what he had done in Apple. Many great scientists in the past were also great philosophers.

Those good in math and sciences usually become top employees. Those good in language usually become their own boss.

PS
Sorry mis-read your question.

In secondary school, for the first 2 years, the math/science guys are definitely more successful because they have common subjects. By year 3 and 4, after streaming, the language guys can outshine the math/science guys (usually in the top schools because the language guys in other schools are not really that \"powderful\" in their language and it is harder to \"learn\" those subjects. Nevertheless, with the science subjects removed, many of the language guys will starts to get better grades than his contemporaries who remain in math/science) In JC, we will find the percentage of language guys (in top schools) taking up top positions to be greater than math/science (note that the number of classes of language guys are much smaller so relatively speaking their success rate is higher although the absolute number is smaller. Usually top scholars come from language guys)

[oldies]

Thanks atutor2001.