Bell Curve - To remove or not to remove?
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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.
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:goodpost:
AWSP:
:goodpost: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. -
atutor2001:
:thankyou: . I always find T score thingy confusing. Thanks for explaining. In any case, T score is necessary as it is a placement score. It is not to reflect how well a child did in what, but rather to show what position a child be placed in national wide cohort.
I find the T-score formula very interesting and have been playing with it. Lets look at the following situations :lotus123:
my gal used to be top 6 in her std even though her MT was not very strong. and for psle she was the 15 th top in her sch and students who took Malay as MT got better T-score than her even though in sch exams these students used to be 20+ in std. I don't understand how and why. I assume it's because for MT as there are several sub-populations and the mean score and std deviation differ, this has an advantage for 1 or 2 sub- population over the rest. as for MT shouldn't MOE use raw score?
Situation 1
Mean = 75 higher average means EASY paperand SD = 13
For raw score of 100, T score = 69 pts
For raw score of 50, T score = 31pts (it is LESS than half of 69 pts - the T score for 100 marks)
Situation 1
Mean = 60 lower average means DIFFICULT paperand SD = 13
For raw score of 100, T score = 81 pts
For raw score of 50, T score = 42.5pts (it is MORE than half of 82 pts - the T score for 100 marks)
Therefore, the mean, i.e. the level of difficulty of the paper will affect the T-score. Imho, T-score can stay but not the current way of ranking by aggregate T-score (where the T-score of each subject is added up.) They should use the Total Raw Score to convert to T-score for ranking the students. In this way, the advantage of a low mean (as in MT paper) will be shared by all. Similarly, the effect of a high mean will also be applied to all.
Perhaps, only Singapore can do this.
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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 -
all day happy day:
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.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
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. -
all day happy day:
The distribution shown in the MOE's slides are all based on a nice normal distribution balanced on both sides of the mean.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
What happens if it is skewed left or skewed right because of the cohort's profile?
There is more leverage if you are strong in the subjects skewing left than if you are strong in the subjects skewing right.
I am making a guess that perhaps English appears to be the least \"weighted\" amongst all the subject.
Perhaps also thats why the primary schools with a heavier emphasis in Chinese score well consistently especially the Hokkien Clan Schools. -
slmkhoo:
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.
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.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. -
atutor2001:
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
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.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
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.
-
atutor2001:
Agree with your analysis but not sure that I agree with your conclusion.
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.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
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 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. -
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….
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