Bell Curve - To remove or not to remove?

[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.

[jtoh]

oldies:

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

Thanks!

In my personal observation, students who are good in languages/arts subjects do better in Sec 1/2. That's bec in Sec 1/2, aside from English and MT, there's 3 humanities subjects (Lit, History and Geog), Social studies, Math & Science. So there are in total about 5 subjects (languages, lit, history, geog, social studies) which a student strong in languages and humanities can excel in. Whereas the Science/Math student has just 2 subjects to excel in. But in Sec 3/4, it's equal opportunity for all students bec you choose your subject combination to your strengths. Students strong in Math/Science can choose a Trip Sci combination with double math. Students strong in Humanities can choose trip humanz. So it doesn't really matter.

[oldies]

Thank you jtoh and atutor2001 for providing the different views.

[bupashu]

Will_lim:

I've come across a great blog and want to share it here:


http://hedgehogcomms.blogspot.sg/2012/10/piecing-together-psle-puzzle.html

The article has really made me to ponder over my views about PSLE results. As they are calculated based on the bell curve or t-score (your relative score), I'm more convinced that this is a fairer type of assessment since it takes into account other variables (e.g. difficulty of the papers). But witnessing so many children nowadays have been stressed, pressured and even gone hysterical, I wonder if it can help to de-stress the kids if the bell curve system is removed.

The blogger has pointed out:

\"Ranking fosters competition and discourages collaboration because it becomes a race where it's about outrunning your rivals rather than performing to the best of your ability. I'd rather score an A and have my schoolmates score Bs than score an A* along with everyone else.\"

I quite agree with him on this idea that this system is actually promoting an unhealthy competition.

For myself personally, I have been discouraged and depressed very much during my school years as despite how hard I kept trying, I seldom got the grades I wanted. I guess maybe a sense of achievement or a little of satisfaction could have made my school life better and more enjoyable!

whether the bell curve is removed or not, it does not matter - it still exist. The normal distribution of people of diff degree of cleverness or dumbness exist in the population, even if every one denies it.

if you are depressed or discouraged, then work on understanding the truth and the truth will set you free. changing the presentation of talent distribution of removing the curve does not solve the problem. your problem is understanding yourself, your ability, and your definition of achievement. you are so far following other people's definition of achievement to be your own target and hence find yourself discouraged

[enoawng]

Will_lim:

http://hedgehogcomms.blogspot.sg/2012/10/piecing-together-psle-puzzle.html

I don't want to debate on the pros and cons of the bell curve but the author is right in that moe should be more transparent to provide the raw scores of each subject, the average and the standard deviation.

The 12 year olds can work out the t-scores themselves.....

[bupashu]

enoawng:

Will_lim:

http://hedgehogcomms.blogspot.sg/2012/10/piecing-together-psle-puzzle.html

I don't want to debate on the pros and cons of the bell curve but the author is right in that moe should be more transparent to provide the raw scores of each subject, the average and the standard deviation.

The 12 year olds can work out the t-scores themselves.....

lots of parents already have problem & difficulties understanding the t-score formula....u think the students at P6 can handle statistics, mean, median & standard deviation and 45,000 x 4 raw scores ?

but if you don't trust the t-score given, you can always request to review the t-score from MOE, and if you are still not satisfied, go file a court order to order MOE to reveal all the stats and get an independent committee of inquiry to audit the t-score process and procedures, including the computer software codes for it