Bell Curve - To remove or not to remove?
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bupashu:
You missed my point. While I agree with you on that we may need a granular formula which is because of the competition for places into the IP school., my hypothesis is
by raw scores, there will be many pupils with the same aggregate scores
hence the raw scores have to be transformed (hence the name t-score = transformed score) to take into account how \"easy\" or \"difficult\" of each subject (measured by mean & SD)...in order to rank the pupils for the purpose of sec one posting
the whole exercise of t-score is just for the single purpose of sec school allocation by merit and nothing else. the guy ranked higher will choose his sec school first. that's it
t-score is not a measure of cleverness or ability (in a narrow sense) but it takes into account carelessness on the actual exam day
and it is totally meaningless to compare t-scores across different years / cohort...as there is zero meaning to rank one guy from this year against another guy from another year...
if everyone is given unlimited amount of time, everyone will score full marks and have the same score
the guy who \"invented\" the t-score formula is now the principal of NUSH
well, for those people who demand for \"transparency\" aren't they insinuating there is cover up ? after all the t-score formula is not a state secret, and the PSLE markers are their teachers
a) the t-score is designed SOLELY for data fitting into nice channel of 0-100 ( or even less) and NOTHING ELSE.
b) we have over speculated on that a difficult paper equate to low SD etc. I can easily design a paper where everyone score 0-10 marks for a difficult paper(low SD) or everyone score 90-100 for an easy paper (low SD again). Anything in between is unpredictable and pure speculation. AND it is not in the design.
There is no need to name the architect fof T-score although I know who he is as you have known.
I am re-engineering the thought process in the design as a point of interest and not because I am crying foul.
c)By virtue of points a and b, there are unintended effects which will be interesting to study as well. -
Hmm… need not name who the architect behind T-score, most of us aware….formula not a secret, it’s how and what values used to transformed
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bupashu:
thanks for a good summary for the need for t-score.
by raw scores, there will be many pupils with the same aggregate scores
hence the raw scores have to be transformed (hence the name t-score = transformed score) to take into account how \"easy\" or \"difficult\" of each subject (measured by mean & SD)...in order to rank the pupils for the purpose of sec one posting
the whole exercise of t-score is just for the single purpose of sec school allocation by merit and nothing else. the guy ranked higher will choose his sec school first. that's it
t-score is not a measure of cleverness or ability (in a narrow sense) but it takes into account carelessness on the actual exam day
and it is totally meaningless to compare t-scores across different years / cohort...as there is zero meaning to rank one guy from this year against another guy from another year...
if everyone is given unlimited amount of time, everyone will score full marks and have the same score
the guy who \"invented\" the t-score formula is now the principal of NUSH
well, for those people who demand for \"transparency\" aren't they insinuating there is cover up ? after all the t-score formula is not a state secret, and the PSLE markers are their teachers
Do you know the reason(s) why raw scores cannot be published to the individual student in addition to the t-score? -
enoawng:
ok if they give you the raw scores, are you going to collect all 45000 x 4 raw scores to compute the mean and the SD ?
thanks for a good summary for the need for t-score.bupashu:
by raw scores, there will be many pupils with the same aggregate scores
hence the raw scores have to be transformed (hence the name t-score = transformed score) to take into account how \"easy\" or \"difficult\" of each subject (measured by mean & SD)...in order to rank the pupils for the purpose of sec one posting
the whole exercise of t-score is just for the single purpose of sec school allocation by merit and nothing else. the guy ranked higher will choose his sec school first. that's it
t-score is not a measure of cleverness or ability (in a narrow sense) but it takes into account carelessness on the actual exam day
and it is totally meaningless to compare t-scores across different years / cohort...as there is zero meaning to rank one guy from this year against another guy from another year...
if everyone is given unlimited amount of time, everyone will score full marks and have the same score
the guy who \"invented\" the t-score formula is now the principal of NUSH
well, for those people who demand for \"transparency\" aren't they insinuating there is cover up ? after all the t-score formula is not a state secret, and the PSLE markers are their teachers
Do you know the reason(s) why raw scores cannot be published to the individual student in addition to the t-score?
it is meaningless -
AWSP:
the t-score formula is NOT just for competition for IP places.
You missed my point. While I agree with you on that we may need a granular formula which is because of the competition for places into the IP school., my hypothesis isbupashu:
by raw scores, there will be many pupils with the same aggregate scores
hence the raw scores have to be transformed (hence the name t-score = transformed score) to take into account how \"easy\" or \"difficult\" of each subject (measured by mean & SD)...in order to rank the pupils for the purpose of sec one posting
the whole exercise of t-score is just for the single purpose of sec school allocation by merit and nothing else. the guy ranked higher will choose his sec school first. that's it
t-score is not a measure of cleverness or ability (in a narrow sense) but it takes into account carelessness on the actual exam day
and it is totally meaningless to compare t-scores across different years / cohort...as there is zero meaning to rank one guy from this year against another guy from another year...
if everyone is given unlimited amount of time, everyone will score full marks and have the same score
the guy who \"invented\" the t-score formula is now the principal of NUSH
well, for those people who demand for \"transparency\" aren't they insinuating there is cover up ? after all the t-score formula is not a state secret, and the PSLE markers are their teachers
a) the t-score is designed SOLELY for data fitting into nice channel of 0-100 ( or even less) and NOTHING ELSE.
b) we have over speculated on that a difficult paper equate to low SD etc. I can easily design a paper where everyone score 0-10 marks for a difficult paper(low SD) or everyone score 90-100 for an easy paper (low SD again). Anything in between is unpredictable and pure speculation. AND it is not in the design.
There is no need to name the architect fof T-score although I know who he is as you have known.
I am re-engineering the thought process in the design as a point of interest and not because I am crying foul.
c)By virtue of points a and b, there are unintended effects which will be interesting to study as well.
it is used for ranking for the whole cohort to determine who has the right to choose his school before the next guy, including the guy with t-score of 43
why are people so fixated with IP or the top 10%? the root cause is really the sour grapes attitude mixed with kiasu mentality
why can't people recognise and accept that normal distribution of talent and examination ability exist in the population ? what is wrong by accepting such truth ?
do you guys seriously expect everyone to be able to score the same top marks ? then the questions will be set even more difficult to differentiate the differing ability of every pupil...want more stress ? -
bupashu:
the t-score formula is NOT just for competition for IP places.
You missed my point. While I agree with you on that we may need a granular formula which is because of the competition for places into the IP school., my hypothesis isAWSP:
[quote=\"bupashu\"]
by raw scores, there will be many pupils with the same aggregate scores
hence the raw scores have to be transformed (hence the name t-score = transformed score) to take into account how \"easy\" or \"difficult\" of each subject (measured by mean & SD)...in order to rank the pupils for the purpose of sec one posting
the whole exercise of t-score is just for the single purpose of sec school allocation by merit and nothing else. the guy ranked higher will choose his sec school first. that's it
t-score is not a measure of cleverness or ability (in a narrow sense) but it takes into account carelessness on the actual exam day
and it is totally meaningless to compare t-scores across different years / cohort...as there is zero meaning to rank one guy from this year against another guy from another year...
if everyone is given unlimited amount of time, everyone will score full marks and have the same score
the guy who \"invented\" the t-score formula is now the principal of NUSH
well, for those people who demand for \"transparency\" aren't they insinuating there is cover up ? after all the t-score formula is not a state secret, and the PSLE markers are their teachers
a) the t-score is designed SOLELY for data fitting into nice channel of 0-100 ( or even less) and NOTHING ELSE.
b) we have over speculated on that a difficult paper equate to low SD etc. I can easily design a paper where everyone score 0-10 marks for a difficult paper(low SD) or everyone score 90-100 for an easy paper (low SD again). Anything in between is unpredictable and pure speculation. AND it is not in the design.
There is no need to name the architect fof T-score although I know who he is as you have known.
I am re-engineering the thought process in the design as a point of interest and not because I am crying foul.
c)By virtue of points a and b, there are unintended effects which will be interesting to study as well.
it is used for ranking for the whole cohort to determine who has the right to choose his school before the next guy, including the guy with t-score of 43
why are people so fixated with IP or the top 10%? the root cause is really the sour grapes attitude mixed with kiasu mentality
why can't people recognise and accept that normal distribution of talent and examination ability exist in the population ? what is wrong by accepting such truth ?
do you guys seriously expect everyone to be able to score the same top marks ? then the questions will be set even more difficult to differentiate the differing ability of every pupil...want more stress ?[/quote]a) I dont think the guys on this thread are sour grapes or fixated over the IP schools placing. For me, PSLE is over and this PSLE has no bearing on me or my kids as the youngest have DSAed into an IP school and is not taking part in the S1 posting. (her Tscore is sufficient to qualify her into the school any way)
b) the point of interest is that I am trying to get people to open their eyes and not take too many things for granted like
i) normal distribution - even in finance and economics, researchers are shifting out of normal distribution into fat tailed distributions and skewed distribution (power law distribution). Can we be so sure?
ii) are there some unintentional effects in the design of the T-score. Does it cause distortion?
iii) what is the thought process in the design of the T-score
I re-emphasize that this is just a discussion of interest.
There are other issues that kiasuparents should examine carefully:
a) are we on the right track with the type of testing in Science and Maths?
b) are we making a big detour doing models and heuristics in Maths which all the kids ditch in secondary school?
c) can pure rhetoric that all schools are the same solve the stress and competition issue without bringing the secondary schools more or less in line in terms of quality and facilities?
d) should we adjust the requirements in mother tongue so that it is not so \"punishing\" while we want to encourage or promote the learning.
T-score is but one small part of the broadbased issues that we are facing.
I am not one to accept all \"truths\" without examining the \"truths\" first. -
I thought I could make the argument more rigorous in maths in addition to some of the numerical examples from atutor2001 since I am quite free this morning. Here is the working.
z= std deviation, x= raw score and y = mean.
Tscore= 50 + (10/z) (x-y)
Taking derivative and holding x constant to assess the effect on Tscore.
d(Tscore) = -(10/(zz)) (x-y)dz -(10/z)dy
The equation is in fact very ‘rich’ and gives a lot of insight.
The first term is the contribution of changes in standard deviation and the second term is contribution from changes in the mean. Both are negative signed meaning the increases in z and y results in decreases in Tscore.
The net effect would depend on z movement in relation to y movement. A simple measurement could be the skewness of the distribution.
Also atutor2001’s number example highlights the effect of landing on the wrong side of the mean where x-y changes sign.
But the crucial point which I would like to highlight is that it is very easy to note that even if a person’s percentile does not change, the cohort’s mean and standard deviation changes can have quite a strong impact especially across subjects. AND it is not a "moderation effect" as we always thought.
Moderation effect is about percentile ranking using a bell curve where a person can still score an A despite getting 40 marks if he is in the say top 10%.
In a certain sense, I would agree with Tharman that the T-score is too granular.
I hope the above will be interesting enough to share. Sorry for the calculus if you couldnt understand. -
bupashu:
the t-score formula is NOT just for competition for IP places.
You missed my point. While I agree with you on that we may need a granular formula which is because of the competition for places into the IP school., my hypothesis isAWSP:
[quote=\"bupashu\"]
by raw scores, there will be many pupils with the same aggregate scores
hence the raw scores have to be transformed (hence the name t-score = transformed score) to take into account how \"easy\" or \"difficult\" of each subject (measured by mean & SD)...in order to rank the pupils for the purpose of sec one posting
the whole exercise of t-score is just for the single purpose of sec school allocation by merit and nothing else. the guy ranked higher will choose his sec school first. that's it
t-score is not a measure of cleverness or ability (in a narrow sense) but it takes into account carelessness on the actual exam day
and it is totally meaningless to compare t-scores across different years / cohort...as there is zero meaning to rank one guy from this year against another guy from another year...
if everyone is given unlimited amount of time, everyone will score full marks and have the same score
the guy who \"invented\" the t-score formula is now the principal of NUSH
well, for those people who demand for \"transparency\" aren't they insinuating there is cover up ? after all the t-score formula is not a state secret, and the PSLE markers are their teachers
a) the t-score is designed SOLELY for data fitting into nice channel of 0-100 ( or even less) and NOTHING ELSE.
b) we have over speculated on that a difficult paper equate to low SD etc. I can easily design a paper where everyone score 0-10 marks for a difficult paper(low SD) or everyone score 90-100 for an easy paper (low SD again). Anything in between is unpredictable and pure speculation. AND it is not in the design.
There is no need to name the architect fof T-score although I know who he is as you have known.
I am re-engineering the thought process in the design as a point of interest and not because I am crying foul.
c)By virtue of points a and b, there are unintended effects which will be interesting to study as well.
it is used for ranking for the whole cohort to determine who has the right to choose his school before the next guy, including the guy with t-score of 43
why are people so fixated with IP or the top 10%? the root cause is really the sour grapes attitude mixed with kiasu mentality
why can't people recognise and accept that normal distribution of talent and examination ability exist in the population ? what is wrong by accepting such truth ?
do you guys seriously expect everyone to be able to score the same top marks ? then the questions will be set even more difficult to differentiate the differing ability of every pupil...want more stress ?[/quote]Your arguments are easy to comprehend, very sound and indeed commendable. I concur with your view 100%. -
:goodpost:
But I think your effort is falling on deaf ears.
I suggest that we leave this forum since both you and I are done with PSLE.
Don't waste your effort.AWSP:
I thought I could make the argument more rigorous in maths in addition to some of the numerical examples from atutor2001 since I am quite free this morning. Here is the working.
z= std deviation, x= raw score and y = mean.
Tscore= 50 + (10/z) *(x-y)
Taking derivative and holding x constant to assess the effect on Tscore.
d(Tscore) = -(10/(z*z)) (x-y)dz -(10/z)dy
The equation is in fact very 'rich' and gives a lot of insight.
The first term is the contribution of changes in standard deviation and the second term is contribution from changes in the mean. Both are negative signed meaning the increases in z and y results in decreases in Tscore.
The net effect would depend on z movement in relation to y movement. A simple measurement could be the skewness of the distribution.
Also atutor2001's number example highlights the effect of landing on the wrong side of the mean where x-y changes sign.
But the crucial point which I would like to highlight is that it is very easy to note that even if a person's percentile does not change, the cohort's mean and standard deviation changes can have quite a strong impact especially across subjects. AND it is not a \"moderation effect\" as we always thought.
Moderation effect is about percentile ranking using a bell curve where a person can still score an A despite getting 40 marks if he is in the say top 10%.
In a certain sense, I would agree with Tharman that the T-score is too granular.
I hope the above will be interesting enough to share. Sorry for the calculus if you couldnt understand. -
AWSP:
:goodpost:
iii) what is the thought process in the design of the T-score
I re-emphasize that this is just a discussion of interest.
There are other issues that kiasuparents should examine carefully:
a) are we on the right track with the type of testing in Science and Maths?
b) are we making a big detour doing models and heuristics in Maths which all the kids ditch in secondary school?
c) can pure rhetoric that all schools are the same solve the stress and competition issue without bringing the secondary schools more or less in line in terms of quality and facilities?
d) should we adjust the requirements in mother tongue so that it is not so \"punishing\" while we want to encourage or promote the learning.
T-score is but one small part of the broadbased issues that we are facing.
I am not one to accept all \"truths\" without examining the \"truths\" first.
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