Bell Curve - To remove or not to remove?
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The T-score formulation is interesting, its complication is probably unwarranted for. The point is not about trusting or not trusting it but to understand its effect first. That has sort of eluded us.
If you look at the formulation and try to understand the intuition. It looks weird. First, it tries to "recenter" the scores around the 50 mark by "differencing the score and the mean and adding to 50.
Secondly, it also tries to rescale the difference by a factor of 10/(standard deviation). I can only guess that 10 appears to be some form of "historical standard deviation".
It may appear that the guys formulating it assume that the standard deviation will be wide for an easy paper and narrow for a difficult paper. I think that is a disputable assumption.
However my guess is that the guys are merely trying to fit the scores into a channel by rescaling it using a standard deviation. And that channel happens to be 0-100.
The more I look at it, the more likely that my guess is correct.
It is possibly something that only Singaporeans can create. Uniquely Singapore!
And we boast that we are more advanced than everyone else who use the good old percentile to grade!
PS I dont think it is our intent to take them(MOE) to court. We are just discussing this out of interest and for the fun of it. -
AWSP:
The T-score formulation formulation is interesting, its complication is probably unwarranted for. The point is not about trusting or not trusting it but to understand the effect first. That has sort of eluded us.
If you look at the formulation and try to understand the intuition. It looks weird. First, it tries to \"recenter\" the scores around the 50 mark by \"differencing the score and the mean and adding to 50.
Secondly, it also tries to rescale the difference by a factor of 10/(standard deviation). I can only guess that 10 appears to be some form of \"historical standard deviation\".
It may appear that the guys formulating it assume that the standard deviation will be wide for an easy paper and narrow for a difficult paper. I think that is a disputable assumption.
However my guess is that the guys are merely trying to fit the scores into a channel by rescaling it using a standard deviation. And that channel happens to be 0-100.
The more I look at it, the more likely that my guess is correct.
It is possibly something that only Singaporeans can create. Uniquely Singapore!
PS I dont intend to take them to court. I am just discussing this out of interest.
my guess is, in MOE Not more than 5 persons involved in T-score , processes, formulation and final approval including the minister… just a wild guess! given the fact it's like state secret….just the chief statistician and Directors of examination branch & minister etc.. -
VALyap:
It is extremely weird that the only consideration in the T-score is data fitting into 0-100 range. Reflects the state of affairs in our civil service, perhaps. Ngiam Dong Tow is right in his recent comments on the civil service perhaps.AWSP:
The T-score formulation formulation is interesting, its complication is probably unwarranted for. The point is not about trusting or not trusting it but to understand the effect first. That has sort of eluded us.
If you look at the formulation and try to understand the intuition. It looks weird. First, it tries to \"recenter\" the scores around the 50 mark by \"differencing the score and the mean and adding to 50.
Secondly, it also tries to rescale the difference by a factor of 10/(standard deviation). I can only guess that 10 appears to be some form of \"historical standard deviation\".
It may appear that the guys formulating it assume that the standard deviation will be wide for an easy paper and narrow for a difficult paper. I think that is a disputable assumption.
However my guess is that the guys are merely trying to fit the scores into a channel by rescaling it using a standard deviation. And that channel happens to be 0-100.
The more I look at it, the more likely that my guess is correct.
It is possibly something that only Singaporeans can create. Uniquely Singapore!
PS I dont intend to take them to court. I am just discussing this out of interest.
my guess is, in MOE Not more than 5 persons involved in T-score , processes, formulation and final approval including the minister… just a wild guess! given the fact it's like state secret….just the chief statistician and Directors of examination branch & minister etc.. -
let me repost in simpler english:
x is the score; y is the mean and z is the standard deviation.
x-y = difference between mean and score.
50 + (x-y) = recentering a score around 50. if score is 70 and mean is 60,
the score is shifted to 60 ie 50 + (70-60).
50 + (10/z)*(x-y)= rescaling (x-y) by a factor of 10/Z and recentering to 50.
If we try to put intelligence into the rescaling factor, we should weigh the factor 10/Z lower for an easy paper and higher for a difficult paper. That means the standard deviation is higher for easy paper and lower for difficult paper. Is that TRUE always?
Or is it just a pure data fitting exercise, fitting the range of marks into a channel of 0-100? -
AWSP:
by raw scores, there will be many pupils with the same aggregate scoresThe T-score formulation is interesting, its complication is probably unwarranted for. The point is not about trusting or not trusting it but to understand its effect first. That has sort of eluded us.
If you look at the formulation and try to understand the intuition. It looks weird. First, it tries to \"recenter\" the scores around the 50 mark by \"differencing the score and the mean and adding to 50.
Secondly, it also tries to rescale the difference by a factor of 10/(standard deviation). I can only guess that 10 appears to be some form of \"historical standard deviation\".
It may appear that the guys formulating it assume that the standard deviation will be wide for an easy paper and narrow for a difficult paper. I think that is a disputable assumption.
However my guess is that the guys are merely trying to fit the scores into a channel by rescaling it using a standard deviation. And that channel happens to be 0-100.
The more I look at it, the more likely that my guess is correct.
It is possibly something that only Singaporeans can create. Uniquely Singapore!
And we boast that we are more advanced than everyone else who use the good old percentile to grade!
PS I dont think it is our intent to take them(MOE) to court. We are just discussing this out of interest and for the fun of it.
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 -
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 ?
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