Ok. My first post after skimming over the T-score calculation discussion. Here's what I can offer (which I'm sure has been posted countless times on KSP forums) although I have no wish to start a nuclear stand-off.


T-score is calculated based on the following formula.

https://s18.postimg.org/6pjcdufbt/T-score.png\">

where
T = Subject T-score your DC achieved
x = Subject raw score your DC obtained
m = mean (average) of raw scores of the close to 39,000 students (may be less students) for that subject
s = Standard Deviation of raw scores of all students for that subject

The standard deviation (s) describes the spread of the bell curve. For example, the mean (average) raw score of a subject, from 39,000 students, is 70 marks and has a calculated standard deviation of 5 marks. What it means is 99.7% of the raw scores fall within m+/-3s (i.e. 70+/-15 or 55-85 marks). If another subject has mean 70 but standard deviation of 8 marks, it implies that 99.7% of the raw scores fall within 70+/-24 or 46-94 marks. The latter subject would have a greater spread (or variance) compared to the first one even though both have the same mean (average) marks.

In PSLE, all subject raw scores are transformed to subject T-scores. The reason for doing this is two-fold:

1. Removing bias between subjects - Every subject's mean raw score is transformed to a subject T-score of 50 points (called moderation). Hence, regardless of how one subject could turn out to be harder than another subject, the moderation of mean raw scores, for each of the four subjects, to 50 points eliminates this \"unfairness\". This is important because your DC may be strong in Maths but the paper turns out to be harder than other subjects which robs him/her of a good aggregate (of 4 subjects) score. The argument is also true vice versa, i.e. the paper turns out to be easier than other subjects which gives him/her an unfair advantage.

2. Removing bias between subject spreads - Not every subject has the same spread. As mentioned in the paragraph above, one subject can have a wider raw score range than the other. To \"standardized\" the spread of each subject, the standard deviation transformation is introduced i.e. every standard deviation from the mean raw score is equivalent to 10 T-score points deviation from the mean T-score of 50 points.

Combining both the above factors would give rise to the T-score formula of T=50+10*(x-m)/s. What this means is every subject's raw score is fitted to identical bell-curves with the same mean (50 points) and standard deviation (10 points). Therefore, every subject is given equal weightage in the most equitable way. The aggregate T-score your DC obtains in the PSLE is the sum of the four subjects (EL, MTL, Math, Science) T-scores.

Example of T-score calculation
If your DC has a raw score of 77 marks for a subject with population mean=70 and standard deviation=5 marks, then the T-score is T=50+10*(x-m)/s=50+10*(77-70)/5=64 points. See image below for illustration.


https://s18.postimg.org/jwhz515a1/T-score_calculation.jpg\">

Everything is RELATIVE and not ABSOLUTE

Schools may have a prescription table that bands raw scores to grades e.g. A* is >= 91 marks, A is 75-90 marks etc. These are for their own school's internal-exam administration purposes. However, in the PSLE national exams, it is the bell-curve that dictates the grades your DC gets. In PSLE 2017, nationally, those that obtained A/A* are
(i) EL = 44.3%
(ii) Math = 44.4%
(iii) Science = 41.1%
(iv) CL = 68.3%

http://ngeeannpri.moe.edu.sg/qql/slot/u501/Achievements/PSLE%202017/PSLE%20Result%20Day%20%2824Nov%202017%29_final.pdf

Effectively, your DC needs to be in the top 44.3% in order to gain at least an A for EL. So the question is what T-score is required to be in the top 44.3% to get an A? I'll come back to this.

Z-scores and Implications

Back to the example of raw score 77 marks with mean 70 and standard deviation 5 marks, the calculated T-score is 64 points. What this also means is that a T-score of 64 points is equivalent to a top 8% placing (or 92nd percentile). To calculate this, we need to know the Z-score i.e.

Z = (x-m)/s

Therefore, in this example, Z=(x-m)/s=(77-70)/5=1.4. To calculate the percentile, we use the link

https://measuringu.com/pcalcz/

https://s18.postimg.org/hqs9ogm49/Z-score.jpg\">

Conversely, we can use the following link to back-calculate the T-score based on a certain percentile. Like for example, you want to know the T-score needed to achieve the top 10% (or 90th percentile).

https://measuringu.com/zcalcp/

https://s18.postimg.org/5q6tnh6x5/Percentile.jpg\">

The app throws up a Z-score of 1.2816. Remembering that T=50+10*(x-m)/s and Z=(x-m)/s, it implies that

T=50+10*Z

Therefore, T=50+10*1.2816=62.8 points. So to be in the top 10% of the cohort for the subject, a T-score of 62.8 points is needed. If we assume that all four subjects just barely make the cut of top 10% (90th percentile), the aggregate T-score will be 62.8*4=251. This is roughly the COP for IP programmes.

The real strategy to achieving your DC's aggregate T-score is to understand how well he/she is placed in each subject nationally. This can be done by inference. If you know your primary school's mean T-score, you can benchmark your DC's school's aggregate T-score (or aggregate percentile) to gauge the final PSLE T-score outcome. For example, your DC studies at NYPS and they reported a mean T-score of 242. Your DC may have a school's prelim T-score of 200, you can infer that your DC will score around 242 in the PSLE, barring any surprises, ceteris paribus.

I've done a table to show the percentile vs T-score relationship below. If you can gauge your DC's placing (or percentile) for each of his/her subjects, you may be able to give a good estimate of the final PSLE T-score.

https://s18.postimg.org/5fzb4bfi1/T-score_Table.jpg\">

Now back to the question of what T-score is required to be in the top 44.3% to get an A for EL? Based on the app, the proportion of area needed for 44.3% is 0.557 (55.7th percentile). This translates to a Z-score of 0.1434 which gives us a T-score of T=50+10*0.1434=51.4. So if your DC barely scores 4As, it would mean that the the aggregate T-score is

EL=51.4 + Math=51.4 + Science=52.1 + CL=45.2 ===> 200

Therefore, you can work out the upper range of 4As if you assume the top 10% to score A* for each subject.

In conclusion, this is not a full expose of the T-score system or how you can exploit it. But, rather, if you understand the statistics behind it, it can help you make better informed decisions, on how you can help your DC on improving weaker subjects or calibrate yours and your DC's expectations in the PSLE exams. And yes, with all these science and statistics behind the T-scoring system, we can officially declare the PSLE as an Olympic sport.

Just my 2 cents.

PHEW!