How PSLE Aggregate and T-Scores are calculated

To understand how PSLE Aggregate Scores are calculated, we must first understand T-Score. T-Score is the adjusted score a student will get for a subject, after a series of tabulations has been made.

T=50 + 10 x (X-Y)/Z

Formula for T-Score

X = Raw score of student
Y = Average Score of the whole cohort
Z = Standard Deviation* (SD)

Standard Deviation* (SD) is the spread of the marks around the average.

What is Standard Deviation (SD)
If the average score of 100 pupils who sat for English Test is 50 marks and the SD is 5, it means that 2/3 of the 100 pupils have scored 5 marks around the average, which means 66 of the students scored from 45 to 55 marks.

Similarly, if the average score of the same 100 pupils who sat for Mother Tongue Test is 50 marks and the SD is now 10, it means that 2/3 of the 100 pupils have scored 10 marks around the average, which means 66 students scored from 40 to 60 marks.


Example of how T-Score is calculated
Student A’s score for Science – 90 (X)
Average score of cohort – 70 (Y)
Standard Deviation - 25 (Z) (this means 2/3 of cohort scored from 45 to 95)

Using the T-Score formula

T = 50 + 10(X – Y) / Z
= 50 + 10 x (90 – 70) / 25
= 50 + 10 x 20/25
= 50 + 10 x 0.8
= 58

Student A’s T-Score for Science is 58.

Using T-Score to Calculate PSLE Aggregate Score
Let’s now take a look at Student A’s total performance

If the scores for the the subjects English, Mother Tongue, Mathematics and Science are 175, 170, 90 and 90 respectively, and the average score of the cohort are 120, 130, 75 and 70 respectively, and the SDs are 30, 35, 20 and 25 respectively, the T-Scores are 68.33, 61.43, 57.5 and 58 respectively. The Aggregate Score is 245.

The cohort’s average and standard deviation plays a big part in Student A’s score. Now, let’s move the average scores of all subjects down by 10 marks each, keeping all other variables (raw score and SD) constant.

The T-Scores will be71.67, 64.29, 62.5 and 62 respectively and the Aggregate score becomes 260.

Student A’s aggregate goes up from 245 to 260 when the averages of all subjects went down by 10 marks each. This shows that if the cohort is weaker, Student A’s aggregate score will increase, even if he/she scores the same marks for all the subjects.

It is therefore not accurate to compare a student’s Aggregate Score in a particular year, to the Aggregate Score of another student in a different year. Each year will have a different average for all the subjects.

Hence, it is not a good practice for parents who have more than 1 child, to compare each child’s PSLE Aggregate Score with his/her sibling's score. This is not a very fair comparison.

Conclusion

Because PSLE Aggregate Score is based on T-scores, theoretically, there is no such thing as “maximum aggregate score”.

Suppose Student A’s score are full marks for all his/her subjects (200 for English and Mother Tongue respectively and 100 for Mathematics and Science respectively), using the same averages and SDs earlier.

The T-Scores become 80, 72.86, 67.5 and 66 respectively. The Aggregate Score becomes 286.

Although Student A scored 100% marks for all subjects, his/her PSLE Aggregate Score is only 286. The only way to score that 300 (or even above that), is to have a very weak cohort in your year.

So if Student A scored 100% for all his/her subjects and still only scored 286 for his/her PSLE Aggregate, how did it happen that the highest Aggregate Score for the PSLE for 2007 was 294 (the lowest Aggregate Score was 87)? The lowest score for 2011's PSLE is 43 but the highest score is 283.