mummy so kiasu:

ruohoo97:

The SD in my children's school were in the range of 14-11, where as in national level, SD could be up to 30, so in theory, it is not possible for school to calculate T score, am I right?

The SD in your children's school is small is probably due to the standard of their school cohort is good or the school set easy papers. Actually, nobody know the national level's SD. However, the SD for Math is generally biggest & language papers is the smallest. By using the school's SD to derive T score is just like doing sampling. You have to take it with a pinch of salt.

ruohoo97:

The SD in my children's school were in the range of 14-11, where as in national level, SD could be up to 30, so in theory, it is not possible for school to calculate T score, am I right?

ruohoo97:

atutor2001:

However, if the SD remains as 14 but the average score is increased to 75, the conversion factor is 0.68 if the raw score is 100 marks and 0.36 for raw score of 10 marks. The conversion factor works in favour of higher raw score.

Conversely, if the SD remains as 14 but the average score is decreased to 60, the conversion factor is 0.79 if the raw score is 100 marks and 1.43 for raw score of 10 marks. The conversion factor works in favour of lower raw score.

That is interesting. In my DD's school, the class was praying for the harder papers as they thought that would be \"in favor\" to the top class? :?

AnnyTan:

Now that the dust has settled, we can perhaps take a look at the most asked, yet least answered question about the PSLE. That question is – How are PSLE Aggregate Scores 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.

Formula for T-Score
T= 50+10 [(X-Y)/Z]

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.

Example 1 -
Boy A, B & C have $45, $50 and $55 respectively. They have an average of $50 each.

Example 2 -
Girl D, E & F have $10, $50 and $90 respectively. They also have an average of $50 each.

In Example 1, the spread ($45 to average of $50 and $55 to average of $50) is smaller than the spread in Example 2, where the spread is bigger ($10 to average of $50 and $90 to average of $50)

As such, Example 1 will have a smaller SD, as compared to Example 2.

Simpler Way to read Standard Deviation (SD)
If the average score of 3000 pupils who sat for Science Test is 50 marks and the SD is 5, it means that 2/3 of the 3000 pupils have scored 5 marks around the average, which means 2000 of the students scored from 45 to 55 marks.

If the average score of the same 3000 pupils who sat for Mathematics Test is 50 marks and the SD is now 10, it means that 2/3 of the 3000 pupils have scored 10 marks around the average, which means 2000 students scored from 40 to 60 marks.

Example of how T-score is calculated

Carol’s score for Mathematics – 90 (X)
Average score of cohort – 75 (Y)
Standard Deviation - 20 (Z) (this means 2/3 of cohort scored from 55 to 95)

Using the T-Score formula
T = 50 + 10(X – Y) / Z
T = 50 + 10 x (90 – 75) / 20
= 50 + 10 x 15/20
= 50 + 10 x 0.75
= 57.5

Carol’s T-score for Mathematics is 57.5

Now that we have covered T-score, we can take a look at PSLE Aggregate Score.
Using T-Score to Calculate PSLE Aggregate Score

Let’s now take a look at Carol's total performance

Table 1:
English = 175/200 [let's say score of cohort 120, SD is 30] then her T-score is 68.33
Mother tongue = 170/200 [let's say score of cohort 130, SD is 35] then her T-score is 61.43
Maths = 90/100 [let's say score of cohort 75, SD is 20] then her T-score is 57.50
Science = 90/100 [let's say score of cohort 70, SD is 25] then her T-score is 58.00

Add up all 4 subjects' T-score: 68.33 + 61.43 + 57.50 + 58.00
Carol's T-score is 245

The cohort’s average and standard deviation plays a big part in Carol's score. To demonstrate, let’s move the average scores of all subjects down by 10 marks each, keeping all other variables (raw score and SD) constant. This is how Carol’s score will now look like.

Table 2:
English = 175/200 [let's say score of cohort 110, SD is 30] then her T-score is 71.67
Mother tongue = 170/200 [let's say score of cohort 120, SD is 35] then her T-score is 64.29
Maths = 90/100 [let's say score of cohort 65, SD is 20] then her T-score is 62.50
Science = 90/100 [let's say score of cohort 60, SD is 25] then her T-score is 62.00

Add up all 4 subjects' T-score, Carol's T-score is now 260

Take note that Carol’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, Carol’s aggregate score will increase, even if 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.

Parents who have more than 1 child, tend to compare each child’s PSLE Aggregate Score with his/her sibling's score. This is not a very fair comparison.


Final Note –

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

Many parents believe the (non-existent) maximum aggregate is 300. That is a misconception.

To demonstrate, I have maximise Carol’s score (in Table 3) to full marks for all her subjects, using the same averages and SDs found in Table 2.

Table 3:
English = 200/200 [score of cohort 110, SD is 30] then her T-score is 80
Mother tongue = 200/200 [score of cohort 120, SD is 35] then her T-score is 72.86
Maths = 100/100 [score of cohort 65, SD is 20] then her T-score is 67.50
Science = 100/100 [score of cohort 60, SD is 25] then her T-score is 66.00
Add up all 4 subjects' T-score, Carol's T-score is now 286

Note that although Carol scored 100% marks for all subjects, her PSLE Aggregate Score is only 286. She did not score the (imaginary and non-existent maximum) PSLE Aggregate Score of 300!

The only way to score that 300 (or even above that), is to have a very weak cohort in your year.


I hope the explanation in this post gives parents and students a better picture how PSLE Aggregate Scores are calculated.

atutor2001:

Conversion of the raw score to the T-score depends on the average and the standard deviation (SD). In another word, we can simplified the formula for T-score :


T-score = Conversion Factor x Raw score (this conversion factor depends on the average, SD and the raw score.

In most estimates, we use 0.75 i.e. 3/4 as the conversion factor.

What is more interesting is that for each pair of Average score and SD, the conversion factor may not be a \"constant.\" It may or may not depends on the raw score.

Just for example :

For a SD of 14 and an average score of 70, the conversion is constant at 0.7142857

However, if the SD remains as 14 but the average score is increased to 75, the conversion factor is 0.68 if the raw score is 100 marks and 0.36 for raw score of 10 marks. The conversion factor works in favour of higher raw score.

Conversely, if the SD remains as 14 but the average score is decreased to 60, the conversion factor is 0.79 if the raw score is 100 marks and 1.43 for raw score of 10 marks. The conversion factor works in favour of lower raw score.

If we analyse carefully, it is a fair system because it favours the weaker students when the average is low (i.e. paper is difficult), to offset the level of difficulty of the paper. On the other hand, when the average is high (i.e. an easy paper), it favours the better raw-score so as to reward those who perform much better than the average.

Just to share my toying with the T-score formula to understand it better.

AnnyTan:

Now that the dust has settled, we can perhaps take a look at the most asked, yet least answered question about the PSLE. That question is – How are PSLE Aggregate Scores 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.

Formula for T-Score
T= 50+10 [(X-Y)/Z]

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.

Example 1 -
Boy A, B & C have $45, $50 and $55 respectively. They have an average of $50 each.

Example 2 -
Girl D, E & F have $10, $50 and $90 respectively. They also have an average of $50 each.

In Example 1, the spread ($45 to average of $50 and $55 to average of $50) is smaller than the spread in Example 2, where the spread is bigger ($10 to average of $50 and $90 to average of $50)

As such, Example 1 will have a smaller SD, as compared to Example 2.

Simpler Way to read Standard Deviation (SD)
If the average score of 3000 pupils who sat for Science Test is 50 marks and the SD is 5, it means that 2/3 of the 3000 pupils have scored 5 marks around the average, which means 2000 of the students scored from 45 to 55 marks.

If the average score of the same 3000 pupils who sat for Mathematics Test is 50 marks and the SD is now 10, it means that 2/3 of the 3000 pupils have scored 10 marks around the average, which means 2000 students scored from 40 to 60 marks.

Example of how T-score is calculated

Carol’s score for Mathematics – 90 (X)
Average score of cohort – 75 (Y)
Standard Deviation - 20 (Z) (this means 2/3 of cohort scored from 55 to 95)

Using the T-Score formula
T = 50 + 10(X – Y) / Z
T = 50 + 10 x (90 – 75) / 20
= 50 + 10 x 15/20
= 50 + 10 x 0.75
= 57.5

Carol’s T-score for Mathematics is 57.5

Now that we have covered T-score, we can take a look at PSLE Aggregate Score.
Using T-Score to Calculate PSLE Aggregate Score

Let’s now take a look at Carol's total performance

Table 1:
English = 175/200 [let's say score of cohort 120, SD is 30] then her T-score is 68.33
Mother tongue = 170/200 [let's say score of cohort 130, SD is 35] then her T-score is 61.43
Maths = 90/100 [let's say score of cohort 75, SD is 20] then her T-score is 57.50
Science = 90/100 [let's say score of cohort 70, SD is 25] then her T-score is 58.00

Add up all 4 subjects' T-score: 68.33 + 61.43 + 57.50 + 58.00
Carol's T-score is 245

The cohort’s average and standard deviation plays a big part in Carol's score. To demonstrate, let’s move the average scores of all subjects down by 10 marks each, keeping all other variables (raw score and SD) constant. This is how Carol’s score will now look like.

Table 2:
English = 175/200 [let's say score of cohort 110, SD is 30] then her T-score is 71.67
Mother tongue = 170/200 [let's say score of cohort 120, SD is 35] then her T-score is 64.29
Maths = 90/100 [let's say score of cohort 65, SD is 20] then her T-score is 62.50
Science = 90/100 [let's say score of cohort 60, SD is 25] then her T-score is 62.00

Add up all 4 subjects' T-score, Carol's T-score is now 260

Take note that Carol’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, Carol’s aggregate score will increase, even if 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.

Parents who have more than 1 child, tend to compare each child’s PSLE Aggregate Score with his/her sibling's score. This is not a very fair comparison.


Final Note –

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

Many parents believe the (non-existent) maximum aggregate is 300. That is a misconception.

To demonstrate, I have maximise Carol’s score (in Table 3) to full marks for all her subjects, using the same averages and SDs found in Table 2.

Table 3:
English = 200/200 [score of cohort 110, SD is 30] then her T-score is 80
Mother tongue = 200/200 [score of cohort 120, SD is 35] then her T-score is 72.86
Maths = 100/100 [score of cohort 65, SD is 20] then her T-score is 67.50
Science = 100/100 [score of cohort 60, SD is 25] then her T-score is 66.00
Add up all 4 subjects' T-score, Carol's T-score is now 286

Note that although Carol scored 100% marks for all subjects, her PSLE Aggregate Score is only 286. She did not score the (imaginary and non-existent maximum) PSLE Aggregate Score of 300!

The only way to score that 300 (or even above that), is to have a very weak cohort in your year.


I hope the explanation in this post gives parents and students a better picture how PSLE Aggregate Scores are calculated.

AnnyTan:

In any case, 294 is a respectable score, and we should give credit where it is due. Natasha definitely deserves the recognition for her outstanding performance.

MeKiasuLeh:

@AnnyTan, excellent T-score illustration! :goodpost:


This makes one wonder how Natasha manage to achieve a T-Score of 294. Absolutely mind-bobbling!

KawaiiVim:

Hey everybody :)... I really need your help with this. It is the first time that my child is taking PSLE. She just finished with her EL paper. So... I was just wondering... Will her PSLE aggregate score be higher or lower than her real marks? :xedfingers: