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
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 -
Allan, Bernard and Charles have $45, $50 and $55 respectively. They
have an average of $50 each.
Example 2 -
Dan, Edward and Frank 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.
A more detailed explanation of how SD is calculated can be found
in this
link.
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
Li Ting’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
Li Ting’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 Li Ting’s total performance
The cohort’s average and standard deviation plays a big part in Li
Ting’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 Li Ting’s score will now look
like.
Take note that Li Ting’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, Li Ting’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 bumped up Li Ting’s score (in Table 3) to
full marks for all her subjects, using the same averages and SDs
found in Table 2.
Note that although Li Ting 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.
So if our imaginary Li Ting scored 100% for all her subjects and
still only scored 286 for her PSLE Aggregate, how did Ms Natasha
score a PSLE Aggregate of 294 for the year 2007? I don’t have the
stats, but my guess is that the averages and SDs of the individual
subjects of the cohort played a big role.
In any case, 294 is a respectable score, and we should give credit
where it is due. It is an all time high and Ms Natasha definitely
deserves the recognition for her outstanding performance.
I hope the article in this post gives parents and students a better
picture how PSLE Aggregate Scores are calculated.
