Here are a few thoughts of mine on PSLE 2013 results.  MOE/SEAB should be publishing the t-score distribution which would greatly help pupils to understand where they are in the cohort so they could apply the right schools. But I never found these info from MOE/SEAB web site.

1. What could be PSLE 2013 T-score distribution?

If we treat the raw scores of English/Math/Science/MT as random variables, the total sum of the raw scores should be approximately normally distributed. It’s also true for the total T-score which should also be in normal distribution. This can be proved by mathematical simulations and is also guaranteed by the central limit theorem.

To determine the total T-score (i.e. the sum of 4 subjects’ t-scores) distribution, we need know the number of pupils (43047 for 2013), the average of total T-scores (it should be 200) and the standard deviation std. The std is greatly impacted by the raw score’s distribution. If we assume all 4 subjects raw scores are in normal distribution, we can prove that the std of total T-score should be around 20 by doing Monte Carlo simulation. This is illustrated in the following chart.

Thanks to the readers who questioned me why there are so few pupils over 250 or 260? After I modified the distributions of raw scores and played with the simulation parameters in late nights of last two days, I think to assume the std = 20 is not the best estimation.

My revised simulation results shown that std=25 is a better choice. We can conclude the following from the mathematical simulation (i.e. Monte Carlo). The cumulated % of pupils is shown as the curve in brown.

Note: the above results are based on the parameters specified in the chart. Only MOE/SEAB knows the accurate std value. The std of 25 in above chart is just my estimation. Please use the data wisely to make your own decisions.

 

2. How could the simulated T-score distribution help us?

From the simulation data (std=25), we could predict the cut-off points for different streams.

P6-2013 Non-Affiliated	Normal (T)	Normal (A)	Express	Tscore >=233	Tscore >=250	Tscore >=260
Min	~152	~173	~190
Max	~172	~189	275 (?)
Pupils	4575	8631	28778	4311	1107	415
Pupils%	10.63%	20.05%	66.85%	10%	2.57%	0.96%
Pupils% (MOE)	10.90%	19.90%	66.70%

If we compare the predictions with MOE’s official data listed at the bottom of the table, this simulation results are pretty close in terms of streams%. Note: The above predictions are very sensitive to the std value. If std changes, the cut-off point and % all will change.

We could also compare the predictions with 2012 & 2011 cut-off T-score data (summarized from MOE data). For Express stream, predicted 190 for 2013 is close to last two year cut-off point of 188. Other two streams are also in the range. Why the minimum cut-off points raised up? Please see explanations in next section.

Non-Affiliated	Normal (T)	Normal (A)	Express (+AT)	Express Only
Min (2012)	72 – 151	152 – 199	188 – 246	234 – 265
Max (2012)	143 – 159	179 – 199	215 – 274	250 – 284
Min (2011)	72 – 150	152 – 198	188 – 245	232 – 262
Max (2011)	141 – 159	180 – 199	220 – 267	251 – 283

 

3. Why are the top scores of PSLE 2013 lower than previous years?

As you can see, there is a list of top scores from the KSP web site. The highest so far is about 275.

The MOE minister also explained that PSLE 2013 papers are designed for pupils to gain marks of difficult questions step by step. So more pupils would get higher raw scores (name it as x). This will push up the average score of the whole cohort. The standard deviation won’t change too much. So according to the t-score formula:

The numerator will be smaller – that’s why the t-score will be lower.

Some pupils felt that this year’s Math is easier, they would expect to get full raw mark of 100. Since x is capped at 100 maximum, higher average scores make it impossible for pupils to reach higher t-score. See the following examples below – a 6.7 marks of t-score difference!

t=50+10*(100-65)/15=73.3

t=50+10*(100-75)/15=66.7

I would say that the improvements of this year’s PSLE papers will push lower scores up (so the average is higher)  and drag down the top scores a little bit. So it’s reasonable to say that the cut-off mark for each stream should go up.

 

I am sharing these analysis and data with you. Please be mindful to make your own decisions – if you are using some of analysis results above (which are based on mathematical simulations) as reference.

If it helps, do let me know. But I am not taking any legal responsibilities of above sharing 🙂

Regards,

A P6 Boy’s Father