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PSLE T-Score Secrets Revealed PDF Print E-mail
Written by Administrator   
Wednesday, 21 December 2011 07:53

PSLE T-Score Secrets Revealed

Most of parents know the PSLE T-score Formula is 50+ 10 * (x-Average)/SD. However nobody knows what's Average and SD value of each subject. People also think A = 75 and Pass = 50, but all these assumptions are wrong. Actually A and Pass mark is not a constant. The only information we can get from MOE is pass rate and quality pass rate. Based on those data, we did reverse engineering and drew the conclusions as below. You can also find details from this article.

 

Conclusion:

1) A and Pass mark is not a constant

2) SD is in the range of 9~14

3) SD order:  Chinese < English < Science < Maths, it means every one extra mark from language subjects will help you get higher T-score than one extra mark from maths and science.

4) More accurate T-score formula is below:

T = 200 + 10* ((English-70.23)/10.43+(Maths-62.80)/12.93+(Science-65.90)/12.33+(Chinese-73.3)/9.43)

5) Since every year pass rate and quality pass rate are quite consistant, it means each subject's SD is also quite consistant. every year the difficult level of PSLE test  is different, you can do fine tuning by adjusting the average value of each subject. one recommended T-score formula is list below:

T = 200 + 10* ((English-70)/10.43+(Maths-64)/12.93+(Science-66)/12.33+(Chinese-73)/9.43)

6) According to the formula above, we can know highest achieveable T-score is below:

Engilish : 50 + 10* (100-70)/10.43 =  78.76

Maths ; 50 + 10* (100-64)/12.93 = 77.84

Science : 50 + 10* (100-66)/12.33 =  77.58

Chinese : 50 +  10* (100-73)/9.43 =  78.63

Normal Distribution Table
                     
  0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
 
0 0.5 0.504 0.508 0.512 0.516 0.5199 0.5239 0.5279 0.5319 0.5359
0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753
0.2 0.5793 0.5832 0.5871 0.591 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141
0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.648 0.6517
0.4 0.6554 0.6591 0.6628 0.6664 0.67 0.6736 0.6772 0.6808 0.6844 0.6879
                     
0.5 0.6915 0.695 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.719 0.7224
0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549
0.7 0.758 0.7611 0.7642 0.7673 0.7703 0.7734 0.7764 0.7794 0.7823 0.7852
0.8 0.7881 0.791 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133
0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.834 0.8365 0.8389
                     
1 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621
1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.877 0.879 0.881 0.883
1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.898 0.8997 0.9015
1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177
1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9278 0.9292 0.9306 0.9319
                     
1.5 0.9332 0.9345 0.9357 0.937 0.9382 0.9394 0.9406 0.9418 0.943 0.9441
1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545
1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633
1.8 0.9641 0.9648 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.97 0.9706
1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.975 0.9756 0.9762 0.9767
                     
2 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817
2.1 0.9821 0.9826 0.983 0.9834 0.9838 0.9842 0.9846 0.985 0.9854 0.9857
2.2 0.9861 0.9864 0.9868 0.9871 0.9874 0.9878 0.9881 0.9884 0.9887 0.989
2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916
2.4 0.9918 0.992 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936
                     
2.5 0.9938 0.994 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952
2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.996 0.9961 0.9962 0.9963 0.9964
2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.997 0.9971 0.9972 0.9973 0.9974
2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.998 0.9981
2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986
3 0.9987 0.999 0.9993 0.9995 0.9997 0.9998 0.9998 0.9999 0.9999 1
                     
71%   0.56                
56%   0.17                
81%   0.88                
90%   1.29                
97%   1.94                
84%   0.99                
                     
PSLE test Result for every year (Average):      
        A/A* rate   Pass rate    
English        43%     97%      
Maths       43%     84%      
Science       43%     90%      
Chinese     81%     97%      
                     
                  95% ref. score
Subject   SD   Average A   Pass Ave+ 2*SD
Engilish   10.427   70.227   72   50   91.081
Maths   12.931   62.802   65   50   88.664
Science   12.329   65.904   68   50   90.562
Chinese 9.434   73.302   65   55   92.17
                     
Conclusion : SD is in a range between 9~14, A and Pass mark is not a fixed value
                     
                     
T-score formula is below (Through reverse engineering):    
                     
T = 200 + (English-70.23)/10.43+(Maths-62.80)/12.93+(Science-65.90)/12.33+(Chinese-73.3)/9.43
                     
                     
Here I assume all subject's full mark is 100, you can do your own convertion, for example if full mark is 200, you just need devide original score by 2
Z=(0,1)                    
English P(70.23,10.43)                
English P(X>pass)=P(x>50)=Z((70.23-50)/10.43) = Z(1.94) = 97.38%      
  P(X>A)=P(x>72)=1-Z((72-70.23)/10.43) = 1-Z(0.17) = 1-56.75%=43.25%  
Maths  P(62.80,12.93)                
Maths  P(X>pass)=P(x>50)=Z((62.80-50)/12.93) = Z(0.99) = 84%      
  P(X>A)=P(x>65)=1-Z((65-62.80)/12.93) = 1-Z(0.17) = 1-56.75%=43.25%  
Science P(65.90,12.33)                
Science  P(X>pass)=P(x>50)=Z((65.90-50)/12.33) = Z(1.29) = 90%      
  P(X>A)=P(x>68)=1-Z((68-65.90)/12.33) = 1-Z(0.17) = 1-56.75%=43.25%  
Chinese P(73.3,9.43)                
Chinese P(X>pass)=P(x>55)=Z((73.30-55)/9.43) = Z(1.94) = 97.38%      
  P(X>A)=P(x>65)=Z((73.30-65)/9.43) = Z(0.88) =  81%        

 

 

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