A statistical perspective on the 2013 scores
Posted: Thu Oct 18, 2012 1:57 pm
I have entered the scores posted in this forum into an excel spreadsheet and compared it to previous years'. Here are some of my observations...
1. The results posted in these forums are not a representative picture of the overall results as these forums contain an over-representation of higher scores, 2013 even more so than 2012
Standardised score
2009: mean 347.56, st dev 31.9 (sample size 13)
2010: mean 349.51, st dev 19.0 (sample size 19)
2011: mean 344.18, st dev 21.4 (sample size 49)
2012: mean 340.08, st dev 20.4 (sample size 73)
2013: mean 346.55, st dev 28.8 (sample size 70)
Comparing 2012 and 2013 where the sample size is larger, and hence we can have more confidence into any statistical comparison, the mean standardised score has gone up from a high 340.08 to a really high 346.55. In theory, the distribution of scores from one year to another should be consistent - after all, this is what standardisation is supposed to achieve. Assuming CSSE have not done things differently (!?), then do not overly worry that lots of people in this forum appear to have high scores..
2. The Verbal Reasoning paper in 2013 was much easier than 2012
Mean and standard deviation scores are based on VR raw scores only
2009: mean 70.3%, st dev 13.3%, mean overall standardised score 348 (sample size 13)
2010: mean 78.1%, st dev 9.1%, mean overall standardised score 350 (sample size 19)
2011: mean 79.6%, st dev 10.5%, mean overall standardised score 344 (sample size 49)
2012: mean 74.8%, st dev 10.0%, mean overall standardised score 341 (sample size 73)
2013: mean 77.6%, st dev 15.9%, mean overall standardised score 347 (sample size 70)
A comparison of the mean verbal reasoning shows an increase in the mean of the scores posted in this forum from 74.8% to 77.6%. More telling is if we look at the distribution of the very high scores...
............................................ 2011 2012 2013
Score in VR paper of 95% and above 2% 0% 7%
Score in VR paper of 90% and above 19% 4% 30%
Score in VR paper of 85% and above 31% 16% 38%
Score in VR paper of 80% and above 50% 30% 49%
In 2012 none of the scores posted in this forum scored 95% and only 4% scored 90% or above. The corresponding figures for 2013 showed 7% of candidates achieving 95% and a whopping 30% of 90% (72+/80). There is no reason to believe that the 70 or so candidates last year were of a significantly different ability to this year's.
3 The English paper continues to be the hardest paper with the lowest scores. In these situations, every mark matters so getting the easier spelling and punctuation marks is imperative.
Mean and standard deviation scores are based on English raw scores only
2009: mean 67%, st dev 11%, mean overall standardised score 348 (sample size 13)
2010: mean 66%, st dev 8%, mean overall standardised score 350 (sample size 19)
2011: mean 51%, st dev 11%, mean overall standardised score 344 (sample size 49)
2012: mean 58%, st dev 8%, mean overall standardised score 341 (sample size 73)
2013: mean 53%, st dev 13%, mean overall standardised score 347 (sample size 70)
4. The Maths scores have rebounded following the change in format in 2012
Mean and standard deviation scores are based on maths paper only
2009: mean 65%, st dev 14%, mean overall standardised score 348 (sample size 13)
2010: mean 68%, st dev 17%, mean overall standardised score 350 (sample size 19)
2011: mean 73%, st dev 15%, mean overall standardised score 344 (sample size 49)
2012: mean 64%, st dev 11%, mean overall standardised score 341 (sample size 73)
2013: mean 74%, st dev 13%, mean overall standardised score 347 (sample size 70)
2012 saw the introduction of sequential parts to a question which meant that you really needed to get the first part correct to get the second and similarly to the third part. The mean scores in maths have rebounded from 64% in 2012 to 74% which is similar to previous years.
5. Combining the points above means that a child scoring 26/50 in English, 30/40 in Maths, and 62/80 in VR would result in a standardised score of around 347. Increase or decrease the scores accordingly, but this can help set a target for any child taking the exam next year..
1. The results posted in these forums are not a representative picture of the overall results as these forums contain an over-representation of higher scores, 2013 even more so than 2012
Standardised score
2009: mean 347.56, st dev 31.9 (sample size 13)
2010: mean 349.51, st dev 19.0 (sample size 19)
2011: mean 344.18, st dev 21.4 (sample size 49)
2012: mean 340.08, st dev 20.4 (sample size 73)
2013: mean 346.55, st dev 28.8 (sample size 70)
Comparing 2012 and 2013 where the sample size is larger, and hence we can have more confidence into any statistical comparison, the mean standardised score has gone up from a high 340.08 to a really high 346.55. In theory, the distribution of scores from one year to another should be consistent - after all, this is what standardisation is supposed to achieve. Assuming CSSE have not done things differently (!?), then do not overly worry that lots of people in this forum appear to have high scores..
2. The Verbal Reasoning paper in 2013 was much easier than 2012
Mean and standard deviation scores are based on VR raw scores only
2009: mean 70.3%, st dev 13.3%, mean overall standardised score 348 (sample size 13)
2010: mean 78.1%, st dev 9.1%, mean overall standardised score 350 (sample size 19)
2011: mean 79.6%, st dev 10.5%, mean overall standardised score 344 (sample size 49)
2012: mean 74.8%, st dev 10.0%, mean overall standardised score 341 (sample size 73)
2013: mean 77.6%, st dev 15.9%, mean overall standardised score 347 (sample size 70)
A comparison of the mean verbal reasoning shows an increase in the mean of the scores posted in this forum from 74.8% to 77.6%. More telling is if we look at the distribution of the very high scores...
............................................ 2011 2012 2013
Score in VR paper of 95% and above 2% 0% 7%
Score in VR paper of 90% and above 19% 4% 30%
Score in VR paper of 85% and above 31% 16% 38%
Score in VR paper of 80% and above 50% 30% 49%
In 2012 none of the scores posted in this forum scored 95% and only 4% scored 90% or above. The corresponding figures for 2013 showed 7% of candidates achieving 95% and a whopping 30% of 90% (72+/80). There is no reason to believe that the 70 or so candidates last year were of a significantly different ability to this year's.
3 The English paper continues to be the hardest paper with the lowest scores. In these situations, every mark matters so getting the easier spelling and punctuation marks is imperative.
Mean and standard deviation scores are based on English raw scores only
2009: mean 67%, st dev 11%, mean overall standardised score 348 (sample size 13)
2010: mean 66%, st dev 8%, mean overall standardised score 350 (sample size 19)
2011: mean 51%, st dev 11%, mean overall standardised score 344 (sample size 49)
2012: mean 58%, st dev 8%, mean overall standardised score 341 (sample size 73)
2013: mean 53%, st dev 13%, mean overall standardised score 347 (sample size 70)
4. The Maths scores have rebounded following the change in format in 2012
Mean and standard deviation scores are based on maths paper only
2009: mean 65%, st dev 14%, mean overall standardised score 348 (sample size 13)
2010: mean 68%, st dev 17%, mean overall standardised score 350 (sample size 19)
2011: mean 73%, st dev 15%, mean overall standardised score 344 (sample size 49)
2012: mean 64%, st dev 11%, mean overall standardised score 341 (sample size 73)
2013: mean 74%, st dev 13%, mean overall standardised score 347 (sample size 70)
2012 saw the introduction of sequential parts to a question which meant that you really needed to get the first part correct to get the second and similarly to the third part. The mean scores in maths have rebounded from 64% in 2012 to 74% which is similar to previous years.
5. Combining the points above means that a child scoring 26/50 in English, 30/40 in Maths, and 62/80 in VR would result in a standardised score of around 347. Increase or decrease the scores accordingly, but this can help set a target for any child taking the exam next year..