Correlation between SD score and Raw Score for CEM TEST

[vza]

Correlation between SD score and Raw Score for CEM TEST

For CEM test, few results have been posted for Raw Scores and corresponding Age-Standardised Scores. The available data are:

School - Exam Year - SD score - % raw Score - Ref/Post
KE, 2004, 116.0, 65.5%, KenR
KE, 2004, 114.0, 62.7%, KenR
KE, 2004, 113.0, 61.5%, KenR
KE, 2006, 101.3, 48.1%, KenR
ND, 2008, 127.3, 72.2%, May 05, 2009, Warwickshire
ND, 2008, 142.0, 85.0% , March 05, 2009, Warwickshire
QM, 2009, 111.7, 65.2% , March 04, 2010, Birmingham
QM, 2009, 131.0, 81.9% , March 04, 2010, Birmingham
QM, 2010, 108.0, 53.3% , March 06, 2011, Birmingham
QM, 2010, 107.0, 52.9% , March 06, 2011, Birmingham
QM, 2010, 113.0, 56.1% , March 07, 2011, Birmingham
QM, 2010, 89.0, 36.5%, March 06, 2011, Birmingham
QM, 2010, 125.0, 74.2%, March 07, 2011, Birmingham
KE, 2010, 130.0, 79.1% , March 05, 2012, Birmingham

The data shows a correlation:

Y = 0.9864 x Z – 50.9 , Where Y is % Raw Score and Z is Age-Standardised Score ( R-squared 0.9542).

The correlation estimate a theoretical maximum SD score of 153 (for raw score 100%) and a minimum score of 51 (for raw score of 0%). However, the very low scores (below 70) and very high scores (above 140) cannot be calculated with statistical reliability.
The correlation also predicts approximately 1 SD score increase for every 1% increase in the raw score. For example, using the above correlation, the raw scores can be calculated for a given SD Score:

SD Score - Actual Raw Score - Calculated Raw Score (difference from the actual data)
142.0 - 85.0%….. 89.1% (+5.1%)
131.0 - 81.9%….. 78.3% (-2.7%)
130.0 - 79.1%…… 77.3% (-1.7%)
127.3 - 72.2%….. 74.7% (+2.5%)
125.0 - 74.2%……. 72.4% (-1.8%)
116.0 - 65.5%…… 63.6% (-1.9%)
114.0 - 62.7%…… 61.6% (-1.1%)
113.0 - 61.5% …… 60.6% (-0.9%)
113.0 - 56.1%……. 60.6% (+4.5%)
111.7 - 65.2%….. 59.3% (-5.9%)
108.0 - 53.3%….. 55.7% (+2.4%)
107.0 - 52.9%….. 54.8% (+1.8%)
101.3 - 48.1%.... 49.1% (+1.0%)
89.0 - 36.5%…… 36.9% (+0.4%)


The age-profile for the data is unknown, therefore it is assumed that the correlation only predicts the Raw Sores for children in middle of the age profile (born in March).

The calculated raw scores deviate from the actual data between 0.4 to 5.9%, which can be explained in terms of many unknown variables and their impact on the raw scores:
1- Age-Standardisation effect (probably can explain only +/- 1.5% - maximum of 7 to 8 mark from total of 252, KE consortium Age-Standardisation table for 2006 CEM Test , reference KenR).
2- CEM test-to-test variation and differences in mix of questions.
3- Age-Standardisation methods used/ to be used (two papers, each paper separately or separate standardisation for Eng/VR, Math and NVR).
4- How the average of SD scores were/will be calculated (average of Eng/VR, Math and NVR scores or average of Eng/VR and NVR/Math)?

In conclusion, with great deal of caution, the above correlation could be a used to estimate the raw percentage needed to obtain a minimum pass mark.

Request for more data
To those parents who have their children raw scores and standardised score (and age at the time of exam) please posted it so that the observed correlation can be refined. If any one does not want to post the data publicly, please reply by a private message.

Regards
VZA

[nervousmom]

Correlation between SD score and Raw Score for CEM TEST

For CEM test, few results have been posted for Raw Scores and corresponding Age-Standardised Scores. The available data are:

School - Exam Year - SD score - % raw Score - Ref/Post
KE, 2004, 116.0, 65.5%, KenR
KE, 2004, 114.0, 62.7%, KenR
KE, 2004, 113.0, 61.5%, KenR
KE, 2006, 101.3, 48.1%, KenR
ND, 2008, 127.3, 72.2%, May 05, 2009, Warwickshire
ND, 2008, 142.0, 85.0% , March 05, 2009, Warwickshire
QM, 2009, 111.7, 65.2% , March 04, 2010, Birmingham
QM, 2009, 131.0, 81.9% , March 04, 2010, Birmingham
QM, 2010, 108.0, 53.3% , March 06, 2011, Birmingham
QM, 2010, 107.0, 52.9% , March 06, 2011, Birmingham
QM, 2010, 113.0, 56.1% , March 07, 2011, Birmingham
QM, 2010, 89.0, 36.5%, March 06, 2011, Birmingham
QM, 2010, 125.0, 74.2%, March 07, 2011, Birmingham
KE, 2010, 130.0, 79.1% , March 05, 2012, Birmingham

The data shows a correlation:

Y = 0.9864 x Z – 50.9 , Where Y is % Raw Score and Z is Age-Standardised Score ( R-squared 0.9542).

The correlation estimate a theoretical maximum SD score of 153 (for raw score 100%) and a minimum score of 51 (for raw score of 0%). However, the very low scores (below 70) and very high scores (above 140) cannot be calculated with statistical reliability.
The correlation also predicts approximately 1 SD score increase for every 1% increase in the raw score. For example, using the above correlation, the raw scores can be calculated for a given SD Score:

SD Score - Actual Raw Score - Calculated Raw Score (difference from the actual data)
142.0 - 85.0%….. 89.1% (+5.1%)
131.0 - 81.9%….. 78.3% (-2.7%)
130.0 - 79.1%…… 77.3% (-1.7%)
127.3 - 72.2%….. 74.7% (+2.5%)
125.0 - 74.2%……. 72.4% (-1.8%)
116.0 - 65.5%…… 63.6% (-1.9%)
114.0 - 62.7%…… 61.6% (-1.1%)
113.0 - 61.5% …… 60.6% (-0.9%)
113.0 - 56.1%……. 60.6% (+4.5%)
111.7 - 65.2%….. 59.3% (-5.9%)
108.0 - 53.3%….. 55.7% (+2.4%)
107.0 - 52.9%….. 54.8% (+1.8%)
101.3 - 48.1%.... 49.1% (+1.0%)
89.0 - 36.5%…… 36.9% (+0.4%)


The age-profile for the data is unknown, therefore it is assumed that the correlation only predicts the Raw Sores for children in middle of the age profile (born in March).

The calculated raw scores deviate from the actual data between 0.4 to 5.9%, which can be explained in terms of many unknown variables and their impact on the raw scores:
1- Age-Standardisation effect (probably can explain only +/- 1.5% - maximum of 7 to 8 mark from total of 252, KE consortium Age-Standardisation table for 2006 CEM Test , reference KenR).
2- CEM test-to-test variation and differences in mix of questions.
3- Age-Standardisation methods used/ to be used (two papers, each paper separately or separate standardisation for Eng/VR, Math and NVR).
4- How the average of SD scores were/will be calculated (average of Eng/VR, Math and NVR scores or average of Eng/VR and NVR/Math)?

In conclusion, with great deal of caution, the above correlation could be a used to estimate the raw percentage needed to obtain a minimum pass mark.

Request for more data
To those parents who have their children raw scores and standardised score (and age at the time of exam) please posted it so that the observed correlation can be refined. If any one does not want to post the data publicly, please reply by a private message.

Regards
VZA

Hi, I have just been refered to your post as i am trying to find what the actual scores relate to as a %. I assume when you talk about KE this means Camp Hill?

Would you also know what the maximum score available on the Birmingham paper is and the South Warwickshire and do you have any % comparisons for Warwickshire?

Thanks

[vza]

Hi Nervousmom,

It is not straightforward to give the actual score with the corresponding percentage because the max score vary from year to year and from test to test. However, an increase of 2.3 to 2.5 in the raw score correspond to about 1% point increase, which correspond to about 1 point increase in age-standardised score.

You must also consider how the raw scores are age standardised. For example, NGHS last year used 3-way standardisation (English/VR, NVR and Maths/Numerical) but KE Schools used 2-way standardisation (English/VR and NVR/Numerical/Maths).

The data I posted before were collected from scores reported in the forum over several years. I believe, but not certain, that the data for KE 2010 (SD 130.0, 79.1% ) was for KE Camp Hill and the data for KE (SD 101.3, 48.1%) was for 2007 KE consortium exam.

The maximum raw score possible (i.e. 100% correct answers) reported in the forum:

Queen Mary 2011 exam- 234 (English/VR 123, Maths/Numerical 67, NVR 44)
Queen Mary 2010 exam- 244
Queen Mary 2009 exam- 227
KE consortium 2004 exam - 252
KE consortium 2007exam – 235
South Warwickshire 2009 exam - 245

The actual high scores achieved are not often reported but two that I know are:
QM Boys 2009 exam- raw score of 186 out of 227 (82%, ranked 4th) corresponding to standardised score of 131.
South War. 2008 exam- raw score of 85%, ranked 1st with standardised score of 142.

For CEM test a child needs to achieve a raw score of 60 to 65% or more to obtain a grammar school place. 55 to 60% will possibly achieve the waiting list and score of 80% or more will be the top or near the top. However, 60 to 65% in the CEM test does not compare to the scores children achieve at home or in a mock exam based on GL assessments practice papers or practice papers of similar difficulties. DD last year was scoring in the range of 86% to 92% at home (GL assessment practice papers packs 1 to 4) but only scored about 65% in the NGHS CEM test.

If you or anyone else interested , I have the correlation data in a graph form which is much more informative and I can email it by a private message.

regards
VZA

[ChessDadPlus]

My focus is on raw score and a high one, as that is something that we can control

The standardised score will mean moot if your raw core is low, as then you are working on the premise of hope and something outside your control

Put it this way, do you want to aim to win the premiership comfortably, or do you want to chance it near relegation zone hoping teams below you and above you lose a few games...

[vza]

My focus is on raw score and a high one, as that is something that we can control

The standardised score will mean moot if your raw core is low, as then you are working on the premise of hope and something outside your control

Put it this way, do you want to aim to win the premiership comfortably, or do you want to chance it near relegation zone hoping teams below you and above you lose a few games...

I strongly disagree with your comments, specially your analogy of the premier league. Most of the children who take these tests work very hard and try to do their best in the exam. Unfortunately, due to the scarcity of grammar schools, majority of them will be very disappointed and some heartbroken. I do not think it is fair to them, or their parents, to compare them to football teams near relegation zone in the premier league.

[nicolajane1971]

I have to confess to all of the above being gobbledygook.

I'll be ecstatic if he gets a GS place, if he doesn't I'll be happy that he worked his socks off, showed excessive amounts of maturity for a 10 year old, and kept a smile on his face 95% of the time.

It's a bit like NVR, important info ie an offer is what counts, and then a well deserved year off before they start 'big school'. Anti SATS much, moi?!

[um]

I really do feel for the many children out there, who are under so much pressure and who are working so incredibly hard. They are still so young - some are not even 10 until the end of the month.
I hope their parents value them for being amazing kids, whatever the outcome of the exam. Sadly, it is true that not every child who wants a place at a Grammar school will get one. Some may not gain admission because it simply wasn't the right school environment for them; others would have really benefited from the place but sadly there just aren't enough available.

Sadly can't post the link here (don't know why!) but if you type in the address of a very well known video sharing website and then copy and add this 'suffix' /watch?v=kZlXWp6vFdE
there is an amazing video there about not giving up, making it to the end - and that sometimes, this can be even as amazing as winning too.

[KenR]

The age-profile for the data is unknown, therefore it is assumed that the correlation only predicts the Raw Sores for children in middle of the age profile (born in March).

I've actually got some figures on age for the VR test in 2004

In the Birmingham KE VR Tests in 2004 , to achieve a Standardised Score of 118 a child aged 11.18 years on the exam day would have to achieve score 71/100, whereas a child who was only 10.22 years would only have to score 65/100.

[Okanagan]

That's quite scary to think that an early September child could have to get a 10% higher raw score (71 vs 65) than some of the other candidates to get the same standardised score, when they've all actually had the same amount of schooling and at least in theory covered the same curriculum content. Those figures looks suspiciously close to age 10 gets marked as scored, older gets reduced proportional to chronological age - e.g divide marks by actual age, then multiply by 10? so at 11 they'd be credited with 10/11 of the marks gained, at 10 and 6 months they'd get 10/10.5 of the marks gained, etc.

I had heard anecdotally that the older children in the cohort are much less likely to get places (in fact we were told that it wasn't even worth entering a early Autumn born child) - is there any evidence for this?

[DIY Mum]

I think it's the other way around...fewer August born children in GS than September ones. Dec/ Jan birthdays also appear to be quite popular, though.

Yes, the difference in marking seems unfair but anyone who has a summer born child (who isn't their eldest), will know how summer borns are not really on par with their Autumn born peers at primary school. I could see this difference during my teaching practice between some of my pupils at KS1.

But also, as a parent of 'Irish twins' there was a marked difference between ds2 and dd1 during their primary years. Just to add, dd1 is in the same academic year as ds2, (her dob: end of August whereas ds2's dob is mid-September).

Whilst both dc were in the same school (and set) in class; covered the same curriculum with the same teachers and received the same homework etc... dd1 took much longer to grasp concepts in comparison to ds2. It was always so fascinating working with them!

It's been 2 yrs since they sat the test and despite knowing their results, I still think that if I had to hazard a guess as to who was more likely to pass (even with the SD difference), it would still be a September born child over an August born one.

Anyhow, this study is an interesting read and on here.