highest range of standardised score.

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herty
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Joined: Tue Nov 24, 2009 11:23 pm

Re: highest range of standardised score.

Post by herty »

Thanks bel - that's how I understood it too.

100% is 100% however you calculate it - to make sense, standardisation must mean that full marks = the highest score achieved, which can't be over 100%. In fact, in a hard test, you'd expect the maximum standardised score to represent a raw score of less than 100% as it is measuring candidates against each other not an abstract 'full marks'.
jzw22
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Joined: Wed Oct 03, 2012 1:10 pm

Re: highest range of standardised score.

Post by jzw22 »

This is part of the table for the 2012 KS2 Maths paper standardisation which was scored out of 80 (you can find the full spreadsheet on the govt site somewhere). I've hidden most of the table so you can just see the headers + last few lines.

You will notice that some cells are marked '***' because there is no statistically sensible score you can assign. These scores are arbitrarily made 141.

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Last edited by jzw22 on Thu Nov 01, 2012 1:18 pm, edited 1 time in total.
Hera
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Re: highest range of standardised score.

Post by Hera »

herty wrote: In fact, in a hard test, you'd expect the maximum standardised score to represent a raw score of less than 100% as it is measuring candidates against each other not an abstract 'full marks'.
Exactly as I understand it too. :D

(What I would like to know is if it is standardized nationally or just amongst the kids that take the test for the schools)?

Just seen your table jzw22. That makes it very clear for the OP.
jzw22
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Joined: Wed Oct 03, 2012 1:10 pm

Re: highest range of standardised score.

Post by jzw22 »

3b1g wrote:If you have a paper (let's say in Maths) that is 'too easy' then the mean raw score would be very high (let's say somewhere in the forties out of fifty). This would affect the standardisation table in such a way that even dropping one or two marks from the raw score would lead to a massive drop in the standardised score. This would mean that children who are confident in Maths and were regularly getting over 90% in practice papers could feel that they had performed really well on the day and then receive an email with a score below 120. I'm just speaking hypothetically, of course...
I think that this is the case for the maths paper for the SW Herts consortium. The paper is simply too easy for a competent child. You can see from the KS2 maths table that dropping 1 raw mark, can be worth 4 or more standardised marks, when you are high up in the tail of the distribution.

If you look at the KS2 maths
raw 90% (72/80) = 116
raw 96% (76/80) = 124

In the real world, there is not much if any, difference in ability between the children scoring those scores, but you can see that to score a combined 240+ for a place, scoring highly on an easy paper is a must.

Its possible that the test is standardised against the children taking the test but I would have thought that there were not enough children to make it statistically valid.

By contrast KS2 maths is taken by 60,000 I think, and it is standardised against the cohort who took the test.
3b1g
Posts: 403
Joined: Sun Oct 14, 2012 3:11 pm

Re: highest range of standardised score.

Post by 3b1g »

bel wrote:Older children do not lose or get lower marks than younger children.
In jzw22's example table, a child getting a raw score of 78 would get a standardised score of 133 if they were 10y9m, but only 129 if they were 11y9m. So if two children get the same raw score, I'm reading that the older child does get a lower standardised score. Am I reading these tables wrongly?

I admit that my comments about the top end of the table were wrong and I accept that a child who gets 50/50 in a Maths test should get 141 or "off the scale but recorded as 141" regardless of their age.

However, what happens if quite a few children (say 5% of those who took it) get 50/50? Not as impossible as you might think, with this particular test. How can 5% of the cohort be awarded a standardised score of 141? That doesn't make sense to me from a statistical point of view.
jzw22
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Re: highest range of standardised score.

Post by jzw22 »

3b1g wrote:.. raw score of 78 would get a standardised score of 133 if they were 10y9m, but only 129 if they were 11y9m.
Correct
3b1g wrote:However, what happens if quite a few children (say 5% of those who took it) get 50/50? Not as impossible as you might think, with this particular test. How can 5% of the cohort be awarded a standardised score of 141? That doesn't make sense to me from a statistical point of view.
You are right, it does not make sense. Its places too much weight on not dropping marks on the maths papers because a mark on on the maths might cost you 4 points but 1 on VR only 2.

You are already trying to differentiate DCs within the top 20% (comfortable L5) of the ability range, and a test suitable for the general KS2 ability range will not do that. That is why the independent school papers are so much harder.

The problem with the maths is that if it is a similar standard to the KS2 maths papers then all it tests is basic numeracy and most bright DCs could get every question right. Whether they do is another matter but they will certainly have the ability to do that.
3b1g
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Re: highest range of standardised score.

Post by 3b1g »

Thank you jzw22 for clarifying. I'm not as confused as I thought I was. :)

I am under the impression that the object of age standardisation is to ensure that a similar proportion of September-born children "pass" as the proportion of August-born children. A small variance within the range of scores that we are discussing here (135+ or combined 270+) would not cause any child to miss out on a school, which is the important thing.

I do think the Maths paper is set at a level that makes it difficult to differentiate between the top 5%, the top 10% and the top 20%; which is what one would have thought the schools would be trying to do. As the Maths paper contains 50 questions and the VR contains 100, one would expect each Maths question to have as much weighting as two VR questions, but I have been speculating whether the relative simplicity of the Maths paper has led to such a high mean raw score that getting one Maths question wrong reduces the standardised score more than getting two VR questions wrong.

When I prepared my first child, I didn't realise any of this. I thought that as the Maths paper was rumoured to be straightforward, it would be wise to spend more time on VR. Thankfully he was offered a place at his first choice school on 1st March anyway.
3b1g
Posts: 403
Joined: Sun Oct 14, 2012 3:11 pm

Re: highest range of standardised score.

Post by 3b1g »

3b1g wrote:If you have a paper (let's say in Maths) that is 'too easy' then the mean raw score would be very high (let's say somewhere in the forties out of fifty). This would affect the standardisation table in such a way that even dropping one or two marks from the raw score would lead to a massive drop in the standardised score. This would mean that children who are confident in Maths and were regularly getting over 90% in practice papers could feel that they had performed really well on the day and then receive an email with a score below 120. I'm just speaking hypothetically, of course...
The last sentence was meant sarcastically. Sorry, I couldn't find an emoticon to convey sarcasm. I was referring specifically to the Maths paper from the S.W.Herts Consortium test. DS2 scored 136, but several of his friends (all very able children and confident in Maths, all considered to be in the top 10% of the eighty children in the year) scored in the 110-119 range, which really surprised me. It has made me realise that DS1 must have either got a place on the strength of his VR, or just had a good day. Quite glad I was oblivious at the time.
jzw22
Posts: 17
Joined: Wed Oct 03, 2012 1:10 pm

Re: highest range of standardised score.

Post by jzw22 »

3b1g wrote:... would not cause any child to miss out on a school, which is the important thing.
...I thought that as the Maths paper was rumoured to be straightforward, it would be wise to spend more time on VR. Thankfully he was offered a place at his first choice school on 1st March anyway.
Congrats - he must have dropped 1 maybe 2 marks at most. I know a DC who got 100% on their maths. The margins are very small.

Going back to your first point - I'm not sure you can say that. I believe that around ~2500 DCs take the Herts test. So after making a number of assumptions, a 240 score would rank 228 and a 243 score 156. So those 3 marks put you some 70 places higher.

Still you have to age standardise otherwise the test is definitely unfair to later born children. There have been studies done on this I believe that show that summer born children do worse at school and that effect is quite noticeable upto GCSE.
cindrella
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Re: highest range of standardised score.

Post by cindrella »

3b1g wrote:On a typical standardisation table, a child who was 10y0m with a raw score of 100% would be given a standardised score of 141, whereas a child who was 10y11m with a raw score of 100% would be given a standardised score somewhere in the one-hundred-and-thirties, depending on the mean raw score and the standard deviation. For example, my DS1 scored 100% in his Y4 CATs, but was given a standardised score of 139 as his birthday is in February, not August. If you could get some high-end scores from some of the children who just took the test (along with their month of birth) then you could possibly speculate on the top end of the standardisation table,i.e. how a raw score of 100% would translate into different standardised scores for children of different ages.
I gather that February born child who scores 100% is awarded 139 std. score.
Whereas if one is August born std.ed score would be 140 -141.
so I think it could be that a Sept born 133 or 134 max. ie is nearly 6 -8 points less, and that would cost DC nearly 60 - 80 places !! Because by my general observation there are about 8- 10 children on the same score.
this is a rough guesswork but for sure it does cost a lot. Standardisation also varies according to the 'easiness' of the paper,subject matter and subject itself.
I was told that for each and everypaper they have a special standardisatin mark scheme, so it is not that simple to just rattle out a paper, because that paper has to be odne by a mass of children, consider their age, average scored for that particular paper by each age group and then standardise it - produce a mark scheme.... which is why it is easy for schools to use just the past papers.
Cinderella
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