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 Post subject: Standardisation
PostPosted: Wed Nov 25, 2009 11:01 am 
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Joined: Wed Sep 02, 2009 7:16 pm
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WP - as you seem to understand it, please can you explain standardisation further? I've tried following various links that explain it and understand it gives extra points to those born younger, but didn't understand when you said 'standardize to an average of 100 and a standard deviation of 15'. What does this mean, just out of curiosity?

My son scored 141 out of 141 and is December born, does this mean he didn't necessarily get 100%? Not that I mind if he didn't, just looking for enlightenment!


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PostPosted: Wed Nov 25, 2009 1:00 pm 
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Joined: Thu Jan 03, 2008 8:26 am
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Location: Watford, Herts
Let's ignore age differences for the moment. If you take the score of a large number of children of the same age doing some test, and make a histogram of the number of children getting each score, you'd expect the histogram to approximate a bell-shaped curve (called the normal distribution) like this:
Image
For different tests, you'd see distributions that had the same bell shape, but differed only in being moved left or right, or in being stretched sideways. In order to compare these, it's common to scale the marks to make these curves line up -- that is standardization. A common choice is an average of 100 and a spread so that the proportion of candidates in each band of scores looks like this:
Image
For example, 34% of the population ends up with a score between 100 and 115.

Now suppose you do the above for a group of children of 10 years 1 month, and then do it separately for a group of children of 10 years 9 months. The younger children will tend to score lower, so in standardizing their marks the curve will have to be moved further to the right (to get the average at 100) than the curve for the older children will. (I believe the actual process is more complicated, based on determining an overall relationship between age and score, but the effect is much the same as standardizing each age group separately.)

Finally, the scores are truncated at the ends: everyone who would have got a standardized score of greater than 140 is reported as 141 (or 140), and everyone less than 70 is reported as 69 (or 70).

So the relationship between raw marks and standardized scores is obscure. 141 may not represent 100%, but it is a very high score, corresponding to the top 0.3% of the population.


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PostPosted: Wed Nov 25, 2009 1:18 pm 
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Joined: Mon Oct 12, 2009 1:30 pm
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Hi

Hope you can help WP, as I'm sure this is the question everyone want to know.

If you have three chidren that get the same score. 1 born in November, another in March and the final child in August. What would happen to their scores?

Ally


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PostPosted: Wed Nov 25, 2009 1:30 pm 
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Joined: Thu Jan 03, 2008 8:26 am
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Location: Watford, Herts
Ally wrote:
If you have three children that get the same score. 1 born in November, another in March and the final child in August. What would happen to their scores?

If they all get the same raw score, the youngest child will end up with a higher standardized score than the others, because their score places them higher in their age group than the same score places the other two in theirs. You probably want numbers, but I can't help there. In any case it will vary between tests. There are too many unknowns to give actual numbers. The only thing that's fixed is the relationship between standardized scores and your child's position compared with others of the same age.

Short answer: the precise calculation is unpredictable, but it's fair, so there's not much point in worrying about it.


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PostPosted: Wed Nov 25, 2009 1:36 pm 
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Wow! Thank you for that excellent & most comprehensive explanation. :D


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PostPosted: Wed Nov 25, 2009 2:35 pm 
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Thanks, we'll just have to wait and see what happens on 1st March.
Any chance of a Sticky a about Standardisation ?


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PostPosted: Wed May 12, 2010 8:48 pm 
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Joined: Tue Mar 23, 2010 2:51 pm
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posting.php?mode=reply&t=12525

Check this to understand the standardisation scores rocket science!!


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