To give DD school (and the SATs agency) some basic statistical literacy?

The school couldn't have explained what you want to know, because they don't have that information. SATs scores say something about ability to learn and remember (not actual ability), motivation and executive functioning skills. That's all, but there is quite a bit of correlation between them and GSCE scores.

this is where I’m confused though as for a child to the sats the head teacher must be sure they are
“ working at the key stage 2 level “
“ have completed the key stage 2 curriculum “
“ are physically / mentally well enough to take them.

so if those who have done the test are all working at key stage 2 curriculum and managed to get a score but low are in bottom set

where are the kids that wouldn’t reach the 80 whatever it is ?

She got 107 in reading comprehension
99 in maths
98 in spag

they seemed very excited about the scores and then I read on mumsnet means will struggle to get 4s but suppose that’s the issue with comparing nationally it doesn’t take in to account other things happening at the time.

she is going to a small independent school for secondary with speech and OT provision which would likely help ?

My experience as I secondary school teacher is those scores will mean she is in the lowest approximately 5% of attainment and will probably be in the lowest attainment set, if they set students.

It sounds like your DC has a more complex background than others, and hopefully she will have support going into secondary school.

I've shared the actual distribution of scores for each previous year upthread.

Considering her SEND and then such a serious illness and consequentially attending for the equivalent of one half term, to then only just fall under 100 by probably one question? She's absolutely going to smash her GCSEs.

Ok - I think it should be possible to calculate what you want to know. We know what the raw scores are for each scaled score and I think that it is reasonable to assume that the raw scores are normally distributed as there is a lot of people doing these tests.

We know what the median result is. (About 106 I think.) We know what proportion get a scaled score of 100 or higher (70 something percent depending on the subject) and we know what proportion get a scaled score of 110 or higher. Translate these all into raw scores and it should be pretty easy to work out a rough standard deviation and then a confidence interval.

Am I being an idiot or does OP not understand statistics? It's been ages since I studied statistics but why would the standard deviation be 15 even if it was a normal distribution? Is this because OP thought it was a standardised score?

Why does being within 1 standard deviation of the median mean an individual result is not statsicially significant? Is this not standard error which varies?

Ultimately its not the school who've said your Dd is below standard it is the government. A quick Google could have told you how the SATs scores work. It's pretty arrogant to think you can go in and educate the school on statistics when I don't think you have a good grasp yourself

Not everyone knows the detailed back story of every poster, plus really these things mean nothing in the context of the post which was that OP thought she knew better than the school and even the people who set the exams.

Why do you keep repeating yourself about IQ tests and scores? They have absolutely no relevance to Y6 SATs scores, quite the opposite in fact. You're tying yourself in knots to try and prove a point that doesn’t seem to exist.

You’ve had some really good advice from people who have explained the levels, what they mean and how they compare to other children which seems to be something that is important to you. But ultimately SATs scores really aren’t that important. In a years time will they matter? No, the progress your child has made will and how she has settled into her new school. I hope she enjoys her summer.

Your kid sounds like she's had a hell of a time lately, on top of some existing pretty hefty challenges, and still in these tests she's meeting the expected standard in one and only just below for two others.

These scores are a pretty crude measure of predicting future success because so many factors play into them. It shows you where they were on test day, and on a population level they can be used as a predictor of future success based on what's happened in the past - with a built in margin of error. Those predictions aren't good for outlying cases like this though.

For a kid who has missed most of Year 6 which is so devoted to these tests, I'd say she's bloody smashed it. Depending on which subject, a 107 puts her above at least half the kids in the country. Given the circumstances I'd say that's pretty exceptional. But yeah, it's a confusing system and what it means seems to be communicated pretty poorly!

Huge congratulations to her and if as you say, her health improves from here on in so she gets more school time, then hopefully she'll have the opportunity to really fly.

I didn't see adoption or SEN mentioned in the OP so I didn't have the background. Thank you for the context.

@cantkeepawayforever
Agree. I had problems getting clear info from schools for both my DC.
I raised concerns and was pushed back. I thought maybe my baseline expectations were wrong. They weren't as it turned out, but my DC didn't get the support they needed from schools until much later than they should have done.``

I don’t think it’s fair to put the boot in as it sounds like the OP was slightly misled by the school. It also sounds as though the OP’s child was adopted from abroad, English is not their first language (so a far from run of the mill start in life), and also that they are already gradually rising up the ranks. From that I’d suggest by the end of secondary school, the OP’s child is going to be doing incredibly well whatever their SATS say now. I don’t think you need to worry OP, just make sure you access all support and try to foster a constructive relationship with your child’s secondary school when she gets there.

I don’t think this is the case here, where adoption and (iirc) another child with SEN are in the mix.

What may well be the case, though, is a parent so used to battling, to deliberate or well-meaning obfuscation or misinformation (‘oh, they’re doing fine [compared with the meltdown yesterday] / they’ve made progress [very much more slowly than others] / they need to be at least 2 years behind for an EHCP [rubbish] / yes, they have an additional adult with them [and a group of 5 others, rather than 1:1]) that it’s hard to know when to stop and who to trust. It’s hard to know when you have the best possible information, and when to rely on yourself as the best advocate and most knowledgeable about your child.

Where academics of the parent may come into play is how they do that advocacy and what form of knowledge they feel most comfortable with’ - data, emotion, anger, pleading etc. None are wrong if they come from the same root of intense care for a child.

I feel like you're hyper-focused on the distribution and the confidence interval, that to be honest don't actually mean terribly much on an individual level - in much the same way as other test results, such as GCSEs. These aren't a likelihood that Child X is above or below the expected level - it is the number of points they scored on exam. They publish CIs for progress scores at a school level - rightly, given variations in pupil cohort characteristics year on year.

Meanwhile, the distribution of scaled scores from 2018/19 to 2023/24 is available with loads of other statistics here, showing exactly how many pupils attained each scaled score in each subject.

100 is based on the raw scores of each test.

Below 100 means the child is performing "below" expected standard for their age. 110 plus means performing above. This is not organised by your child's school, this is set across the country, hence why all y6s sit the SATs. Other year bands do different tests with similar scoring.

But these are not decided by individual schools.
Also it isn't like the 11+ which is a pass or fail and ultimately it's more to measure the performance of a school.

I work with progress children who would be scoring around 85 to 90, meaning in class they are not working at their year band expectations but below.

I think it can be very hard for academic parents to accept that their child may struggle somewhat academically.

You're being purposely obtuse now, I expect you're in defence mode because you don't want your daughter to be below average but the fact is, she is. She is quite a bit below average.

IQ is one of the most measured and studied metrics in the social sciences/psychology, yet the idea that it’s all voodoo persists, mainly because it’s fashionable to say so, because ‘well, it’s complicated’ is true of almost anything, and can be mistaken for sophistication. But if IQ fails to meet the bar then not much of social sciences or psychology can remain standing because it typically replicates worse.