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

I'm not saying that.

I'm saying that the school originally explained things in a way that said 100 was BOTH the average score AND the pass mark i.e. they were suggesting half of children always fail.
I'm happy DD will get extra help in Y7 but I already knew that so this makes no difference to us.
I'm not happy that they aren't explaining it right and aren't (probably aren't able to) giving a margin of error.

If you've ever had an EP report for a child you will have been given this margin of error. It's pretty important. DD scores could be even lower, in reality, if the margin of error is big.

I'm not saying that.

I'm saying that the school originally explained things in a way that said 100 was BOTH the average score AND the pass mark i.e. they were suggesting half of children always fail.
I'm happy DD will get extra help in Y7 but I already knew that so this makes no difference to us.
I'm not happy that they aren't explaining it right and aren't (probably aren't able to) giving a margin of error.

If you've ever had an EP report for a child you will have been given this margin of error. It's pretty important. DD scores could be even lower, in reality, if the margin of error is big.

You need to take note of this post and accept your child’s ability.

This is all you need to look at

What's the score range of the SATs?

Here's a breakdown of the score ranges and what they mean:

120 – This is the highest score available in the KS2 SATs

110-119 – Any score above 110 (including 120) means that a child has exceeded the expected standard in the test and is working at greater depth.

100 – This is the expected standard for children. It basically means they are working at an age-related expectation.

80-99 – Any child awarded a scaled score of 99 or below has not met the expected standard in their SATs. Often, schools refer to these children as ‘working towards the expected standard’.

80 – The lowest scaled score that can be given

I am aware of that - I'm talking about how IQ tests are constructed.

At first I thought we knew the distribution and the SD of the SATs.
But apparently we don't.
Just how sure you can be that a child with 115 and a child with 100 are genuinely different depends on the SD.
Which neither you or I know.
They could be really accurate with very little error and the CI could be 2.
Or they could be really poor with a massive CI bigger than the difference between the mean and the maximum score.
Maybe we will get the full data some time, I don't know (now I've looked into it further) whether they routinely release it.

I saw that thanks @Ffion56 but as you don't know all the other pupils scores it doesn't help me much with how she's done compared to other DCs her age.

I realise, of course, that I've said mean in my OP when I mean median. Gah! My supervisor would have my guts for garters.

But these aren't standardised scores - they are scaled scores - so if you aren't clear on the difference here's a handy crib sheet.

kb.insighttracking.com/article/0egdg261ko-the-difference-between-standardised-and-scaled-scores

There's masses of error in any test, including IQ tests. You can't be any more than 95% confident that a child scoring 115 on an IQ test is more intelligent than a child scoring 85. Of course, that's probably close enough for government work (as they used to say).

I saw that thanks @Ffion56 but as you don't know all the other pupils scores it doesn't help me much with how she's done compared to other DCs her age.

You should be entitled to see the distribution of whatever if they are giving you a result with no context it’s pointless.

My child’s private school wouldn’t show your child’s full report, they would put numbers in an email. Infuriating as they think parents are stupid. I have a gifted child and they would always tell me he was “well placed in his year group with many bright children”. Hundred percent hiding his results to keep him at their mediocre school. My other child struggled with some subjects and they would say same thing. A huge effort to keep the parents ignorant and happy paying fees. They pretended the results were just a single number.

Needless to say, moved them to a more communicative school which met both their needs. Gifted has graduated Oxbridge w a first … would never if stayed at the school hiding the results. Other got great support and at good Uni.

Press them for more comprehensive results.

DD has her SATs report with her end of term report.
She got 89 in her English grammar and 93/94 in her other English and in Maths.
This has been reported as "not reached standards" or similar by school.
As a PhD in a subject requiring statistics I know that 85 would be one standard deviation below the mean (100) and that scores of between 85 and 115 are statistically indistinguishable from 100.
Put another way, if you have to have 100 to "reach standard" they are assuming that half the children automatically won't reach the required standard.
AIBU to explain this to you and to school and my fellow parents?
DD was in a group of 2 struggling with maths at the bottom of the class for several years and I'm really proud not just that she's progressed but also that she's now in the middle of the national scores.
This is a ridiculous way to "explain" to parents (unless their explanation is wrong and it's not a normal distribution with a median of 100?)

My DC haven’t done SATs yet so I’ve got that to look forward to, but why on earth is it so complicated?? Who is that meant to help? Our school got really good results looking at the final percentages, but I can’t get my head around the different ‘pass/fail’ numbers. Is this all explained to parents in Yr6?

Why can’t we just let teachers blooming well teach?!

I saw that thanks @Ffion56 but as you don't know all the other pupils scores it doesn't help me much with how she's done compared to other DCs her age.

Standardised scores aren’t spread across a bell curve. They take their raw scores and adapt it to allow for age differences within a year group because there’s a big difference between a child born in August and one in July taking the same test - standardised scores even this indifference out.

A standardised score of 100 shows average level intelligence. 115 is children who are performing very well. 85 less so. The school isn’t wrong, you’re applying your statistical background inaccurately within this context. There’s a big difference between those scores, sorry.