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

[drspouse]

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?)

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.

No, that's not what I meant: we know the mean but we don't know what proportion score between the mean and 89. Unless you can find that data, in which case I can find out.

But, again, why does it matter? Why is it so important to you?
They are SATS so, while they can indicate future achievement, they don't set that achievement in stone and all children develop at different stages.

@TeenToTwenties thanks for that but she's already doing a language at home and we chose this school because it offers a language from her home country (she's adopted from overseas). Evidence shows knowing two languages helps with general learning and she's already understood more from Duolingo and me talking it over with her, about some aspects of grammar. Plus she's proud to learn it.

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

It is coming across that OP isn't happy with her DDs scores and wants to find something that will tell her the opposite of what those scores are currently telling her.
I feel sorry for her DD.

@twistyizzy the point of the thread was, the school had told us that the average child gets 100 and it's called a 'standard score' and if you don't get that many you haven't passed - but the mean child gets more than that, and it's not a standard score (which has confused quite a few people on this thread, though that's not too surprising), it's a scaled score.

If the school had understood what a scaled score was, or hadn't said that an average child gets 100, I'd have understood what they were saying!

The rest of this is me trying to explain confidence intervals, more or less.
The SATs distribution will have a confidence interval that can be calculated, but it might not be something they release.

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.

The school don't calculate the result though. The exam board do and work to DfE guidance as to boundaries.

@SophieJo "accepting your child's ability" sounds an awful lot like "don't bother making any plans for your child that involve academic achievement".
(And as others have said, these aren't ability tests...).
But as I have said, we already know she's getting help at secondary, she already has maths tuition and is moving up the ranks in her class in that after a very low start post pandemic.
So I don't think it's either a foregone conclusion she's "low cognitively" as a delightful teacher said of my other DC, or a point where we should rest on our laurels.

Honestly though these are only SATS. They only matter to the school.
I hope you don't have the same attitude when it comes to GCSEs otherwise you're going to be expending a whole lot of needless energy

As another statistician I feel confidence intervals are a step too far for this chat 🤣

No, other PPs have said they aren't intelligence tests, they are certainly ability tests. However are only a snapshot of ability to get a certain score on those particular tests.

That's good. (I wondered if this was your AC, didn't remember she was from overseas). A disrupted start to life may well negate my If the scores are a reasonable reflection of her ability comment. My eldest AC (came to us y3) outstripped her Maths SATs and went up a set every year at Secondary.

My interest in my DC’s SATs results extends as far as whether they tried hard and did their best and whether I think their results are a reasonable picture of what they’re capable of for the sake of their secondary education. I don’t care shout the statistical analysis of it, that’s for the school and education bodies to worry about. What difference does it make to my child, me or their future school to know that information? I did care that, for example, their maths papers tended to show they struggled with fractions and that’s something we could work on.

I can’t understand why you need to know this information and how that helps you in any constructive way. Is it just some attempt to prove a school you clearly have a fractious history with has misjudged your child? If both your children have now left the school why worry about it anymore? Or you think the SATs results portray a child with a different attainment level to your opinion of her and you worry she’s being written off?

It isn’t possible to work this out exactly BUT the best case scenario for a score of 90 would be that half the students who score less than 100 score less than 90 (ie the graph is flat between 80 and 100).

So the best case scenario is that at 89 she’s in the bottom 12%.

As it is very unlikely that the graph looks like this, and much more likely that the gradient of the graph gradually increases between 80 and 100, a reasonable guess might be that your daughter is in the bottom 10% of those who took the test for spelling and grammar.

Her position in the other two tests would be slightly higher, so maybe bottom 15% or so would be a sensible guess for you to work with.

If your DD’s scores are very much lower than the school would have expected, they may well attach a note to them as part of transition. However if she was anyway receiving intensive small group help, then these sound in line with expectations.

The question is what you do next. Reading is critical - is her low score likely to be pace? Vocabulary? Ability to infer? Keeping reading as a priority over the summer, perhaps through the summer library challenge, and also reading lots of non-fiction (reading short pieces at pace and making a game of ‘give me 3 new things you’ve found out’) will be helpful and will give her a head start against those children who do nothing between SATs and September.

Similarly, Y7 Maths content overlaps strongly with primary content but may be structured or presented slightly differently. Making sure that she remains fluent in times tables and number bonds, and can carry out the written methods for all 4 operations without thinking, will give her a good start.

I'd argue that achievement tests are rather different to ability tests, which are more like intelligence tests, but tomato tomato.

Sats are more for the benefit of the school and not the child secondary schools don’t take much notice of them might use for putting in sets but they are not important

You won’t get the full data from the school. You’ve had her results which are national. I can’t understand what more you need?

They have explained the results - my post of 12.16.

Are you happy with your child’s scores @drspouse ?

Exactly this.

Not sure what you are trying to achieve here, or how it is going to help your DD prepare for secondary school.

The 95% confidence interval around the mean won’t include 85! If you performed a statistical test to assess if a score of 100 is the same as 85 then you’d find it highly statistically significant meaning that there is a very strong evidence that they differ (given the number of children measured - the confidence intervals will be narrow). Sounds as if it’s a skewed distribution with a mean quite a bit higher than 100. It sounds as if you’re querying the statistics and trying to argue that your child should have a higher score. You may feel that’s the case, but it is what it is. You’d have to speak to the school but it might be that work in school is better than the SAT result and your child just struggled with the test itself. It’s best to accept it and get help if you feel it’s needed given what school says in relation to general work in school. Clearly might be difficult to get information from the school now though!

I found that they did use SATs results in Year 6 to assign children to classes for maths and English in Year 7 in my child’s secondary school. Just used them as a guide but can change classes a bit later if your child is in the wrong class. Your child should get extra support anyway if the scores are lower or they may just improve anyway if something clicks or - as you say - they’ve been problems at school with other children / distractions.

People worry about these things but it gives you an idea of where your child is, and allows you to get them help and allows more support in secondary. So good that you know the level that they are at.

It’s possible that the school used inaccurate language in describing the scoring levels but pitching it right for all parents is difficult, and I can’t think of a single other person who is scrutinising the scores in this way.

I guess my question would be whether you’d be agonising over the scoring and levels in the same way if your child scored 115… I would suspect not.

However you try to manipulate the data, your daughter has a low score. There may be multiple reasons for this. The important thing is that there’s support in place for her going forward, and it sounds as if that’s the case.

I’m really unclear what you’re hoping to achieve. It sounds as if you have a difficult history with this school; just let this go and focus on helping your daughter make a positive start at her secondary school. Obsessing over points on a score is going to change nothing.