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?)

The most recent data showing distribution of scores is for 2023/24 however, this data shows that

Reading - a scaled score of 94 or less was achieved by 10% of all pupils
Grammar - a scaled score of 89 or less was achieved by 4% of all pupils
Maths - a scaled score of 93 or less was achieved by 10% of all pupils

It’s the cumulative percentages for each scaled score. The data isn’t for this year, but it doesn’t change very much year on year since 2018/19 so is likely to be similar. It’s all on the government website.

Schools can be v poor at giving clear info, so I can see why the OP is questioning. My DD did some assessments at school and we were told she was 'below average' in some things. At the time I had no idea how low a percentile 'below average' was in official SEN speak, I just thought 'well yes we know that'.

After her getting an EHCP in y12 where we found she was bottom 5% for some things and even lower for others, I wrote back to her old school saying that if only they had explained what they meant at the time ...

@drspouse the vast majority of secondary schools use CAT testing and most schools have mixed ability classes in Year 7.

But OP didn't start with that sentiment. She started post with an extremely arrogant Q that she thought she could give the school a lesson in statistics which implied they had got the scores wrong. It became apparent she didn't understand SATS scores but had kept querying them like she is determined that they are wrong.

Where I teach, we have a wide range of ability from should be in SEN school to gets into high performing grammar.

82% got 100 plus for the grammar, 80% for reading and 78% for maths.

89 on SATs is well below average, high 90s just below 97 plus really. Only a very few get below 95.

They do publish mean scores for each years' tests , they are usually around 104 / 105.

The ‘margin of error’ of the precise score is perhaps less relevant than the ‘margin of error of the band’ (GD, Expected, Working Towards).

I don’t think the margin of error is so great that your DD’s ‘true’ result is likely to be Expected (which you know anyway, because of the extra help she is receiving). On the other hand, nor is it so great that your DD is not able to access the Y6 tests and thus should gave been assessed in a different way. She is squarely ‘working towards the expected standard’, and if you know her weak areas, you can continue to help her in that working towards.

I know that EP tests etc do include additional statistical information, but SATs, GCSEs, A levels, degrees etc do not - you do not get to say ‘I got a 5 / B / 2:1 but was within 1 standard deviation of the next grade / scored more highly than exactly x% of candidates in that cohort’. It may not be what you want, but it is just how these things are reported.

Thanks. I thought my guesses were a bit on the optimistic side.

You can use the tables provided to work out your child's raw score and percentage from their scaled score. The average scaled score is usually 106/107 iirc. A scaled score of 85 in the maths test would equate to around 10% of questions answered correctly. A scaled score of 115 would have meant around 94% of questions answered correctly. A scaled score of 100 would mean they answered around 51% of questions correctly.

There are also percentages calculated for all English schools re how many get expected standard each year, for each subject and reading, writing and maths combined. So you couid look those up, though this year's won't be out till the Autumn. A score of 100 does not mean a it's an average score (majority get higher), its just the standard set to indicate having met the expected standard in that subject. They are standardised in the sense that the tests are checked out over a cohort of children to indicate a similar level of expectation over the years.

Originally they said 80% should be within expected but national scores have usually been a bit less, and technically 10% more should be above, so it would be 90% really. I always though it crazy that they couid just assume the standards set were reasonable, but the test results over the years now give data to measure against so I suppose that helps keep standards up.

@drspouse
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.

That’s not true at all. If you think that’s a property of the +/-1sd interval, think how different a woman measuring 5’1” and one measuring 5’7” are. You can be more than 95% sure they are different heights.

It is a property of test accuracy. Proper IQ tests have a standard error of measurement of about 3-5. So 95% confidence interval is +/-6 to 10 Put that around 85 and 115 and they don’t overlap.

There’s a much better than 95% chance that the higher-scoring child is more capable.

For scaled SATs, DfE says the SEM is 3, so there’s a 95% chance that the ‘true’ score is within six either side. Six either side of those numbers doesn’t overlap at all. Should be 99%+ chance that the 115 is smarter than the 85.

National data

Writing 72% Greater depth 13%
Reading 75% average scaled scores 106 33%
Maths 74% 105 26%
GPS 73% 105 30%
Science 82% - -
WRM 62% 8%
Combined

100 is not supposed to be the median score, I don't think, otherwise half the children would not reach the expected standard, which isn't the case I thought the median was usually around 105 or 106?

The sats confuse me to be honest

we was originally told they daughter wouldn’t be taking them because she had not completed “ key stage 2 curriculum “

she is very high send needs ( autism, speech disorder, cerebral palsy ) and then only attended school 18 percent of the time due to a life threatening illness - her attendance should increase from now.

last minute they decided she was doing the SATS she scored
107, 98 and 99.
super proud of her but what I didn’t get was she was as I can read in this thread bottom 25 percent which is to be expected but the school are saying that she has the ability based on those score to smash her GCSEs but mumsnet says differently on everything I’ve read.

I can see why it’s confusing for parents 😂

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.

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.

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

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 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.

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 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.

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

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.

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.

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.