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

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 😂

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?

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

@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.

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.

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.

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

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.

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.

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.

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

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 ...

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.

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.

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.

Exactly this.

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

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

They have explained the results - my post of 12.16.

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?

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

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.

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?

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.

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.