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?)

We don’t know what the school said. How do we know they didn’t perfectly explain the statistics? They most likely have nothing else to do at the end of a school term than explaining statistics to parents…

This tells you her raw scores. https://www.gov.uk/government/publications/key-stage-2-tests-2025-scaled-scores/2025-key-stage-2-scaled-score-conversion-tables

Based on the scales scores you gave
Grammar - scaled score of 89 was 13 or 14 marks out of a possible 70.
English (reading) - scaled score of 93 was 18 marks out of a possible 50
Maths - scaled score of 94 was 34,35,36 or 37 marks out of a possible 110

To get the expected standard children needed
Grammar - at least 35/70
English Reading - at least 28/50
Maths - at least 58/110

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.

Dfe don’t release the distribution.

FFT data lab do some sampling most years.

cumulative frequencies for some years are in with this article.

https://ffteducationdatalab.org.uk/2022/07/key-stage-2-2022-how-have-things-changed-since-2019/

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

Quite!!!

Having taught hundreds of y6 children, I can assure you that children getting 85 and 115 are very very different. A child scoring 85 will be struggling with maths. A child scoring 115 will be extremely good at maths. A child scoring 85 one day will not just happen to score 115 the next and vice versa (bad days and extremely lucky guesses aside!) Whereas, a child scoring 99 and one scoring 101 may well be indistinguishable.

given the lowest possible score is 80 and the highest 120 how can 85 and 115 be ‘statistically indistinguishable’?!

also, SATS scores are not age standardised, as someone else above seems to think they are.

Yes it does, that's literally what the statements are.

More important than her results though is why does that even matter? Do you compare her to other children? Do you let her know thats what you do?

75% reached expected standard in reading
73% reached expected standard in grammar
74% reached expected standard in maths
62% reached expected standard in all 3

Your school is thoroughly confused about how the scores word. Neither median nor mean are relevant. 100 represents the threshold for having met the expected standard - it's the pass mark.

The STA sets out here how the scoring system works.

What is it that you meed to know, precisely?

Do you need to know exactly where in the centiles she lay? For what purpose? You know she’s below c.75% of her peers because she’s below 100, and she’s a distance off (as the peak of the distribution will fall above 100, the distribution graph will be rising above her scores and falling below them).

Are you worried about eg setting in her secondary? Do they set on the basis of SATs? As a non-grammar in a grammar county, the highest attainers will not be in her school, so she will be closer to ‘the middle’ of her school’s ability range than she would be in a full comprehensive in a non-selective county.

I have already posted about how her trajectory may well be seen by her secondary. One real advantage for her and for you is that she has a genuine opportunity to ‘beat her predictions’ and reap the self-esteem that comes from that.

Also, the narrow range of subjects vs secondary could hide her strengths - art, drama, sport, music, DT etc etc are all utterly unlinked to her SATs, as is ‘being a genuinely nice person who tries her best and everyone likes’.

Go for it op
drop the head teacher an email

I dare you! 😊

Focus on educating the school

rather than trying to improve your daughter’s educational attainment

Trouble is that a 'simple link' is not accessible to all parents, whether for reasons of literacy, language or numeracy; you'd still have some asking 'but what does this mean?'. It's difficult to find a way of conveying the information without at least some people becoming confused, upset or offended.

If you pick a shorthand of High, Mid, Low, people get upset. If you use the attempt at neutrality of met the expected standard/working towards the standard/exceeded the standard, people get upset, if you link to a document containing words or explanations that they don't understand, people get upset, if you reduce it to 'she's at the level we expected for her, everything is fine, she hasn't fallen back', people get upset. We have posts this week from people upset that school reports have mentioned areas children find difficult because reports should be hagiographies and others upset that there isn't any actual indication of the level/progress their children are at because it's all generic phrases that sound nice but mean nothing.

There is no way for schools to win with communications reporting on assessment and progress; you just can't please all of the people all of the time.

SATs scores have nothing to do with intelligence. SATs don’t test intelligence.

In short, not as well. Hence the scores being at the lower end.

It’s very straightforward - look at my post of 12.16
The OP is making it overly complicated

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.

Take it you have no experience of SATs and how they are calculated? These aren't school scores, they are national tests.

It is not a normal distribution with a mean of 100. It is a distribution designed to obfuscate and confuse. (The median score for maths is normally 105/6).

The conversion tables from raw to scaled scores are here:
https://www.gov.uk/government/publications/key-stage-2-tests-2025-scaled-scores/2025-key-stage-2-scaled-score-conversion-tables

The scores you quote are quite low.

94 in maths means a maximum of 37 marks out of 110.

Leaving aside the fact that you've now been informed that the results are not normally distributed with a mean of 100, your op seems to suggest that you think all distributions with a mean of 100 have a standard deviation of 15 which is categorically wrong. The whole point of a standard deviation is to tell you how widely spread the data is about the mean. Knowing the mean of a sample or population tells you nothing about the standard deviation - which is precisely why people use not just the mean but also the s.d to describe normally distributed data.

But you do know how she’s doing as against the expected standard for children her age, that’s the whole point of setting an expected standard for your child’s year, which has an adjustment for age baked in, and then telling you how your daughter is performing compared to that standard?

Put it another way, every child of your daughter’s age will have been assessed against that same expected standard and given the same adjustment for age. It’s not the case that everyone born in September passes, and everyone born in June fails. That’s the whole point of adjusting the raw data to a scaled score which accounts for age. You may not know how every other child of your daughter’s age has performed but what more would that give you?

It does slightly sound as though the school
confused you but also a bit like you’re trying to undermine the data slightly because you’re a bit worried about your daughter. Completely understandable but remember no stats are perfect, but they’re not completely useless either. And your daughter’s scores are decent, with good support at secondary and at home
i am sure she’ll progress really well.

OP I wouldn’t worry about the scores too much. They are a measure of the school and a guide for secondaries as you which children might need extra help or extra stretching.

your DDs are quite low particularly in grammar so I would concentrate my efforts on making sure she has any help she’s entitled too. Academics isn’t everything encourage her in other ways

SATs don't measure intelligence, they measure attainment. It's pretty clear that the kid scoring 115 has done better on the test than the kid scoring 85.

Prior attainment is also a reasonable predictor of future attainment. The kid who got 115 is more likely to do well in their GCSEs than the kid who got 85.

@drspouse With those scores I would expect your DC to be in bottom quartile sets for any subjects they set in immediately. (Comparing the scores my DD had and her initial sets in her comp).

If the scores are a reasonable reflection of her ability she is likely to struggle to get to grade 4 in English & Maths in year 11 without strong intervention.

Her literacy may well mean she struggles to show what she knows in other written subjects.

I would be looking at her not doing an MFL in y7 if that is an option at all to be replaced with English intervention. If she has been unable to learn the stuff for the SPaG test then learning the grammar and spelling for say French may be a waste of effort (it was for DD).

You literally do though... They are published nationally and Ffion56 has posted the percentages above. If you mean for your dcs school, they will also publish those. I am an experienced Year 6 teacher and a scaled score of 89 is very low in most cohorts.

Perhaps that's not what you meant... if so sorry please ignore