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?)

But do you know that it's a normal distribution they are working with?

I assess pupils for something else and 89 is seem (and unfortunately reported) as low average

It’s not a normal distribution. Not even close.

They should give you a range for each category. In my daughter's school report this year (not year 6) it said 95-115 is standard expected for year group and 85-94 is working towards those standards.

I wouldn’t over think the statistics, SATs just give a basic overview of where kids are at with core subjects. Your DC hasn’t passed, she isn’t the only one and secondary school should be able to support her going forward.

It sounds like you’ve done more analysis but I can’t work out your point. Aren’t the national figures something like 62% reached the expected standard in everything (meaning over 100)? With variations across the individual subjects (i.e in reading it was 75% achieved over 100). I can’t work out whether you’re saying that the standard is set too high, or that your school don’t understand the figures.

The mean isn't 100 for each anyway - even after scaling!
Also you seem to have made up the standard deviation of 15.

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

this is helpful to show you exactly what DC got in the tests

It's not a normal distribution. It's a standardised score, we have a broad, large intake of 300+ and in that it is definitely not half below 100 and half above, that's not how it works.
I would say that in our area about 65-70% of children will be 98+ it's not half and half.

By the way schools are also assessed on progress so you may be able to get your daughter’s progress scores if you ask? And most schools I know are really good at highlighting individual progress even if the child is still below the nationally expected standard.

OP, I would concentrate on the pride you feel in your DD and ensuring she receives all the support to kick on in secondary school. Well done to her.

Hopefully this link will work but I saw this earlier which breaks down the figures. I don’t think the scores are normally distrubuted around 100

Data

scores of between 85 and 115 are statistically indistinguishable from 100.

If you look at the raw scores needed to generate a scaled score of 85, 100 and 115 this just isn’t true.

Instead of trying to be smart about it, I’d concentrate on how hard your DD has been working at school and that her SAT results will be good indicators for her teachers at secondary to understand the support she needs going into KS3.

No, you are incorrect. It's not 50/50 at all. Between 70-75% of pupils passed each subject last year meaning they scored 100 or over in the scaled score(75% in reading, 74% in maths, 72% in writing and 73% in grammar and spelling)

I think 100 is just the 'scaled score' to meet the 'expected standard' - whatever that standard is judged to be. The 'scaling' adjusts raw scores for small differences in test difficulty between years.

So, no I don't think you're right when you say that half of children will underperform.

However, it's right to highlight some of the problems with testing. For instance, if you re-tested all the children who fell below 100 one week later, many would improve without any extra help. Explanation: because you're selecting the lowest performers, some of whom may have had a 'bad day' or not been feeling well or just randomly underperformed on the original test.

All testing is imperfect system.

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.

As an ex teacher who is reasonably mathematically literate,I have had this conversation with senior leaders many times.
It's very disappointing how mathematically illiterate many SLT and so called data managers are. A combination of poorly written assessments and poorly designed algorithems often lead to an output of total garbage, but as long as it prints a report with lots of pretty colours many school leadership teams are satisfied.
Ask them about the degree of uncertainty on the algorithem they are using and the size of cohort needed to give statistical significance.
I hate the way dodgy data is used to label children

Even if it were a normal distribution, the assertion that scores between 85 and 115 are statistically indistinguishable is a stretch.

There clearly is a vast difference between a score of 85 and 115 in any scenario

The raw scores will have a normal(ish) distribution (not completely normal, as those who would have very low scores do not take the tests and are assessed in an alternative way).

However, the standardised scores do not. The lowest possible standardised score is c. 80, the highest 120, and the 100 is artificially forced to create the right percentage of ‘expected standard’ - ie that the right number of children get 100-109; then the right number 110-120.

It’s a similar process for GCSE and A levels, where artificial ‘lines’ are drawn on the normal distribution of marks to give top and bottom of each grade.

Probably better to think of it - if you want to think of ‘expected is a range’, that the range of expected is 100-109. The actual peak of the normal distribution will be somewhere within that range.

The government's figures for this year's SATS are that approximately three quarters of children reached required levels in reading and maths, slightly less for writing. Children's attainment does not fit a standard bell curve.; It's skewed.
Also there's a scaling model on the results, to ensure fairness, and the size of the population would support the result being statistically accurate. 120 is the highest score possible. 80 is the lowest score you can achieve, below which the student doesn't receive a score, they get an 'N'. So it's just not true to say that marks between 85 and 115 are statistically indistinguishable from 100.

I understand that you are disappointed but this model was designed by people with experience in the field, it wasn't sketched up on the back of a fag packet by your DC's headteacher. Unless you have reviewed the full data and the model, you should focus your energy on your daughter's hard work, and congratulate her on her progress not her position relative to her peers.

Just reiterating - to say that 85 and 115 are statistically indistinguishable in a set of scores where the minimum is 80 and the maximum 120 , and 100 is artificially set at ‘a politically set number of around 75% pf children are above this level’ is obviously false.

You have to take into account the full range of scores available (so a much wider range than 80-120) and whether 100 is genuinely ‘the middle of the normal distribution’.

It is better for the student to just miss rather than just scrape a pass. If they fail they may get extra help at secondary school

As a PhD in a subject requiring statistics
Well yes - doesn't make you the expert of standardised SATs scores though. You're coming across as rude and arrogant.

As a PhD in a subject requiring statistics I know that 85 would be one standard deviation below the mean (100)

This is where your assumptions have created your error in understanding- 100 is NOT the mean. The mean is actually significantly higher than 100, though it is not a figure disclosed by the Government, iirc.

It's not a stretch, it's statistical nonsense. Assuming a normal distribution (which as others have suggested, isn't reasonable), 1sd just means that ~68% of results fall within that bracket, not that they are indistinguishable.

I'm not sure what subject OPs PhD is in, but I really hope it isn't a science. I'll take a punt on something social sciencey as its a field that has been known to have a fairly dubious relationship with stats - although to be fair I've encountered enough science PhDs who couldn't stat their way out of a wet paper bag.