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?)

And if you actually deal with children and their learning, it's very obvious that a child who has a Standardised Average Score of 85 is a very different child with very different educational needs to a child with one of 110.

If you then look at other modalities of testing, such as CAT4s or the New Group Reading Test, they can help to give a broader/clearer picture - they can highlight areas where there is higher ability or areas of difficulty, such as where literacy levels affect decoding questions or where their spatial reasoning is very high and go some way into identifying reasons or approaches that may be more effective in enhancing understanding of the areas measured in SATs.

Rather than the OP stressing about statistics in a vacuum, it's better to focus upon what the data says about their specific child. It's not an insult, it's not a time to start lecturing staff about it, it's a time to look at what needs the child has to be able to reach their full potential.

Ok, OP, here is a rough explanation of your mistaken though process.

You are confusing repeated measurements of the same thing with multiple measurements of different related things in a population.

So if I measure a length of wood 100 times, I'll get 100 different numbers. These will probably roughly follow a normal distribution. Lets say I get a figure of 1007.1mm and the sd is 2.3mm.

I measure another piece of wood and get a figure of 1004.8. That is just outside 1sd, so we can say that there is a 68% (roughly) chance it is statistically a different length. Most sciences require a minimum of 2sd as proof of difference (so roughly 95% confidence it is different) - in this case it would not be considered different at the 2sd confidence interval.

In your case, you would need your daughter to do many SATS tests, marked and adjusted in the same way in order to assess the precision and accuracy of her score, and to be able to assess whether her score is statistically the same or different from another persons

My DC haven’t done SATs yet so I’ve got that to look forward to, but why on earth is it so complicated?? Who is that meant to help? Our school got really good results looking at the final percentages, but I can’t get my head around the different ‘pass/fail’ numbers. Is this all explained to parents in Yr6?

Why can’t we just let teachers blooming well teach?!

That's handy to know because the wording from school implies it was.

It would be the median, not the mean.
The way it's worded from school suggests it is a normal distribution for which the standard deviation would be 15.
That's how IQ tests, for example, work.

That's not incompatible though with the median for the whole population being 100. Your area could have 60-odd percent being above the median.

They haven't given us these, and the school is now closed for the summer (and, thankfully for us, now for ever).

@sd249 Standardised scores are standardised to 100 but I now see from someone's link that it is not a standardised score but a SCALED score. The wording given by school heavily implied it was a standardised score.
So I will be able to see whether the SDs are reported.
Scaled scores will be validated for that year (if they want to work out a comparison with previous years) and on things like IQ tests they are worked out by age so you can compare a child with themselves in previous years, for example.

For SATs, however, 100 is not the median, nor the mean. It is the bottom of the range of standardised scores that the Government has set such that c.25% fall below this range.

I think your school have confused you with their communication.

As others have said, that’s not how it works.

It’s just a way of standardising test scores which might differ from year to year, so they they can compare across years.

So there is a score they need to achieve to be hitting age-related expectation, which is always equated to 100.

There’s another checkpoint that relates to 110 which is greater depth.

The score changes every year but it’s no different from saying “The pass mark is 34 out of 50” except it’s translated into a standardised score.

It's not a normal distribution. The majority of children meet or exceed the "expected level" (100).

Here's an overview of this year's scores, and scores over time:
www.tes.com/magazine/news/general/sats-results-2025-improvement-in-all-subjects

That doesn't have SDs but it does at least have means (as I say, the school info implies 100 was the median, not the mean which wouldn't help much - but the means are around the 103-106 range).

I think they have. I'm not sure if they don't understand it, or if they think parents don't understand statistics.

This is, in fact, true for a normal distribution centred around 100.
But we can't calculate the SD from the scaled scores, and these aren't standardised scores.

As one of those 'so called data managers', it often rankles to have teachers lecturing me on algorithms developed on the basis of many thousands of children's data over many years as though it's something I've decided to tosh into SIMS for shits and giggles. I know the limitations, I know that a cohort of 60 from an extremely deprived neighbourhood where half hadn't encountered English three years ago isn't going to exactly replicate the expected outcomes arrived at from around 750,000 separate data points collected every year.

I also know that it makes absolutely zero difference to the DfE that Mrs Curly haranguing me is ruining my day, we will be judged on the basis of progress made in relation to the average score of Maths and Reading as measured at the end of KS2. Unfortunately, Mrs Curly doesn't seem to see beyond criticising the data being turned into graphs and charts and her thoughts upon her own numeracy skills to appreciate that fact when, quite frankly, I'm more concerned with doing my job and not appeasing people who don't like what the data says about their class compared to other teachers'.

I realise, of course, that I've said mean in my OP when I mean median. Gah! My supervisor would have my guts for garters.

But these aren't standardised scores - they are scaled scores - so if you aren't clear on the difference here's a handy crib sheet.

kb.insighttracking.com/article/0egdg261ko-the-difference-between-standardised-and-scaled-scores

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. Of course, that's probably close enough for government work (as they used to say).

I think that the description of your DD and her work very much matches the narrative description given for her scores - she is ‘working towards the expected standard’.

The scores that will be important for secondary are the English Reading and the Maths, as they are used to calculate ‘Progress 8’ after GCSEs, the measure of how she does against others with the same starting point nationally.

With 93/94 and a background of support within a smaller group to help her to make better progress, her secondary (if state) will see her as someone within reach of expected standards in key GCSEs when the time comes and (if resources allow by that point) she may well be a candidate for additional boosting. If they can get her to good passes in GCSEs, she will greatly boost their progress scores, whereas had she just scraped 100 that progress might not look as good.

I know from previous posts you are a hugely involved and active parent so in many ways she is ideally set up for the next step.

@WrigglyDonCat I'm not confusing the things you say, though. I'm assuming that when the school said "100 is the middle of the pupils' scores" they meant it was a standardised score.
But it is in no way standardised and (which could be for a number of reasons including a really bad test and a lot of children at the top or bottom end not taking the test) not normally distributed.

Now if they'd release the distribution and the s.d. I could just go away and happily work out exactly where DD was.

(and don't worry, I haven't told her she's "passed" or "failed" - she's had enough worry with her peers going to grammar making her worry she had to do well enough on her SATs to go to her choice of secondary).

(and another reason tests might not be normally distributed is that they are not designed that way on purpose - the phonics screening isn't).

You have made yourself sound like a bit of a dick here because you don't understand the scores for SATS. Certainly go ahead and lecture others about your superior knowledge, let us know how that goes though.

To be fair, the school’s communication was poor. Had they simply given a link to how the scores are calculated, OP would not have been misled.

So she could have just posted "how are SATS scores calculated" instead of the arrogant post she did put up

OP your time might be better spent looking to be kind to others rather than criticising them over their statistical knowledge, especially as yours doesn’t seem that impressive.
Teachers have a really hard job. I’m a TA, the pupils I work with scream, shout, threaten to punch me, try and punch/hit me, overturn furniture, it’s really hard.
I find it a bit petty that you are blaming the school for something the government do and criticising them because your statistical knowledge is oh so much better…

Why don’t leave the school alone, think of something positive to thank them for and move on, focusing instead on your daughter and all she has achieved despite her challenges. It will be much better for your mental health.

The school wasn’t communicating as a statistician. It was communicating in lay terms to parents who need to understand how their child is doing in school compared to how they should be performing at the end of KS2, and compared to their class peers.
It’s to help focus attention and resources on each child in the most effective way going into KS3.

You are going to look like a massive twat if you try to give the school and the DfE some 'basic statistical literacy' based on your fundamental misunderstanding of how the sats scores work.