What the hell does standard deviation mean (in context of standardised assessment)?

[soconfusedandpanicked]

Uni assignment - I'm sitting in floods of tears as so confused and need it finished ideally today . Have emailed course leader to ask for guidance .

(Have changed details)

Person - assessed, score of '20' on standardised assessment .

Norm score for his age is eg 40 (higher than M)

20 is the norm score for person 3 years younger .

Then it says on the assessment - standard deviation is eg 7

What the hell does standard deviation mean? Does that mean the acceptable values for the norms for the age are e.g 'X plus or minus 7'?

So if the normal score was 30, you could get away with saying 23 was at the lower end of acceptable, and 37 was the higher end?

I'm completely confused by it all - I get that the person is performing at a level three years younger than expected which is consistent with other data but what the hell does the standard deviation have to do with anything? It makes no sense at all.

Hello
My understanding (AS stats but a long time ago) is that the standard deviation gives you essentially the range of "normal" ie if mean is 40 and SD is 7 then anything between 33 and 47 is inside the normal range but 32 and below/48 and above are outside the normal range.

Does this link help? It goes through what SD is and how it can be used

www.mathsisfun.com/data/standard-deviation.html

Standard deviations are related to the normal distribution, a pattern which most data follow (quick google will show you the graph). 68% of people fall within one standard deviation of the mean.

So the mean for his age is 40.

68% of people his age will have scores between 33 and 47 (one standard deviation).
95% will have scores between 26 and 54 (2 standard deviations)
99. 7% will have scores between 19 and 61 (3 standard deviations)

They will be equally distributed above and below the mean. The child's score is very low for his age (certainly in the bottom 0.5%).

[quote Tiggles]Does this link help? It goes through what SD is and how it can be used

www.mathsisfun.com/data/standard-deviation.html[/quote]
A bit yes ... figuring out that I've just got that his score is one and a half standard deviations away from the mean . Not sure what that actually means in context but will keep googling ! Thanks :-)

When you have got this one in talk to your tutor and explain how this has thrown you. Get some additional support.

I am not trying to be nasty but this is a basic statistical measure. That it has thrown highlights understanding of stats as a wekaness. Don't ignore it, it will only get worse and you will feel les and less able to complete work.

So be proactive and, when you get a response from the course leader as them how you can access more tuition, help on statistics. They won't mind, it's worse when a student refuses to acknowledge a gap, it becomes far more of a struggle than it needs be.

Oh and when you have it sussed, come back and explain here the solutions.

Nothing like explaining to someone else to test your understanding. Good luck.

@CuriousaboutSamphire

When you have got this one in talk to your tutor and explain how this has thrown you. Get some additional support.

I am not trying to be nasty but this is a basic statistical measure. That it has thrown highlights understanding of stats as a wekaness. Don't ignore it, it will only get worse and you will feel les and less able to complete work.

So be proactive and, when you get a response from the course leader as them how you can access more tuition, help on statistics. They won't mind, it's worse when a student refuses to acknowledge a gap, it becomes far more of a struggle than it needs be.

I will do, I'm two years out of study due to illness and only started back in Jan. This assignment is based on learning that I did back in September 2018-Jan 2019 . I am really, really struggling as can't remember those lectures, I have access to the notes online but cannot remember what we were taught at all - and I need to know this as apart from this assignment, being examined on it in May as well ... it makes absolutely no sense to me at all.

Even with that data that the child is 1.5 SD away from the mean, I've absolutely no idea what that means in context, except that his scores match up to much younger child - but online says he's within 95% of the everyone taking that test so surely he's not done that bad .

Have another assessment to score next which is even more confusing as its just endless numbers and something called scaled score charts . if I could do without panicking id probably get on much better

OK! So get onto student services, your tutor, the course leader, HoD, anyone!, as soon as possible and let them know that your 2 years out have highlighted an issue and you need them, your tutor etc to help you get up to speed.

Be clear, you don't think you will pass without some support with this. That you are confident in your subject knowledge but not in the language of statistics. Tell them that knowing you don't undertsand it is becoming a barrier to your being able to think through it and that you are sure that with some help you'll manage much more easily.

They'll step in, I promise. They don't want you to fail.

And don't feel bad, stats throws a lot of people. I used them a lot, taught some of them too, and I still freeze when I start a new project. I keep books, webpages close! It's often just the language, not the maths, that is the problem!

Best of luck getting rid of that panicky feeling

I used to teach maths and on the whole I’d say that probability and statistics aren’t very intuitive so if it doesn’t ‘make sense’ don’t worry! You just need to get the hang of some basic recipes.

I find the way yeast works making bread is pretty magical and it’s certainly possible to get it wrong.

If you imagine plonking a big lump of dough on a baking tray and cooking it you might end up with a long dome shaped ‘loaf’ and if you cut that in half lengthwise you’d get a shape vaguely similar to a normal distribution. Higher in the middle, going downhill at each end.

If you cut exactly in half across the middle that’s where the mean is with exactly half the loaf on each side.

If the ‘standard deviation’ was a couple of inches you could slice across 4 inches from that centre line to cut off the crust at each end and still leave 95.5% of the loaf.

One and a half standard deviations below the middle would be about 3 inches.

images.app.goo.gl/abtTipQB1TtjDk2n9

Your tutor will help you find the right recipes and if you practice them a bit you don’t need to understand the deep chemistry of baking or gardening or maths you just need to get used to doing the right steps in the right order and it will mostly turn out ok. Well, at least 95.5% of the time.

A big figure means there is a spread of attainment in the class/group that took the exam.
A small figure means the results were broadly similar.
You are aiming for a small figure as that means teaching and attainment has been pretty consistent for all learners.

In your example you could also reference error bars, in other words 'normal' means there is a range of achievement with most people being plotted within that range, but if someone is outside the range, this is not normal for age-related expectations.

The other thing you need to bear in mind is that it's a crap question. They haven't qualified many of the assumptions about the assessment. If you like you can send me the question via DM and I will explain why (I'm a lecturer in education).