Primary School Attainment Data

Last week saw the release of the gorvernments figures on school performance, followed by coverage in the media, like the guardian.


Apparently there are more than 16,000 primary schools in total (my spreadsheet has 15695). and I'll look at the data with particular attention to a handful of statistics released with the data.

These are:

• 1310 schools failing on English and Maths
• 1/3 failed to reach level 4 in reading, writing and mathematics combined
• the proportion of pupils achieving the expected level in English is 82% and Maths 80%

Whether or not a school is deemed as failing is whether it is above or below a `floor' level. A primary school will be below the floor if

1. 60 per cent of its pupil not achieving level 4 or above in Eng and maths combined
2. it is below the England median for progression by two levels in English
3. and it is below the England median for progression by two levels in maths 

Its not very clear from the data and statement exactly what numbers are used so its not straightforward to duplicate the results. I've taken my best guess at some of the figures.
From my calculations, the number of schools below the floor is 1459. This is almost exactly the 1310 given and 150 which may just be a coincidence.
The performance numbers are split into deprived pupils denoted FSM&CLA (Free School Meals and Children Looked After) and others. I've combined these figures for this total number.

 

Generally speaking, using an average for a `floor' seems a bit odd to me. Obviously half of the pupils will be below the average. This doesn't seem very disciminatory or sensible.


Conspicuous by its absence (again!), there is no mention of random variation unfortunately.

Interactive Google chart test

Loose change

I’ve recently read something that describes a plot as “a completed process of  change”. I am not at all experienced or educated in writing so may well be repeating and beginning to understand basic principles but it struck me that this could be generalised to most writing, at least the kind that I’ve been involved in recently. A journal paper in a maths journal or a lighter piece in the newspaper has this property. There is a journey of sorts that starts with enticing the reader and ends with a culminating reason for the whole thing. In actual fact, the newspaper article would be in reverse (the “inverted triangle”) but I think the principle still applies. So I think there should be a change of some sort, however small, even if its in knowledge, understanding or perspective instead of an explicit lesson learnt through a character or event.

Best guessing

This weeks S-word article is about averages. Arithmetic mean, geometric mean, harmonic mean, median and mode. This isn’t even going into maximum likelihood estimates or least squared estimates! All of these things are our best guess at a single summary statistic for the data. If we had to pick one number that represented the data, what would it be? There are all kinds of criteria for judging whether an estimate is any good or not. How does it behave as the sample size gets larger or does it have a tendency to be too high or too low (relative to a known measure like the population mean). Statisticians talk of BLUE (best linear unbiased estimate) and consistency (as the size of the data set gets bigger then our certainty in the number we’re getting out should increase too). The `take home message’ here is that there is no single best estimate of centrality but rather the estimate best for a particular situation could be any of these mentioned. In some cases there may not be much difference between the values anyway to there’s not much to worry about. In other cases, we need to be a bit more thoughtful and choose our estimator with care.

Random Toast

I presented at the knutsford scibar yesterday and greatly enjoyed it. The audience was interested and intelligent. The topic of the talk was Randomness and by-way of demonstrating that human beings see patterns everywhere, even when there are none to speak of, I showed some examples of 'faces' seen on the surface of burnt toast. I wondered whether anyone could make out the face on the toast shown here! Randomness is a funny thing!!!

Stats 101 format

I'm reading a book by David Lodge called "The Art of Fiction". It a collection of short article published in the Telegraph about different aspects of the Novel highlighted through example snippets of text from famous books.
It struck me that this is basically what I want to do with the statistics 101 idea I started on the Media Fellowship placement. I want to highlight statistical ideas by using example found in the media.
Perhaps then I should call this "The Art of  Statistics" or "The Art of Understanding Uncertainty"?

2 albums I've just got

"I've got my double cross to bare..."

"I live in the future, the present is my past, my presence is a present, so kiss my ass...". Hmmm

Romeo and Juliet parody of Bayesian and Frequentist

I thought that a possible joke could be based on rather than Romeo and Juliet being Montegue and Capulet, they could have been Bayesian and Frequentist. I could take an actual passage and change some of the words or just recount a bit of the story??

"What's in a name? That which we call a rose by any other name would smell as sweet". Romeo and Juliet ( Quote Act II, Sc. II).

O Romeo, Romeo! wherefore art thou Romeo?"

Another story would be how a man and woman statistician meet. Could talk about mix with psychology (predominantly boys/girls).

I now think that I should take more than one famous feud/rivalry and put it in this context.

implicit (prior) assumptions

I realised when being briefed about writing newspaper articles that there are some similarities with a statistical hypothesis and more generally similarities with anything that need to be `created'. By that I mean something that is created (superfically as new thing).

What I mean is this: For a new experiment there's assumption made even before you'd done anything. These assumption come from the simple fact that you'd decided to do an experiment in the first place. The motivation to do a particular experiment is already biasing the experiment. Out of all possible experiment, why was this one chosen? Even given the fact that the experiments aim to answer a particular question, then there would be more than one way to skin a cat i.e. the question could be answer in alternative ways. So, what the question is and how we decide to answer it e.g. what type of data do we collect and this is even before we start thinking about how to use the data.
The similarity with writing a newspaper article follows fairly obviously. How is it that one article is written over another hypothetical article? The simple fact that some one has chosen to write an article on a perticular subject has alrready biased the content. And this is before the `angle' of the piece is taken in to account.

Prior implicit assumptions are harder to pin down but are still important when considering the credibility, validity and bias of some knowledge.

John Cleese ideas

I saw John Cleese at the Lowry last week and he gave me some ideas for the standup thing. First theres an easy joke about being good with numbers and then getting something really easy wrong straight afterwards, e.g. I hate a few things about people who can't count: 1. they're stupid and 3. they can't count.

I also liked the 4 line joke poem he did.

e.g
stats is important is my motto
when in a shop, bank or school
but if you think that you'll win the lotto
then you're a massive tool

I also heard a song that basically lists connected things and wondered if I could do this for random stuff:

buses arriving
tossing coins
throwing die
radiation emission
queueing
broken light bulbs
urns and balls
boys and girls
...

kind of like the poem I wrote

If I Didn't Have You Lyrics

Yep yeah
If I didn't have you

If I didn't have you to hold me tight
(If I didn't have you)
If I didn't have you to lie with at night
(When I'm feeling blue)
If I didn't have you to share my sights
(Share my sights)
And to kiss me and dry my tears when I cry...

Well I, really think that I would...

Have somebody else.

(If I didn't have you)
If I didn't have you, someone else would do
Your love is one in a million
(One in a million)
You couldnt buy it at any price
(Can't buy love)

But of the 9 point 9 hundred thousand other loves,
Statistically some of them would be equally nice.

(Equally nice)

Or maybe not as nice but say, smarter than you...
Or dumber but better at sport or...
Tracing

I'm just saying
(I really think that I would)
Probably
(Have somebody else)

Yeah.

(If I didn't have you)
If I didn't have you someone else would do
(Someone else would surely do)

If I were a rich man
And did a diddle diddle diddle diddle diddle diddly
I guess I would be with a surgeon or a model
Or any of the royals or a kennedy
Or a nymphomonical exhibitionist heiress to a large chain of hotels

If I were a rich man maybe I would fiddle
Fiddle diddle diddle with the rich man girls

I'm not saying that I'd not love you if I was wealthy or handsome
But realistically there's lots of fish in the sea
And if I had a different rod I would concievably land some

Even though I am fiscally consistantly pitiable
And considerably less brad pitt than brad pitiful
And I'm really so poor and ugly that you reckon only you could possibly love me
And I
(Really think that I would)
Probably
(Have somebody else)
Oh yeah

Visual.

(If I didn't have you)
(Someone else would surely do)

Look, I'm not undervaluing what we've got when I say
That given the role chaos inevitably plays in the inherently flawed notion of fate,
It's obstruse to deduse that I've found my soulmate at the age of 17
It's just mathematically unlikely that at a university in perth
I happened to stumble on the one girl on earth specifically designed for me

And if I may conjecture a further objection love is nothing to do with destined perfection
The connection is strengthened the affection simply grows over time
Like a flower
Or a mushroom
Or a guinea pig
Or a vine
Or a sponge
Or bigotry

... or a banana (banana)

And love is made more powerful by the ongoing drama of shared experience and synergy
And symbiotic empathy or something like that...

So I trust it would go without saying
That I would feel really very sad if tomorrow you were to fall off something high
Or catch something bad

But I'm just saying
I don't think you're special
I mean... I think your special
But
You fall within a bell curve

I mean, I'm just saying I
(Think that I would)
Probably
(Have somebody else)

I think you are unique and beautiful
You make me happy just by being around
(Being around)
But objectively you would have to agree that baby when I found you
Options are relatively thin on the ground
(Thin on the ground)
Your lovely but there must be girls as lovely as you
Or maybe more open to spanking or scrabble...
I'm just saying

(That I think that I would)
Probably
(Have somebody else)
I mean I reckon it's pretty likely that if for example
My first girlfriend jackie hadn't dumped me
After I kissed winstons ex girlfriend neah at stephs party back in 1993

And our variables would probably have been altered by the absence of that event
To have meant the advent of a tangential narrative and which we don't meet.

Which is to say there exists a theoretical hypothetical parallel life
Where what is is not as it is and I am not your husband and you are not my wife

And I am a stuntman living in LA
Married to a small blonde portugese skier
Who when she's not training
Does abstract painting
Practises yoga
And brews her own beer
And really like making home movies
And suffers neck down alopecia

But with all my heart and all my mind I know one thing is true
I have just one life and just one love and love that love is you
And if it wasn't for you
Baby you
(I really think that I would)
(Have somebody else)
Oh yeah
(If I didn't have you)
If I didn't have you someone else would do
(Someone else would surely do)Youtube video

Kooky Poem Refs

I actually realised that the nerdy poem is similar to the Vogon poem at the start of the Hitch Hikers Guide to the Galaxy and also to one of the songs from Flight of the Concords, Part Time Model.

Alternative statistics definitions

Term	Her Definition
Regression to the mean	showing your true nasty side after the first few months of our relationship
marginalisation	not talking to me on the drive back after saying you were a chubby child at your friends dinner party
integration	making your friends laugh by saying that you were a chubby child at their dinner party
infinity	how long it felt you didn't talk to me after saying you were a chubby child at your friends dinner party
confidence interval	that brief period in a relationship when you think that it going to work out
data	what you think is someone who goes on a lot of dates
singularity	the exact moment of being dumped (LAST)
outlier	being made to sleep on the couch (after saying you were a chubby child at your friend dinner party)
	owning up to how many pints I actually had down the pub
standard deviation	an acceptable amount of bed room experimentation
normal	not me- you think we've grown apart. You want to break-up…

A Statistician's Love Poem

Oh my dearest one, you are truley an outlier!
Your beauty falls outside of the 95% confidence interval,
such that you are significantly different from an average looking girl.
My perception of your good looks is not down to just random noise,
if you were to wear different clothes or wear less make up I would still think the same,
accounting for the measurement error due to me wearing glasses I would still maintain this conclusion.
Oh truely I reject the null hypothesis.
The posterior distribution of your beauty on fixed support is negatively skewed,
such that your median beauty is greater than your mean beauty.
Given 100 other girls I would probably choose you at least 95 times.
In conclusion, I think you're fit.