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!!!