Sunday, 28 August 2016

Quibans 36: School exclusions for assault

This is a lightly rewritten article from the Cambridge News website:

Primary school exclusions on the rise for 'violent behaviour'
More primary school pupils in Cambridgeshire are being excluded from school for violent behaviour, it has emerged.  The figures are especially pronounced amongst primary school pupils, with exclusions for violent behaviour towards adults and other pupils rising.
A spokesman for Cambridgeshire County Council said: “Schools are usually very safe places for pupils and serious incidents of violence against pupils or staff are rare.”
The spokesman said that, while the number of exclusions for violent behaviour had gone up, this may be down to […].
Pupil assaults on an adult
2011/12:  118 primary and 65 secondary
2012/13:  146 primary and 49 secondary
2013/14:  189 primary and 72 secondary
2014/15:  201 primary and 76 secondary
2015/16:  319 primary and 66 secondary
Attacks on other pupils
2011/12:  64 primary and 319 secondary
2012/13:  104 primary and 271 secondary
2013/14:  127 primary and 273 secondary
2014/15:  110 primary and 242 secondary
2015/16:  162 primary and 276 secondary

Possible ways to use this:
First of all, are the claims in the article reasonable ones?
1)  Are “exclusions on the rise”?
2)  Are “serious incidents of violence against pupils or staff rare”?
3)  What else do the figures tell us?
4)  What is wrong with the line: “Pupil assaults on an adult”?
5)  What reasons might the spokesman have given for the rise in exclusions?

Possible ways to approach these questions:
1)  The first of these could be explored by drawing a graph.  What sort of graph might be useful?
Here is the data (in Excel):

And here are some of the graphs I got Excel to draw.  It would be good to ask students to comment on the usefulness of each method of data presentation.

Here are my thoughts about each one:
Line graph:
This is clear.  It shows how the data changes over time.  The lines are not particularly relevant (halfway along a line has no meaning) but this helps our eye to see the pattern.

Stacked column:
These are often used in the media but I think they are unhelpful because the only one it is easy to compare over time is the lowest one.  Is the top part of each bar getting bigger or not?  It is difficult to tell!

3D pie chart:
Only shows the data for one aspect (the number of primary assaults on an adult (so we would need three other graphs).  It shows how the proportion of assaults has changed over the years, but takes the whole pie as being worth all of the assaults on adults over those five years.  The 3D nature of the graph is not helpful …

Clustered column:
This shows all of the data clearly.  If you join up the top of each bar of the same colour you roughly get the line graph.  You can see clearly which ones are going up and which are going down, how much they are doing so and also the relative proportion of assaults in the two age-groups.

Very similar to the line graph (the x-axis wouldn’t behave as I wanted it to!) but without the lines to guide the eye.

100% stacked column:
Like the pie chart, this shows proportion rather than numbers but in a less useful way than the pie chart.  It doesn’t help us to see whether the number of assaults has changed, just how they are distributed.

Those graphs that are useful do seem to show an increase.  (This could be expanded on further.)

2)  To know whether assaults are rare we probably need to know how many school-children there are in Cambridgeshire.  This is ripe for Fermi estimation!  I will assume that the population of the UK is about 70 million and that there are about 50 counties.  Cambridge is clearly not as big as London and other large cities, so I guess that Cambridgeshire has about 1% of the population of the country as a whole.  There are more younger people than older people, so I will estimate that about a fifth of the population are of school age.  70 million x 1% divided by 5 = 140,000 pupils.  (Google suggests the actual number is close to 80,000 pupils, which puts my estimate in the right order of magnitude.  There are likely to be lots of other ways to estimate this.)
There were 823 exclusions for assault in total in the most recent year.  Comparing this to 80,000 pupils who should be attending school for 190 days each year and we get 54 assaults per million school days.  This seems rare to me.

3)  The data also shows us that there are more primary assaults on teachers, whereas at secondary school they are more likely to be on other pupils.

4)  We don’t know how many assaults actually take place because the figures given are for the number of exclusions from school for assault.  Less serious assaults may not be punished in this way, different schools might respond differently, etc.

5)  Here are the full reasons given by the spokesman:
The spokesman said that, while the number of exclusions for violent behaviour had gone up, this may be down to an increase in the number of pupils attending schools, meaning the proportion of exclusions was actually going down.  He added: "Primary schools appear to have reported increases in incidents and this is a matter of concern. However, this may be as a result of better recording of incidents, a change in pupil behaviour, an increase in pupil numbers or a change in teaching practices and expectations."


Quibans 85: Crime and Police figures

From the Cambridge News: Violent crime in Cambridge has nearly doubled in a decade as police numbers drop 9 APR 2018 Bottom of For...