The best statistic I have heard for a long time

BBC Radio 4 has a flagship news and current affairs programme every weekday morning called "Today". Following one interviewer's comment, the presenter commented "The best statistic I have heard for a long time". He then paused and added words to the effect that the statistic was not good news, but had been presented in a clear way so that the meaning was easy to understand. It strikes me that those of us who work with mathematical models could learn from this example.

The interview had been about the social deprivation of parts of the east of London, and the comment was made: "for every tube stop on the Jubilee line [on London Underground] going east, from Westminster to Canning Town, life expectancy decreases by one year". It is not good news. But the information is conveyed in a way that is clear, simple and easy to assimilate. It is not cause and effect. Underground stations do not affect life expectancy. But one has a clear sense that the further you travel along the line, the more social deprivation, leading to lowered life expectancy, you will encounter. And the figure of "one year" is probably a rounded version of the data ... but for the purposes of this graphical illustration, it is precise enough. Someone has found a way to present information, which is of use to planners, in a way that is easy to take in. So we can learn from the example.

But, as usual, the story above is only part of the story. The statistic has been created by using limited information and extending it. The data which had been used said that the life expectancy for residents near Westminster station was seven years more than that for people living near Canning Town. They are eight stations apart. Nobody has written abot the life expectancy at those intermediate stations. All that has been done is to draw a straight line between the two extremes and assume linearity. Even though the method is not rigorous, it is still graphic. How can we learn to strike a balance between rigour and clarity?

How not to display data

In an earlier blog, I quoted one of my email signatures which uses the following quotation:
In the information age, somebody has to specialize in the development and presentation of really useful information. Doing that for management and decision-making applications is the core role of Operational Research scientists. (Randy Robinson, the first executive director of INFORMS)

Ever since I read the books "The Use and Abuse of Statistics" and "How to Lie with Statistics" I have been alert to examples of poor communication of data. Today's example comes, I am afraid, from my own university (Exeter).

Here is a map showing the modes of transport used by a sample of employees of the university. I am not sure whether to point the finger at the university or Devon County Council. So what's wrong? A few thoughts to start with.

1) The map covers far too great an area; there should be enlargements around Exeter.
2) The symbols are horrible. A black parenthesis on top of a coloured exclamation mark.
3) When you magnify the map to see the detail (and in most cases, to see the colour) then the symbols are lost.
4) What is the point? Is it to inform?

Let's be positive: could the information be presented in a different way? Suppose that we separated the modes of transport to see where the walkers come from. And those who use public transport? And those who car share? And those who travel less than 2 miles by car? The maps for many of these could be on a large scale. Then we might apply some contours of equal travelling time. But we still haven't answered the question "what is the point?"

Innumeracy!

For those of us involved with O.R., numeracy is practically second nature. Most O.R. people have above average number skills, however you measure them. So it is sometimes salutary, and even shocking to realise that others are numerically illiterate, even though they may be otherwise well-educated.

Two stories from my experience this week illustrate this:
(1) (and this is horrifying) A radio interview with a debt-counselling service in my home city of Exeter. The speaker described how a door-to-door salesman offered a loan "with 100% interest", which the borrower thought was a very good deal.
(2) My national newspaper headlined a column chart showing the "U.K. Government borrowing" for this year and the previous two. Each column was below the axis, and the amount was clearly marked as being negative, becoming increasingly negative as time progressed. Obviously nobody had realised that borrowing a negative amount meant the opposite of what was intended.

Those of us involved in education can take these as reminders that when we have numerical results to communicate, we need to explain them as clearly as possible.

To end on a lighter note, on the same theme. Another newspaper story concerned with the current credit crunch had obviously been hastily sent through a spell-checker. There were two references to £100bun loans.