How big a sample? Follow up.

The results of my sample (blog of October 25 2010) came back this week, and they show no trace of cancer. Thank God!

However, in these days of customised lettters, it was sad to see that the NHS could not use their data in a friendly way. Part of the letter applied to follow-up tests, which happen every two years between the age of 60 and 75 (don't ask how "every two years" fits into a fifteen year period) and then are optional. It is not too difficult to customise the letter to say either "We will invite you to a test in two years time" or "You have reached the age when testing becomes optional".

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?

Football Statistics

I confess that I do not follow fotball particularly closely, but a column in the Independent on Saturday 15th August caught my eye. It was headed "The Statistics" and below were two bar charts that showed: (1) Points won by champions; (2) Points required to stay up. The two recorded time series are for the last 17 seasons.

I have just run regressions on these (sad, but there seemed to be a time trend) and discovered that the number of points needed to stay up is getting smaller at a statistically significant rate. Now this is curious, as there would seem to be no real reason for such a trend. It cannot continue for ever. But, of course, there is a simple trap that the data led into. The reason that there appeared to be a time trend was that the first three years were all high, and of course, they influenced the regression line. Remove those three outliers and then there is no trend. A caveat for the careless analyst.

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?"

Displaying data provocatively

For many years, I have been interested in the potential for using O.R. in developing countries. By a process of serendipity, I have just discovered Gapminder, where data about the world's nations are shown in original and challenging ways. I wish that I had discovered the site before now!