Exploring data: graphs and numerical summaries

# 2.4 Runners

The next data set relates to 22 of the competitors in an annual championship run, the Tyneside Great North Run. Blood samples were taken from eleven runners before and after the run, and also from another eleven runners who collapsed near the end of the race. The measurements are plasma β endorphin concentrations in pmol/litre. The letter β is the Greek lower-case letter beta, pronounced ‘beeta’. Unless you have had medical training you are unlikely to know precisely what constitutes a plasma β endorphin concentration, much less what the units of measurement mean. This is a common experience even among expert statisticians working with data from specialist experiments, and can usually be dealt with. What matters is that some physical attribute can be measured, and the measurement value is important to the experimenter. The statistician is prepared to accept that running may have an effect upon the blood, and will ask for clarification of medical questions as and when the need arises. The data are given in Table 4.

## Table 4 Blood plasma β endorphin concentration (pmol/l)

Normal runner before race | Same runner after race | Collapsed runner after race
--- | --- | ---
4.3 | 29.6 | 66
4.6 | 25.1 | 72
5.2 | 15.5 | 79
5.2 | 29.6 | 84
6.6 | 24.1 | 102
7.2 | 37.8 | 110
8.4 | 20.2 | 123
9.0 | 21.9 | 144
10.4 | 14.2 | 162
14.0 | 34.6 | 169
17.8 | 46.2 | 414

(Dale, G., Fleetwood, J.A., Weddell, A., Ellis, R.D. and Sainsbury, J.R.C. (1987) Beta-endorphin: a factor in ‘fun run’ collapse? British Medical Journal 294, 1004.)

You can see immediately that there is a difference in β endorphin concentration before and after the race, and you do not need to be a statistician to see that collapsed runners have very high β endorphin concentrations compared with those who finished the race. But what is the relationship between initial and final β endorphin concentrations? What is a typical finishing concentration? What is a typical concentration for a collapsed runner? How do the sets of data values compare in terms of how widely they are dispersed around a typical value?

The table raises other questions. The eleven normal runners (in the first two columns) have been sorted according to increasing pre-race endorphin levels. This may or may not help make any differences in the post-race levels more immediately evident. Is this kind of initial sorting necessary, or even common, in statistical practice? The data on the collapsed runners have also been sorted. The neat table design relies in part on the fact that there were eleven collapsed runners measured, just as there were eleven finishers, but the two groups are independent of each other. There does not seem to be any particularly obvious reason why the numbers in the two groups should not have been different. Is it necessary to the statistical design of this experiment that the numbers should have been the same?

OpenLearn - Exploring data: graphs and numerical summaries
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