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A
contribution from senior Eynsham
resident and
Emeritus Professor DT Elmore, to help
us avoid
being duped by dodgy statistics -
whether the topic is GCSE results
or police crime figures. Taking a
hypothetical example, he explains
the issues in "simple terms involving
nothing more difficult than
primary school arithmetic". Get your
grandson to explain it to you
sometime!
GOOD NEWS: Eynsham
Online user statistics
A considerable proportion of the public suspect politicians and others with executive or influential powers of trying metaphorically to pull the wool over our eyes using statistics. In fact, a popular feeling is summarised in the statement: "There are lies, damned lies and statistics", an order that is supposed to reflect increasing deviousness and mendacity. This conclusion is effected by ignoring one or more basic tenets of statistical theory and practice.
The following example shows how one can bury unfavourable statistics in a larger volume of favourable statistics in order to deceive the receptive public into believing that all is well. The example uses only a small example of data so that the arithmetic is sufficiently simple to be done without the aid of calculators or computers. An imaginary village or town is divided into 30 districts. To each district is attached a score in the range 0-10 where higher scores relate to districts having an unacceptable level of antisocial behaviour and/or vandalism. A hypothetical but illustrative result is given in the following table.
|
No.of districts |
Score |
|
||
|
|
8 |
8 X 0 |
= |
0 |
|
|
12 |
12 X 1 |
= |
12 |
|
|
8 |
8 X 2 |
= |
16 |
|
|
1 |
1 X 8 |
= |
8 |
|
|
1 |
1 X 9 |
= |
9 |
|
Sum = |
30 |
Sum |
= |
45 |
The average score for the village or town is therefore 1.5, apparently a very satisfactory result, but the residents of the last two areas would probably not agree. The average for these two areas is 8.5. The above treatment of the statistical data data disobeys a fundamental law of statistics. When taking the average of a collection (or population using statistical terminology) of data, all the contributory data should fall on a single peak and the width of the peak in normally distributed data can be calculated (standard deviation or standard error). Note that the average value for the first 28 districts is 1.0 quite different from the average for the last two districts. This example illustrates how simple it is to bury or disguise unfavourable data by using the statistically illegal technique of lumping together data from different populations. Another example could be illustrated by measuring the height of all the inhabitants of a village including neonates and members of the local rugby XV. The result would probably come out at around 3 ft, a result consistent with a race of pigmies. Again, the stupid result is due to combining the results of groups of data possessing quite different averages.
To conclude, be wary of a presentation of statistics that hides disparate groups in a larger group which aims to present a particular viewpoint that is statistically invalid. This is not the only method of misusing statistics in order to delude the uninitiated, but it is probably the most prevalent technique.
EYNSHAM
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