False precision is incurred when exact numbers are used for inexact notions. When straightforward statements about experience are decked out in numbers well beyond the accuracy of possible measurement, the precision is false and can mislead an audience into supposing that the information is more detailed than is really the case.
People say the Scots are mean, but they have been shown in surveys be 63 percent more generous than the Welsh.
(What measurement of generosity allows for that kind of a figure to be put on it?)
Both mathematics and science make widespread use of numbers, and both have prestige as sources of authority. The extension of exact numbers into areas quite inappropriate to them is often little more than the attempt to invest certain statements with the aura and prestige attaching to mathematics and science.
The fallacy derives from the use of unjustified material, and from the attempt to impart more confidence in the assertions than the evidence for them actually merits.
Our mouthwash is twice as good, yes two times as good, as its lea competitor.
(On what instrument, do you suppose, can one read off the quality of a mouthwash; and in what units?)
There are several versions of this fallacy, all of which have it in common that the numbers used give a misleading impression of the confidence one can place in the claim.
Four out of five people can’t tell margarine from butter.
(It may be true, but how is it established? If large numbers on a one-against-one test repeatedly fail to distinguish them, we might be impressed. If smaller numbers fail to pick out the one margarine sample from a plateful of crackers covered with different types of butter, we might be rather less impressed.)
Yet another version might talk about quantity, where quality was a highly important factor.
Kills 99 per cent of all household germs.
(A worthy claim, unless the rest happen to be typhoid.)
False precision is as necessary to the continued happiness of many academics as are public money and whisky. Whole departments float upon it, just as some do on the other two ingredients. Those who are engaged in the study of human beings, for example, find few measuring rods scattered about. Because the real qualities of people cannot be measured, indices are constructed which can be measured, and then the indices are passed off as the real thing.
Birmingham children are more racist than their London counterpart study of essays written by 10-year-olds showed that the London group used 15 percent less racial epithets than their peer group in Birmingham.
(The assumptions here are manifold. Maybe one can identify and agree upon what constitutes a racial epithet. Maybe their appearance in essays reflects their importance in the lives of children. Maybe the use of them by children is evidence of racism. Maybe the cultural differences between Birmingham and London are not important etc., etc. None of these doubts qualify the opening line.)
Macroeconomists happily report that growth-rates were only 1.4 percent, instead of the predicted 1.7 percent, without telling us that some measurements of GDP cannot be taken within 5 percent accuracy. Some figures for growth of GDP could be out by up to 10 percent.
Psychologists measure the ability of children to solve set problems and call their answers intelligence. Social scientists measure how people respond to questions and describe the answers as a measurement of attitudes. False precision is like a hastily erected and flimsy bridge to carry our knowledge over from reality into the world of our desire. The load is more than it will bear.
Always use the fallacy when you need more authority for your claims. Behind the figures you quote, your audience will conjure up an army of white-coated scientists with horn-rimmed spectacles, and dedicated doctors with stethoscopes draped in careless urgency. The invisible army will nod sagely in support of each precise statement you make, and if the audience might have doubted you they will be reassured by the phantom legions who underwrite your figures.
Whatever the academic merits, single-stream schooling certainly produces more balanced children. Surveys have revealed 43 percent fewer psychological abnormalities among groups which…
(Just don’t tell them that the abnormalities included self-esteem, competitiveness and the desire to learn.)
Remember to be exact, especially when you are being vague.
We can be 90 percent certain that Bloggs is the guilty man.
(And 100 percent certain that you cannot prove it.)