ARE STATISTICIANS LIARS ?
By MARGARET KNIGHT
T IARS, as we have all heard, are of three grades: liars, 14 damned liars, and statisticians—a gross libel on a harm- less and necessary class.
Undoubtedly, a number of most ingenious and plausible falsehoods can be based on statistics, but this feat is seldom performed by statisticians, who, for the most part, are precise and prudent men, who put forward their results for what they are worth without attempting to draw unjustified inferences. The real perverters of truth are those who come later, and try to use the statistician's results as grind- stones for their own particular axes—in other words, those who approach statistical data, not with the question " What do these figures indicate?" but with the question " Can I get anything out of these figures to support my view?" Figures, unfortunately, by careful selection and " interpret- ing," can be made to appear to support almost any view, and it is this fact that has been so unfortunate for the statistician's reputation.
But, of course, misrepresentations of statistics are not always deliberate: often they are simply mistakes. Statis- tics tell us of the existence of a correlation, or a difference, but in themselves they tell us nothing about its cause. One of the commonest sources of misinterpretation lies in mis- taking the direction of a causal relationship, or in assuming it to be direct and simple when in fact it is indirect and complex. We are liable, in fact, to commit essentially the same mistakes as the child who, seeing the tree-tops lashing in a gale, thinks that the wind is caused by their movement.
A good example of the causal-relation-the-wrong-way- round type of fallacy is provided by figures published many years ago of the average age at death of total abstainers, and of moderate and heavy drinkers. The figures were— abstainers 5i, moderate drinkers 63, heavy drinkers 57. These figures were obviously a godsend to distillers and publicans, who broadcast them widely. But the suggested Implication that total abstinence is more harmful to health than heavy drinking is a complete fallacy. At the time of the inquiry (things may be different now) total abstinence was much more common among younger than among older men. In other words, abstainers as a group were younger than non-abstainers—so, naturally, such deaths as occurred among them would tend to occur at an earlier age. Similarly, the average age at death of curates is much lower than that of bishops, but no conclusions can be drawn about the relative healthiness of these two ecclesiastical offices.
Rather more subtle is the fallacy that modern man must be becoming more susceptible to cancer, since the death-rate from that disease is increasing. Only the factual part of this statement can be ascribed to the statistician. The death- rate from cancer is undoubtedly increasing. But this does not necessarily mean that we are becoming more susceptible to cancer; it may only mean that other causes of death have been reduced. Diseases like smallpox, typhoid and diph- theria no longer kill their thousands every year—with the result that (since everyone must eventually die of something) many who would formerly have died from these diseases are now dying of cancer.
The collection of fallacies of this kind can become a minor obsession. There is a particularly fine specimen in a book called Wasted Womanhood, by Charlotte Cowdroy—a pioneer of the Kiiche, Kirche, Kinder school. On p. 505 she says: " Social workers have been very astounded to find that, in spite of the cleanliness and amenities of maternity homes and the skilled medical and nursing attention the patients receive, the death-rate is higher in these institutions than in the mothers' own homes, though these be unhygienic and unsatisfactory. Statistics bring home to us incontrovert- ibly that there is something intangible in the home, some- thing that affects the spirit of the sick woman for good and transcends the material shortcomings of her surroundings."
This is an up-to-date form of the argument that there is no more dangerous place than bed, since so many people die there. The statement about the higher death-rate in hospitals (I am not in a position to verify it) is almost certainly correct. But it would be surprising if it were not, in view of the fact that usually the only maternity cases admitted to the free hospitals are difficult cases and first births.
A still better example of the same kind is given by Sir Arthur Newsholme in Vital Statistics. Many years ago, in a hospital in Dublin, it was found that a higher mortality prevailed among patients in the wards on the ground floor than among those in the wards above. The greater unhealthiness of the ground floor was therefore in- ferred, and gravely commented on, in the Report of the Medical Officer of the Privy Council. It was subsequently discovered that the porter of the hospital s as in the habit of placing patients who could not walk on the ground floor, and those who could walk on the floors above.
These, however, are genuine mistakes—possibly less dangerous than the misconceptions that can be produced by deliberate " dressing." I have coined the word " dressing " to denote a common practice for which a name is badly needed. To dress results is less drastic than to cook them. Cooking usually implies actual falsification. " To dress " might perhaps be defined as " without actually cooking results, to express them in such a way as to convey a sug- gestio falsi." In this enterprise, there is no more useful aid than the percentage. Whenever a statement is made about a total, or an increase, or a decrease, or a difference of x per cent., without the base on which the percentage was calcu- lated being given, there is prima facie a suspicion of " dressing." The deepest suspicion should be aroused by statements like " 15 per cent. of the national expenditure went on education before the war—now it's only 9 per cent." Obviously, the significance of this statement depends entirely on whether national expenditure has increased, and by how much.
An important function of percentages in " dressing " is to conceal the smallness of the base. When an " efficiency expert " tells us that his system of training typists reduced errors by so per cent., he may have trained several hundred typists, and carefully investigated the errors they made in typing material of exactly similar difficulty before and after training. Or he may, on the other hand, have trained his own typist, given her a letter to type before and after train- ing, and found that she made two errors in the first letter and only one in the second.
This is an imaginary and rather preposterous example, but here is a genuine one of the same kind. In the contro- versy about paying women civil servants on the same scale as men (which produced a Government defeat in the Commons in 1936) one of the arguments used by opponents of the measure was that, while women's salaries were never more than 18 per cent. lower than men's, their sickness rates were no less than 5o per cent. higher. This sounds impressive—until one looks at the actual figures and realises that men average approximately 3 days' sickness absence a year, and women 41-. The difference between women's salaries and men's for the same work starts at is, and in the higher grades is as much as £175 a year—so on this argument the women's extra day and a half of sickness costs them £3 to £116 a day!
But of all principles employed by the " dresser," the most useful is this. If you want to magnify some figure, express it as a percentage of something small: if you want to mini- mise it, express it as a percentage of something large. In a debate I once attended on the sterilisation of mental defec- tives, this device enabled the same figures to be quoted in support of their case by both sides. Both proposer and opposer appeared to agree that there were about 400,000 Mental defectives in the country, and that sterilisation would approximately halve their number in so years. The accuracy of this contention does not, for the moment, matter : what is interesting is the way in which the point was put by the different sides. The proposer said: " The number of mental defectives in this country is 400,00o—equal to about 25 per cent. of the whole population of Wales. Sterilisation would approximately halve their number in 5o years." The opposer said: " Today, mental defectives constitute barely I per cent. of the population. Even to reduce their number to .5 per cent. would take 5o years."
The plain man, in spite of his expressed views on statis- ticians, is apt to be curiously hypnotised by percentages. As I once heard it said, " If you announced that you'd got a new method of determining sex before birth, which was already quite 5o per cent. effective, a lot of people would say ' How wonderful!' " Would it not be a good thing if the courses in civics now included in the curricula of many schools were to include lessons on the principles and pitfalls of statistics?
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