Public ignorance of the laws of evidence and of statistics can hardly
be exaggerated. There may be a doctor here and there who in dealing
with the statistics of disease has taken at least the first step towards
sanity by grasping the fact that as an attack of even the commonest
disease is an exceptional event, apparently over-whelming statistical
evidence in favor of any prophylactic can be produced by persuading the
public that everybody caught the disease formerly. Thus if a disease is
one which normally attacks fifteen per cent of the population, and if
the effect of a prophylactic is actually to increase the proportion to
twenty per cent, the publication of this figure of twenty per cent will
convince the public that the prophylactic has reduced the percentage by
eighty per cent instead of increasing it by five, because the public,
left to itself and to the old gentlemen who are always ready to
remember, on every possible subject, that things used to be much worse
than they are now (such old gentlemen greatly outnumber the laudatores
tempori acti), will assume that the former percentage was about 100. The
vogue of the Pasteur treatment of hydrophobia, for instance, was due
to the assumption by the public that every person bitten by a rabid dog
necessarily got hydrophobia. I myself heard hydrophobia discussed in
my youth by doctors in Dublin before a Pasteur Institute existed,
the subject having been brought forward there by the scepticism of an
eminent surgeon as to whether hydrophobia is really a specific disease
or only ordinary tetanus induced (as tetanus was then supposed to be
induced) by a lacerated wound. There were no statistics available as to
the proportion of dog bites that ended in hydrophobia; but nobody ever
guessed that the cases could be more than two or three per cent of the
bites. On me, therefore, the results published by the Pasteur Institute
produced no such effect as they did on the ordinary man who thinks that
the bite of a mad dog means certain hydrophobia. It seemed to me that
the proportion of deaths among the cases treated at the Institute was
rather higher, if anything, than might have been expected had there been
no Institute in existence. But to the public every Pasteur patient
who did not die was miraculously saved from an agonizing death by the
beneficent white magic of that most trusty of all wizards, the man of
science.
Even trained statisticians often fail to appreciate the extent to
which statistics are vitiated by the unrecorded assumptions of their
interpreters. Their attention is too much occupied with the cruder
tricks of those who make a corrupt use of statistics for advertizing
purposes. There is, for example, the percentage dodge. In some hamlet,
barely large enough to have a name, two people are attacked during a
smallpox epidemic. One dies: the other recovers. One has vaccination
marks: the other has none. Immediately either the vaccinists or the
antivaccinists publish the triumphant news that at such and such a place
not a single vaccinated person died of smallpox whilst 100 per cent of
the unvaccinated perished miserably; or, as the case may be, that 100
per cent of the unvaccinated recovered whilst the vaccinated succumbed
to the last man. Or, to take another common instance, comparisons
which are really comparisons between two social classes with different
standards of nutrition and education are palmed off as comparisons
between the results of a certain medical treatment and its neglect. Thus
it is easy to prove that the wearing of tall hats and the carrying of
umbrellas enlarges the chest, prolongs life, and confers comparative
immunity from disease; for the statistics show that the classes which
use these articles are bigger, healthier, and live longer than the class
which never dreams of possessing such things. It does not take much
perspicacity to see that what really makes this difference is not the
tall hat and the umbrella, but the wealth and nourishment of which they
are evidence, and that a gold watch or membership of a club in Pall Mall
might be proved in the same way to have the like sovereign virtues. A
university degree, a daily bath, the owning of thirty pairs of trousers,
a knowledge of Wagner's music, a pew in church, anything, in short, that
implies more means and better nurture than the mass of laborers enjoy,
can be statistically palmed off as a magic-spell conferring all sorts of
privileges.
In the case of a prophylactic enforced by law, this illusion is
intensified grotesquely, because only vagrants can evade it. Now
vagrants have little power of resisting any disease: their death rate
and their case-mortality rate is always high relatively to that of
respectable folk. Nothing is easier, therefore, than to prove that
compliance with any public regulation produces the most gratifying
results. It would be equally easy even if the regulation actually raised
the death-rate, provided it did not raise it sufficiently to make the
average householder, who cannot evade regulations, die as early as the
average vagrant who can.