Now let us suppose that in the early nineteenth century somebody had come forward with a theory that typhus fever always begins in the top joint of the little finger; and that if this joint be amputated immediately after birth, typhus fever will disappear.  Had such a suggestion been adopted, the theory would have been triumphantly confirmed; for as a matter of fact, typhus fever has disappeared.  On the other hand cancer and madness have increased (statistically) to an appalling extent.  The opponents of the little finger theory would therefore be pretty sure to allege that the amputations were spreading cancer and lunacy.  The vaccination controversy is full of such contentions.  So is the controversy as to the docking of horses’ tails and the cropping of dogs’ ears.  So is the less widely known controversy as to circumcision and the declaring certain kinds of flesh unclean by the Jews.  To advertize any remedy or operation, you have only to pick out all the most reassuring advances made by civilization, and boldly present the two in the relation of cause and effect:  the public will swallow the fallacy without a wry face.  It has no idea of the need for what is called a control experiment.  In Shakespear’s time and for long after it, mummy was a favorite medicament.  You took a pinch of the dust of a dead Egyptian in a pint of the hottest water you could bear to drink; and it did you a great deal of good.  This, you thought, proved what a sovereign healer mummy was.  But if you had tried the control experiment of taking the hot water without the mummy, you might have found the effect exactly the same, and that any hot drink would have done as well.

BIOMETRIKA

Another difficulty about statistics is the technical difficulty of calculation.  Before you can even make a mistake in drawing your conclusion from the correlations established by your statistics you must ascertain the correlations.  When I turn over the pages of Biometrika, a quarterly journal in which is recorded the work done in the field of biological statistics by Professor Karl Pearson and his colleagues, I am out of my depth at the first line, because mathematics are to me only a concept:  I never used a logarithm in my life, and could not undertake to extract the square root of four without misgiving.  I am therefore unable to deny that the statistical ascertainment of the correlations between one thing and another must be a very complicated and difficult technical business, not to be tackled successfully except by high mathematicians; and I cannot resist Professor Karl Pearson’s immense contempt for, and indignant sense of grave social danger in, the unskilled guesses of the ordinary sociologist.

Now the man in the street knows nothing of Biometrika:  all he knows is that “you can prove anything by figures,” though he forgets this the moment figures are used to prove anything he wants to believe.  If he did take in Biometrika he would probably become abjectly credulous as to all the conclusions drawn in it from the correlations so learnedly worked out; though the mathematician whose correlations would fill a Newton with admiration may, in collecting and accepting data and drawing conclusions from them, fall into quite crude errors by just such popular oversights as I have been describing.