4 
The Fatidamental Problem of Practical Statistics 
apt to lead to different conclusions from the plausible one which we have reached 
by accident." 
Edgeworth takes the bull by the horns and broadly speaking asserts that later 
experience has shown us that in innumerable cases where we were a priori ignorant 
the chances of given events really did not cluster. " We take our stand upon the 
fact that probability-constants occurring in nature present every variety of fractional 
value ; and that natural constants in general are found to show no preference for 
one number rather than another. Acting on which supposition, while in particular 
cases we shall err, in the long run we shall find our account" (p. 231). 
In other words Edgeworth returns to the appeal to experience from which Bayes 
and Laplace ought to have started. He asserts that in our ignorance we must 
appeal to our knowledge of kindred experience, and that statistical constants do not 
cluster in such experience. " I submit," he writes, " the assumption that any 
probability-constant about which we know nothing in particular is as likely to have 
one value as another is grounded upon the rough but solid experience that such 
constants do as a matter of fact, as often have one value as another" (p. 230). 
Unfortunately he does not give us any numerical data — except a few isolated 
illustrations — to prove that the universe of statistical ratios exhibits a rectangular 
frequency curve. Some captious critics might assert a conviction that their experience 
showed that chances ranged themselves like the horns of the bull, and that absolute 
non-occurrence and persistent occurrence were in the world at large the most 
emphasised probabilities. Our professor impaled thus upon the horns of the bull 
he has ventured to seize might leave the doctrine of inverse probabilities in a worse 
plight than he found it ! — His practical safety depends on the extreme difficulty of 
testing by actual numerical experience the " fact " that natural constants in general 
show no preference for one number rather than another. At the best we may 
" feel " it is so, rather than hope to demonstrate it by forming a random sample 
which would cover the inmiensely wide fields of natural frequencies. 
It has occurred to me, however, that possibly the bull itself is a chimera, and 
there may be no need whatever to master it. In short, is it not possible that 
any continuous distribution of a 2)rio7'i chances would lead us equally well to the 
Bayes-Laplace result ^ If this be so, then the main line of attack of its critics 
foils. If they then continue their assault on the ground that there are cases in 
which the repetitions of events are not independent, it is conceivable, that we 
who defend inverse probabilities as not only the basis of modern statistical theory, 
but also as the arithmological justification for the most ordinary actions and beliefs 
of the practical man can again counter our adversaries. 
(3) Let us examine the problem on the lines of Bayes' original investigation into 
a priori chances. We may reduce that investigation to its simplest terms as 
follows: A line of length a is taken and a stroke made on it at random, and its 
position at distance x from one end is unknown. Afterwards n strokes are made 
at random on the line, and p fall in the segment 0 to x and q = n—p in the 
segment x to a. The former are looked upon as "successes," the latter as "failures." 
