Karl Pearson 
261 
question : What is the probability that my theory describes adequately my facts 1 
Meanwhile the statistician who examines the physicist's diagrams has often been 
forced to smile by the degree of discordance which the physicist has allowed to 
pass as if some graph could demonstrate adequately the harmony of physical law 
and experiment. I look forward to the time when no physical paper will be 
considered complete unless it provides at the end of each series of experiments the 
value of P, i.e. the measure of the goodness of fit of observations recorded to 
theory adopted. There will be no excuse, there really is no excuse, now that 
tables are provided, for its omission. It is always possible in the course of an 
hour or so's arithmetic to measure the accordance between supposed law and 
recorded observation. 
One of the important steps in the work given is undoubtedly the measurement 
by means of the correlation ratio of the mean square error of the physicist's 
determinations. I think that is undoubtedly the best way of finding it. The 
physicist is apt to use "mean errors'' instead of mean square errors. He does not 
recognise that the probable error of a mean error is sensibly greater than that 
of a mean square error. But he may wish in the present case to have some test 
of the accuracy of the determination of ct„, the standard deviation of an array, 
from other processes. One which it appears to me ought to be satisfactory is the 
following: Let the observations of A for a given value of B be taken in pairs, 
and let all these pairs of A values be formed and their differences x^ — x.^ be taken 
in each case, x-^ being greater than x,, then the following relation should hold if 
the distribution of errors be Gaussian : 
2 Mean (ic^ — x^'^ — (Mean (x-^ — ifg))^ 
^ -72676 ■ 
For Professor Duffield's i-ampere curve this gives 
a„2 = -2444 against a J (1 - t;^) = -0977, 
and for his 2-ampere curve 
= -1987 against a J (1 - rj^) = -2274. 
The latter, considering that we deal only with 13 pairs, is fairly accordant ; the 
agreement in the case of the former is very poor, but in this case there are only 
six pairs. I have purposely introduced this case, because no real verification of 
the 7] method could be obtained on the basis of six pairs only, and yet for the 
4-ampere curve the whole question of whether the graph is a reasonable description 
of the data actually depends on the existence of six paired observations in the 
total of 17. We are really left without adequate material to determine effectively 
the probable error of any observation. This may be of no importance in the 
present case, but the absence of adequate repetition of the value of A for a given 
value of B in order to determine the probable error of observation and so the 
"goodness of fit" of observation to theory is characteristic of much current physical 
research. 
I am much indebted to Mr Andrew W. Young for algebraical and arithmetical 
aid. 
