370 



Prof. Karl Pearson. 



true midpoint to the right in terms of the length of the line as the 

 error. I was then led to realise the importance of what I have termed 

 "spurious correlation" in this use of indices or ratios, and I published 

 a short notice of the subject in the ' Koy. Soc. Proc.,' vol. 60, p. 489, 

 1896. 



It seemed necessary accordingly to make our judgments in a different 

 manner, and a second series of 520 experiments was made by Dr. Alice 

 Lee, Dr. W. F. Macdonell, and myself, in which we observed the motion 

 of a narrow beam of light down a uniform strip of fixed length, and 

 recorded its position at the instant, a priori unknown to us, at which a 

 hammer struck a small bell. The experiment was made by means 

 of a pendulum devised by Mr. Horace Darwin, and the record 

 required a combination of ear, eye, and hand judgment. In the 

 manipulation of the data there was no room for the appearance of 

 " spurious correlation," but to my great surprise I again found sub- 

 stantial correlation in two out of the three cases of what one might 

 reasonably suppose to be absolutely independent judgments. 



This led to a thorough reinvestigation of the bisection experiments, 

 absolute and not ratio errors being now dealt with. We found the 

 same result, i.e., correlation of apparently independent judgments. 

 The absolute personal equations based on the average of twenty-five to 

 thirty experimental sets were then plotted, and found to fluctuate in 

 sympathy, and these fluctuations were themselves far beyond the order 

 of the probable errors of random sampling. Nor were the fluctuations 

 explicable solely by likeness of environment. For in the bright line 

 experiments while the judgments of A and B were sensibly uncorrected, 

 those of G were substantially correlated with those of both A and B. 

 Thus we were forced to the conclusion that judgment depends in the 

 main upon some few rather than upon many personal characteristics, and 

 that while A and B had practically no common characteristics, there 

 were some common to A and C and others common to B and C. We 

 are driven to infer — 



(i.) That the fluctuations in personal equation are not of the order 

 of the probable deviations due to random sampling. 



(ii.) That these fluctuations in the case of different observers, record- 

 ing absolutely independently, are sympathetic, being due to the influ- 

 ence of the immediate atmosphere of the observation or experiment on 

 personal characteristics, probably few in number, one or more of which 

 may be common to each pair of observers. 



In this way we grasp how the judgments of " independent " observers 

 may be found to be substantially correlated. In the memoir attention 

 is drawn to the great importance of this, not only for the weighting of 

 combined observations, but also for the problem of the stress to be 

 laid on the testimony of apparently independent witnesses to the same 

 phenomenon. 



