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V. On the ^latlieniatical 'J'lteory of Errors of Judgment^ luidi Special Reference 
to the Personal Eciiiation. 
By Karl Pearson, F.R.S., University College, London. 
Keceived April 23,—Read June 20, 1901. 
Contents. 
Page 
(1.) Introductory.235 
(2.) Terminology.237 
(3.) Current Theoiy of Errors of Observation.240 
(4.) New Theory of Errors of Observation.242 
(5.) General Description of Experiments.243 
(6.) On the Means and Standard Deviations of Grouped and Ungrouped Observations .... 249 
(7.) On the Constancy of the Personal Equation.253 
(8.) On the Interdependence of Judgments of the same Phenomenon by “independent” Observers 261 
(9.) On the Nature of the Frequency Distribution in the case of Errors of Judgment.271 
(10.) General Physical Characters of a Normal Distribution.274 
(11.) Agreement between Theory and Observation in the General Distrilnition of Errors of each 
particular Size.283 
(12.) Summary and Conclusions.290 
Introductory. 
1. The following investigation has been iii progress for some years and led to a 
})aper, communicated to the Society on December 29, 1896."^ I therein pointed out 
that personal judgments were frequently correlated. This correlation may 1)e of the 
kind which in that paper I termed “ spurious,” or it may be genuine. By “ spurious ” 
correlation 1 understand the quantitative measure of a resemblance in judgments, 
which resemblance is due solely to the particidar manipulation of the observations. 
Very customary treatment of observations will lead to the existence of a spurious 
correlation, which may be and generally is entirely overlooked by the observers. 
For example: if the quantity to be determined by judgment were the time taken 
by a bright point, say a star, in travelling from a position C intermediate between 
spider lines A and B to the line B, and the result were to be expressed by the ratio of 
this time to the known time from A to B, then there would Ise correlation in the results 
obtained by two observers for a number of stars, even if their absolute judgments on the 
* ‘ Eoy. Soc. Proe.,’ vol. 60, p. 489. 
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