V. On the methematical theory of errors of judgement, with special reference to the personal equation

Abstract

1. The following investigation has been in progress for some years and led to a paper, communicated to the Society on December 29, 1896. I therein pointed out that personal judgments were frequently correlated. This correlation may be of the kind which in that paper I termed “spurious,” or it may be genuine. By “spurious” correlation I understand the quantitative measure of a resemblance in judgments, which resemblance is due solely to the particular 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 be correlation in the results obtained by two observers for a number of stars, even if their absolute judgments on the time from C to B were quite independent. Again, if the judgments of two observers be in both cases referred to a standard observer, then such relative judgments will be found to be correlated; and this is true, although if we could find the absolute errors of the two observers, we might discover that these errors were quite uncorrelated. We shall see illustrations below of the manner in which this spurious correlation almost imperceptibly creeps into any ordinary method of manipulating observations, and how very little attention has hitherto been paid to it. But apart from this spurious correlation the experiments described in this memoir seem to show that there exists almost invariably a genuine correlation between the judgments of independent observers. This may be due to two sources: (i.) Likeness of the environment in the case of each individual observation, which leads to likeness of judgment in the individual observers. One experiment may appear to be made under precisely the same conditions as a second, but really it has a certain atmosphere of its own which influences the observers in a like manner, (ii.) Likeness in the physical or intellectual characters of the observers leading to a likeness in their judgments of what took place.