Therefore, it may be said: wherever a group of effects may be considered as having originated each time from the same causal combination, which was subject each time only to so-called accidental disturbances, then these values arrange themselves in accordance with the “law of errors.”
However, the reverse of this proposition is not necessarily true, namely, that wherever a distribution of values occurs according to the law of errors the inference may be drawn that this kind of causation has been at work. Why should nature not occasionally be able to produce an analogous grouping in a more complicated way? In reality this seems only an extremely rare occurrence. For among all the groups of numbers which in statistics are usually condensed into mean values not one has as yet been found which originated without question from a number of causal systems and also exhibited the arrangement summarised by the “law of errors.”[1]
Accordingly, this law may be used as a criterion, not an absolutely safe one to be sure, but still a highly probable one, by means of which to judge whether the approximately constant mean values that may be obtained by any proceeding may be employed experimentally as genuine constants of science. The Law of Errors does not furnish sufficient conditions for such a use but it does furnish one of the necessary ones. The final explanation must depend upon the outcome of investigations to the very foundations of which it furnishes a certain security. That is why I applied the measure offered by it to answer our still unanswered question: If the conditions are kept as much alike as is possible, is the average number of repetitions, which is necessary for learning similar series to the point of first possible reproduction, a constant mean value in the natural science sense? And I may anticipate by saying that in the case investigated the answer has come out in the affirmative.
- ↑ The numbers representing the births of boys and girls respectively, as derived from the total number of births, are said to group themselves in very close correspondence with the law of errors. But in this case it is for this very reason probable that they arise from a homogeneous combination of physiological causes aiming so to speak at the creation of a well determined relation. (See Lexis, Zur Theorie der Massenerscheinungen in der menschlichen Gesellschaft, p. 64 and elsewhere.)
