to the distribution found everywhere in natural science, where repeated observation of the same occurrence furnishes different separate values, I suppose—tentatively again—that the repeatedly examined psychical process in question occurred each time under conditions sufficiently similar for our purposes. This supposition is not compulsory, but is very probable. If it is wrong, the continuation of experimentation will presumably teach this by itself: the questions put from different points of view will lead to contradictory results.
Section 10. The Probable Error
The quantity which measures the compactness of the observed values obtained in any given case and which makes the formula which represents their distribution a definite one may, as has already been stated, be chosen differently. I use the so-called “probable error” (P.E.)—i.e., that deviation above and below the mean value which is just as often exceeded by the separate values as not reached by them, and which, therefore, between its positive and negative limits, includes just half of all the observational results symmetrically arranged around the mean value. As is evident from the definition these values can be obtained from the results by simple enumeration; it is done more accurately by a theoretically based calculation.
If now this calculation is tried out tentatively for any group of observations, a grouping of these values according to the “law of errors” is recognised by the fact that between the sub-multiples and the multiples of the empirically calculated probable error there are obtained as many separate measures symmetrically arranged about a central value as the theory requires.
According to this out of 1,000 observations there should be:
| Within the limits | Number of separate measures | |||
| ± | 1⁄10 | P.E. | 54 | |
| ± | ⅙ | P.E. | 89 | .5 |
| ± | ¼ | P.E. | 134 | |
| ± | ½ | P.E. | 264 | |
| ± | P.E. | 500 | ||
| ± | 1½ | P.E. | 688 | |
| ± | 2½ | P.E. | 823 | |
| ± | 2½ | P.E. | 908 | |
| ± | 3½ | P.E. | 957 | |
| ± | 4½ | P.E. | 993 | |
