Page:Mind (Old Series) Volume 11.djvu/230

 THE TIME TAKEN UP BY CEBEBRAL OPERATIONS. 229 actions measured have been averaged together, or those times which the experimenter thought too long or too short have been altogether ignored. There are however serious objections to both of these methods. The former does not give correct results. Through some abnormal circumstance, a reaction may vary so greatly from the average of the others, that the whole series gets a false value. It might be supposed that this error could be eliminated by making the whole number of experiments, sufficiently large ; this, however, makes necessary a great ex- penditure of time and labour, without altogether correcting the error. In physical experiments, the measurements varying most from the average are equally likely to be positive or negative ; this is not the case in our work. Reactions that are so short as seriously to affect the average can scarcely occur, but through some inner or outer disturbance the reactions are sometimes abnormally long. Thus, even though the average of an in- definitely large number of reactions is taken, the result is not correct, but somewhat larger than the average of the reactions made under normal circumstances. The method introduced by Exner of simply ignoring the reactions which seem to be too long or too short may give correct results, but is undoubtedly un- reliable. The experimenter thinks he has found the proper worth, and then almost unconsciously leaves out of his reckoning the reactions which would invalidate it. For example, Merkel 1 gives fifteen averages in which his ' perception time ' is between 22 and 25<r, and the times in a hundred and twenty other series, made on eight different persons, correspond exactly with this, varying only between 19 and 26<7. These averages correspond to an altogether impossible extent ; we need not therefore be surprised at finding the time quite false. The work of v. Kries and Auerbach 2 loses much of its value from the fact that so many of the determinations have been omitted in calcu- lating the results. I have used a different and, as far as I am aware, new method.. If the apparatus did not work properly, of course no reaction was measured ; but the average of all the reactions measured was calcu- lated. Either 13 or 26 reactions were made in a series ; the average of these reactions was calculated, and the variation of each reaction from this average. Then the reaction having the largest variation was dropped, the average of the remaining 12 or 25 reactions was calculated, and the reaction varying most from this average was again dropped. This process was continued until the 3 or 6 worst reactions had been dropped, I then having the 10 or 20 best reactions, and the variation of each of these from the average. In practice we need not calculate so many new averages, it being only necessary to drop the 3 or 6 reactions -uoion- 1 Philosophische Studien, li. 1. 2 Du Bois-fieymond's Archiv, 1877.