Harvard Psychological Studies, Volume 2

by Unknown

Suppose that the drums have been set in rotation and that the paper is unwinding from (d) and being wound on (d´), Fig. B, and suppose that the subject has ruled series of 20 to 50 lines, as may be desired, regulated by the stop-watch in the hands of the operator. The records will appear much as Fig. 5 under the planimeter discussion, there being for each speed one normal line to start and a series of lines following and intended to be of the same length as the normal line. A series of records, then, consists of 13 records of 20 or 50 lines, each running from 20 to 200 beats per minute, the complete series having not less than 260 and not more than 650 lines.

It should be added that the operator holds a pencil-point on the end of each normal line just after the record of 20 or 50 lines is made and turns the drum (d), thus marking a line nearly perpendicular to the ruled lines and at the average or normal distance from the starting-point; an absolutely correct record would show all ruled lines ending on this line.

The calculation of this series of records by the ordinary method of measuring each line, adding the lines of the series, averaging for the constant error, and repeating the operation in a slightly different form for the mean error or mean variation is of such enormous labor for an extended investigation as to be beyond the capacity of one or of several students; it is fortunate that the planimeter is at hand to be employed in averaging each series, and this instrument has therefore been selected as overcoming this difficulty.

It is desirable to consider the method employed by Dr. Woodworth to overcome this danger of excessive computation, and it will now be subjected to a critical and comparative examination.

He says, page 19 of his monograph on the Accuracy of Voluntary Movement, that the subject's sole duty was to make the present line equal to that immediately preceding, and the width of the slot was so adjusted that the subject could see only the line just ruled. After discussing certain matters of memory and its relation to the memory-image, in the attempt to support this changing normal plan, he confesses, on page 20, that this device is advantageous in much simplifying the most tedious part of the graphic method, that of computation.

While this is undoubtedly true, it needs careful scrutiny before adoption, for, on the same page, he says that one source of error in the method of making each line equal to the preceding one is that the different movements in the same series are not comparable, but the positive constant error is cumulative in its effect, and the normal tends to become longer and longer.

Some relation between this source of error and such a record as shown on page 29, Fig. 2, is evident, for, while it should be noted that this cumulative effect is peculiar to a series of lines for one speed, it has further a tendency to produce overruling at all speeds, and the natural result is to increase the error unduly and unnaturally for the higher speeds or as the speed increases, because there is then less time for the discrimination and choice that will tend to shorten the ruled line. It may be predicted, then, that Dr. Woodworth's method will show a slight lengthening of normal between lines at slow speeds and a much greater one at high speeds, the effect being to introduce a variable factor that would have no existence were a better plan adopted. The computation required for the average error is simple, being dependent only on the first and last lines of a series, and it is suspected that this very simplicity has led to its adoption and the consequent neglect of certain serious sources of error.

He tells us, on page 20, that the constant and variable error may well be isolated and studied separately, but indicates that they must "somehow" be considered combined as nature has made them; that is, analysis is desirable, but the synthetic method is more scientific.

This investigation will present data suggesting that

(1) Such a curve as that on page 29 of his monograph is not a characteristic one and relations of length of ruled line, as well as effects of weight, make it impossible to apply Weber's law or even the law of Fullerton and Cattell in the way proposed by Dr. Woodworth.