Sixteen Experimental Investigations from the Harvard Psychological Laboratory by Hugo Münsterberg (100 books to read .txt) 📕

surface in proximity with which it had been placed. The rod was easily

removable, so that one bearing a different tip could be substituted

when desired. The whole instrument was mounted on a compact base

attached to a short rod, by which it could be fastened in any desired

position in an ordinary laboratory clamp.

During the course of most of the experiments the current was

controlled by a pendulum beating half seconds and making a mercury

contact at the lowest point of its arc. A condenser in parallel with

the contact obviated the spark and consequent noise of the current

interruption. A key, inserted in the circuit through the mercury cup

and tapping instrument, allowed it to be opened or closed as desired,

so that an interval of any number of half seconds could be interposed

between successive stimulations.

In the first work, a modification of the method of right and wrong

cases was followed, and found satisfactory. A series of intervals,

ranging from one which was on the whole distinctly perceptible as

longer than the standard to one on the whole distinctly shorter, was

represented by a series of cards. Two such series were shuffled

together, and the intervals given in the order so determined. Thus,

when the pile of cards had been gone through, two complete series had

been given, but in an order which the subject was confident was

perfectly irregular. As he also knew that in a given series there were

more than one occurrence of each compared interval (he was not

informed that there were exactly two of each), every possible

influence favored the formation each time of a perfectly fresh

judgment without reference to preceding judgments. The only fear was

lest certain sequences of compared intervals (e.g., a long compared

interval in one test followed by a short one in the next), might

produce unreliable results; but careful examination of the data, in

which the order of the interval was always noted, fails to show any

influence of such a factor.

To be more explicit with regard to the conditions of judgment; two

intervals were presented to the subject in immediate succession. That

is, the second stimulation marked the end of the first interval and

the beginning of the second. The first interval was always the

standard, while the second, or compared interval, varied in length, as

determined by the series of cards, and the subject was requested to

judge whether it was equal to, or longer or shorter than the standard

interval.

In all of the work under Group 1, and the first work under Group 2,

the standard interval employed was 5.0 seconds. This interval was

selected because the minimum variation possible with the pendulum

apparatus (½ sec.) was too great for the satisfactory operation of a

shorter standard, and it was not deemed advisable to keep the

subject’s attention on the strain for a longer interval, since 5.0

sec. satisfied all the requirements of the experiment.

In all work here reported, the cork tip on the tapping instrument was

circular in form, and 1 mm. in diameter. In all, except one experiment

of the second group, the areas stimulated were on the backs of the

fingers, just above the nails. In the one exception a spot on the

forearm was used in conjunction with the middle finger.

In Groups 1 and 2 the intensity of stroke used was just sufficient to

give a sharp and distinct stimulation. The intensity of the

stimulation was not of a high degree of constancy from day to day, on

account of variations in the electric contacts, but within each test

of three stimulations the intensity was constant enough.

In experiments under Group 3 two intensities of strokes were employed,

one somewhat stronger than the stroke employed in the other

experiments, and one somewhat weaker—just strong enough to be

perceived easily. The introduction of the two into the same test was

effected by the use of an auxiliary loop in the circuit, containing a

rheostat, so that the depression of the first key completed the

circuit as usual, or the second key completed it through the rheostat.

At each test the subject was warned to prepare for the first

stimulation by a signal preceding it at an exact interval. In

experiments with the pendulum apparatus the signal was the spoken word

‘now,’ and the preparatory interval one second. Later, experiments

were undertaken with preparatory intervals of one second and 1-4/5

seconds, to find if the estimation differed perceptibly in one case

from that in the other. No difference was found, and in work

thereafter each subject was allowed the preparatory interval which

made the conditions subjectively most satisfactory to him.

Ample time for rest was allowed the subject after each test in a

series, two (sometimes three) series of twenty to twenty-four tests

being all that were usually taken in the course of the hour. Attention

to the interval was not especially fatiguing and was sustained without

difficulty after a few trials.

Further details will be treated as they come up in the consideration

of the work by groups, into which the experiment naturally falls.

II. EXPERIMENTAL RESULTS.

1. The first group of experiments was undertaken to find the direction

of the constant error for the 5.0 sec. standard, the extent to which

different subjects agree and the effects of practice. The tests were

therefore made with three taps of equal intensity on a single dermal

area. The subject sat in a comfortable position before a table upon

which his arm rested. His hand lay palm down on a felt cushion and the

tapping instrument was adjusted immediately over it, in position to

stimulate a spot on the back of the finger, just above the nail. A few

tests were given on the first finger and a few on the second

alternately throughout the experiments, in order to avoid the numbing

effect of continual tapping on one spot. The records for each of the

two fingers were however kept separately and showed no disagreement.

The detailed results for one subject (Mr,) are given in Table I. The

first column, under CT, gives the values of the different compared

intervals employed. The next three columns, under S, E and L,

give the number of judgments of shorter, equal and longer,

respectively. The fifth column, under W, gives the number of errors

for each compared interval, the judgments of equal being divided

equally between the categories of longer and shorter.

In all the succeeding discussion the standard interval will be

represented by ST, the compared interval by CT. ET is that CT

which the subject judges equal to ST.

TABLE I.

ST=5.0 SEC. SUBJECT Mr. 60 SERIES.

CT S E L W

4. 58 1 1 1.5

4.5 45 11 4 9.5

5. 32 13 15 21.5

5.5 19 16 25 27

6. 5 4 51 7

We can calculate the value of the average ET if we assume that the

distribution of wrong judgments is in general in accordance with the

law of error curve. We see by inspection of the first three columns

that this value lies between 5.0 and 5.5, and hence the 32 cases of

S for CT 5.0 must be considered correct, or the principle of the

error curve will not apply.

The method of computation may be derived in the following way: If we

take the origin so that the maximum of the error curve falls on the

Y axis, the equation of the curve becomes

y = ke^{-[gamma]²x²}

and, assuming two points (x_{1} y_{1}) and (x_{2} y_{2}) on the

curve, we deduce the formula

____________

±D / log k/y_{1}

x_{1} = –––––––––––

____________ ____________

/ log k/y_{1} ± / log k/y_{2}

where D = x_{1} ± x_{2}, and k = value of y when x = 0.

x_{1} and x_{2} must, however, not be great, since the condition

that the curve with which we are dealing shall approximate the form

denoted by the equation is more nearly fulfilled by those portions of

the curve lying nearest to the Y axis.

Now since for any ordinates, y_{1} and y_{2} which we may select

from the table, we know the value of x_{1} ± x_{2}, we can compute

the value of x_{1}, which conversely gives us the amount to be added

to or subtracted from a given term in the series of CT‘s to produce

the value of the average ET. This latter value, we find, by

computing by the formula given above, using the four terms whose

values lie nearest to the Y axis, is 5.25 secs.

In Table II are given similar computations for each of the nine

subjects employed, and from this it will be seen that in every case

the standard is overestimated.

TABLE II. ST= 5.0 SECS.

Subject. Average ET. No. of Series.

A. 5.75 50

B. 5.13 40

Hs. 5.26 100

P. 5.77 38

Mn. 6.19 50

Mr. 5.25 60

R. 5.63 24

Sh. 5.34 100

Sn. 5.57 50

This overestimation of the 5.0 sec. standard agrees with the results

of some of the experimenters on auditory time and apparently conflicts

with the results of others. Mach[4] found no constant error. Höring[5]

found that intervals over 0.5 sec. were overestimated. Vierordt,[6]

Kollert,[7] Estel[8] and Glass,[9] found small intervals overestimated

and long ones underestimated, the indifference point being placed at

about 3.0 by Vierordt, 0.7 by Kollert and Estel and 0.8 by Glass.

Mehner[10] found underestimation from 0.7 to 5.0 and overestimation

above 5.0. Schumann[11] found in one set of experiments overestimation

from 0.64 to 2.75 and from 3.5 to 5.0, and underestimation from 2.75

to 3.5. Stevens[12] found underestimation of small intervals and

overestimation of longer ones, placing the indifference point between

0.53 and 0.87.

[4] Mach, E.: ‘Untersuchungen über den Zeitsinn des Ohres,’

Sitzungsber. d. Wiener Akad., Math.-Nat. Kl., Bd. 51, Abth.

[5] Höring: ‘Versuche über das Unterscheidungsvermögen des

Hörsinnes für Zeitgrössen,’ Tübingen, 1864.

[6] Vierordt: op. cit.

[7] Kollert, J.: ‘Untersuchungen über den Zeitsinn,’ _Phil.

Studien_, I., S. 79.

[8] Estel, V.: ‘Neue Versuche über den Zeitsinn,’ _Phil.

Studien_, II., S. 39.

[9] Glass R.: ‘Kritisches und Experimentelles über den

Zeitsinn,’ Phil. Studien, IV., S. 423.

[10] Mehner, Max: ‘Zum Lehre vom Zeitsinn,’ Phil. Studien,

II., S. 546.

[11] Schumann, F.: ‘Ueber die Schätzung kleiner Zeitgrössen,’

Zeitsch. f. Psych., IV., S. 48.

[12] Stevens, L.T.: ‘On the Time Sense,’ Mind, XI., p. 393.

The overestimation, however, is of no great significance, for data

will be introduced a little later which show definitely that the

underestimation or overestimation of a given standard is determined,

among other factors, by the intensity of the stimulation employed. The

apparently anomalous results obtained in the early investigations are

in part probably explicable on this basis.

As regards the results of practice, the data obtained from the two

subjects on whom the greatest number of tests was made (Hs and Sh)

is sufficiently explicit. The errors for each successive group of 25

series for these two subjects are given in Table III.

TABLE III.

ST = 5.0 SECONDS.

SUBJECT Hs. SUBJECT Sh.

CT (1) (2) (3) (4) (1) (2) (3) (4)

4. 2.5 2.5 1.5 2.5 0. .5 0. .5

4.5 6.0 3.0 3.5 7.0 5.0 3.5 2.0 .5

5. 14.0 11.0 11.0 11.0 8.5 11.5 4.0 7.0

5.5 11.5 11.5 6.0 12.5