Sixteen Experimental Investigations from the Harvard Psychological Laboratory - Hugo Münsterberg (best life changing books txt) 📗
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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
6.5 1 2 57 2We 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.
2.[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
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