STIMULUS INFORMATION AS A DETERMINANT OF REACTION TIME1
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STIMULUS INFORMATION AS A DETERMINANT
OF REACTION TIME 1
RAY HYMAN
The Johns Hopkins University1
In the typical reaction-time experi- under certain conditions, in a manner
ment, S's reaction time is greater when analogous to this definition of infor-
he has to respond differentially to one mation. When a stimulus is chosen
of two equally probable stimuli in- to which S must make a discrimina-
stead of to just one stimulus. In fact, tory response, his reaction time seems
Merkel (2), using one to ten alterna- to be a monotonically increasing func-
tives, has demonstrated that when S tion of the number of possible stimuli
has to respond to one stimulus chosen from which the stimulus can be chosen.
from a number of equally probable Thus, the choice reaction-time ex-
alternatives, his reaction time increases periment can be looked upon as a
with the number of alternatives. model of a communication system.
The fact that S's response to stim- The display represents a transmitter
ulus A takes more time when A is one of information. Each alternative
of several rather than one of two stimulus or signal represents a mes-
equally probable alternatives is of sage; more information can be trans-
intrinsic interest. But it becomes mitted the greater the number of
even more significant when looked at messages from which one can be
from the standpoint of modern com- chosen. The channel over which the
munication theory. In communica- signal is transmitted can be considered
tion theory the amount of information as the air space between the light and
which a message conveys is an increas- S, and might also include part of S's
ing function of the number of possible visual afferent system. The S also
messages from which that particular acts as a receiver or decoder in that at
message could have been selected.3 some point he decodes the signal into
The S's reaction time seems to behave, its message and reacts with the appro-
1
priate response (the destination of the
Based upon a thesis submitted to the Faculty information).
of Philosophy, The Johns Hopkins University in Setting of the problem.—The experi-
partial fulfillment of the requirements for the
degree of Doctor of Philosophy. The author mental task involved varying the
wishes to express his gratitude to his adviser, amount of information in the display
Dr. W. R. Garner, and to Drs. A. Chapanis and and observing the corresponding
H. W. Hake for assistance in the preparation of changes in S's reaction time to a stim-
this paper.
2
This research was done in cooperation with ulus presentation. The display was
the Systems Coordination Division, Naval Re- a matrix of lights, each light repre-
search Laboratory under Contract NS-ori-166, senting a message. The S's reaction
Task Order I, between the Office of Naval time was registered by means of a
Research and The Johns Hopkins University.
This is Report No. 166-1-163, Project Designa- voice key and timer. The average
tion No. NR 507-470, under that contract. amount of information accompanying
' The amount of information conveyed by the the presentation of a single stimulus
selection of a particular message is defined as the was varied by (a) varying the number
logarithm to the base 2 of the reciprocal of the
a priori probability that this particular message of equally probable alternatives from
will be selected. which a choice could be made, (b)
188REACTION TIME 189
altering the probability of occurrence amount of information at the expense
of particular choices, and (c) introduc- of an increased proportion of incorrect
ing sequential dependencies between responses. The present study ex-
successive choices of alternatives. cludes this possibility by demanding
These three ways of varying the an errorless performance on the part
amount of information per stimulus of S.
have been incorporated into a single The second assumption excludes
formula by Shannon in the formulation those situations wherein S gains new
of his mathematical theory of com- knowledge concerning the statistical
munication (3). Such a unified form- structure of the stimulus series as the
ula represents a convenience for the series progresses in time. The hy-
communication engineer. From the potheses assume that S's average
psychologist's viewpoint, however, the uncertainty -per stimulus presentation
psychological equivalence of these remains constant throughout a par-
three ways of varying information ticular stimulus series. The present
must be demonstrated empirically be- experimental design helps to produce
fore Shannon's formula can be applied such a situation by (a) never present-
to the human component of the com- ing S with the same series for a given
munication system. To demonstrate condition more than once, (b) instruct-
such an equivalence was one of the ing S concerning the statistical prop-
. primary aims of the present study. erties of the series, and (c) giving S
Statement of the problem.—The par- preliminary practice on a series of
ticular hypotheses investigated can be similar statistical construction.
stated as follows:
1. Reaction time is a monotonically PROCEDURE
increasing function of the amount of Apparatus.—The apparatus consisted of a
information in the stimulus series. visual display, a voice key, a chronoscope, and a
2. The regression of reaction time control panel. The display was a square matrix
upon amount of information is the of 36 small lights. These 36 lights were arranged
in six rows and six columns forming a square 3 in.
same whether the amount of informa- on the side. The matrix was so placed that the
tion per stimulus is varied by altering length of a side of the display made a visual angle
the number of equally probable alter- of 5° from where S sat. The diameter of each
natives, altering the relative frequency light in the display made a visual angle of
of occurrence of particular alterna- approximately 36'.
Only eight of the lights were used: the four
tives, or altering the sequential depen- lights which made up the corners of the outer
dencies among occurrences of succes- square of lights and the four corners of the next
sive stimuli. inner square of lights. Such a grouping seemed
These hypotheses assume that (a) to minimize the confusions of one light with
S's responses are completely deter- another on the matrix by S. The S designated
each light by the distinctive names: Bun, Boo,
mined by the stimulus series, and (b) Bee, Bore, By, Bix, Bev, and Bate, respectively.
the occurrences of the successive A masonite screen separated E, the control
stimuli do not alter S's knowledge of panel, and the chronoscope from S. The E pre-
the statistical properties of the stim- selected a light by means of a rotary switch.
After giving S a warning signal, he closed a
ulus series as a whole. switch (2 sec. later) which simultaneously turned
The first assumption demands a on the light and started the clock. The S's
one-to-one correspondence between vocal response stopped the clock by means of a
stimulus and response series. Hick's throat microphone which activated an electronic
experiment (1) indicates that S can voice key.
Subjects.—The four Ss were male undergrad-
decrease his reaction time to a given uates, ages 18—22. Each S attended more than190 RAY HYMAN
40 experimental sessions over a 3-mo. period; the occurrence of these alternatives. Because of
approximately 15,000 reaction times were re- the greater complexity of these conditions, they
corded for each S. One of the Ss, F. K., also are shown in Table 1. In Cond. 1, for example,
took part in 11 sessions of the pilot study during there are just two alternatives, but one occurs
the month previous to the 3 mo. he served as S nine times as often as the other. The stimulus
in the actual experiment. information in bits is shown at the right for each
Experimental conditions.—In all there were component separately and for the weighted aver-
three experiments, each making use of one of the age of the total condition. In Cond. 3 there is a
three different methods of altering stimulus infor- total of four different alternatives, one of which
mation. Each of these experiments consisted of occurs 13/16 of the time, with the other three
eight specific conditions containing different each occurring 1/16 of the time. Conditions 7
amounts of stimulus information. In addition, and 8 each involve the greatest number of differ-
five series of stimuli, each constructed separately ent alternatives (eight), with the proportions of
but according to the same rules, were used for occurrences as shown.
each experimental condition. Experiment III.—In the third experiment dif-
Experiment I.—The first experiment had eight ferent numbers of alternatives were used, and in
conditions which differed from each other only every condition all alternatives occurred equally
in terms of the number of equally probable alter- often. But the probability of the occurrence of
natives from which the stimulus could be chosen. a particular alternative depended upon the
The eight conditions involved numbers of alter- immediately preceding alternative in a manner
natives ranging from one through eight; the shown in Table 2. Condition 1, for example,
respective bits of information attached to each consisted of two alternatives. Whenever one of
condition were 0.00, 1.00, 1.58, 2.00, 2.32, 2.58, these alternatives occurred, it would be followed
2.81, and 3.00. This variable is essentially the by the other alternative 8/10 of the time and by
same as used in the experiments of Merkel (2) itself 2/10 of the time. In Cond. 3, with four
and Hick (1). alternatives, the occurrence of a stimulus meant
Experiment II.—The second experiment had that the probability of its recurring on the next
eight conditions which involved different num- trial was 7/10; the probability of some other
bers of alternatives and different probabilities of alternative occurring was 1/10. Conditions 6,
7, and 8 were constructed in the same manner as
conditions in Exp. I with the exception that a
TABLE 1 particular stimulus was never followed by itself.
THE EIGHT CONDITIONS FOR EXPERIMENT II The experimental sessions.—An experimental
AND THE CORRESPONDING AMOUNTS OF session lasted 1 hr. Each S attended one session
INFORMATION IN BITS PER STIMULUS a day, five days a week, at the same hour each
PRESENTATION
day. Three series (from three different condi-
tions) were run during each session. Since each
series consisted of 120-128 stimuli, each session
Av. yielded a total of 360-384 reaction times. For
Number Probability Amount
Cond. of Alter- of Logs l/i> of Infor- experimental convenience each series was split
natives Occurrence mation in into two parts of 60-64 stimuli each. By desig-
Cond.
nating the three series as A, B, and C, the typical
1 1 9/10 0.15 0.47 counterbalanced order of any session can be
1 1/10 3.32 symbolized in this manner: Practice on A, A,
2 1 8/10 0.32 0.72 Practice on B, B, Practice on C, C, 5-min. rest,
1 2/10 2.32 C, B, A.
3 1 13/16 0.30 0.99
3 1/16 4.00 RESULTS
4 1 15/20 0.42 1.39
5 1/20 4.32 Experiment I.—When the amount
5 1 4/8 1.00 1.75
1 2/8 2.00 of information per stimulus presen-
2 1/8 3.00 tation was varied by varying the num-
6 1 5/10 1.00 2.16
5 1/10 3.32 ber of equally probable stimulus
7 1 8/16 1.00 2.38 alternatives from which E could choose
1 2/16 3.00 the stimulus, the linear correlation
6 1/16 4.00
8 2 4/16 2.00 2.75 between amount of information and
2 2/16 3.00 reaction time was .991, .982, .980, and
4 1/16 4.00
.979 for each of the four Ss. ThereREACTION TIME 191
TABLE 2
THE EIGHT CONDITIONS FOR EXPERIMENT III AND THE CORRESPONDING AMOUNTS OF
INFORMATION IN BITS PER STIMULUS PRESENTATION
Number Probability {p) of Stimulus x Occurring Av. Amount
Cond. of Lights Following Stimulus a Logt 1 IP of Information
*•(*) m Cond.
1 2 Pa 4 ) = 8/10 0.32 0.72
Pa a) = 2/10 2.32
2 3 Pa a) = *>„(192 RAY HYMAN
cases the nonlinear variance is signifi- after the means were adjusted for the
cant at the 1% level. linear trend. Practically all of the
The first five conditions in Table 2 nonlinear variance for each of the four
produced reaction times which were Ss was produced by the one degree of
significantly lower than the reaction freedom used to compare these two
times for the latter three conditions groups of conditions; the nonlinear
o EX P. I
a EXP. n
a EX P. m
600 a
" G. C. F.K.
3
0
400 -
f
f *
-
I 0
Q I
S
O
200
LJ A
Y« 212 + I53X Y« 165 t I27X
r = 985
0 1 1 1 1 1 1
LU
2 F.P. L.S.
800
o
U 600
o:
400
200
Y* IBOt2l5X Y» 160+ I99X
r • .955 r « .938
BITS PER STIMULUS PRESENTATION
FIG. 1. Reaction time as a function of stimulus information (expressed in bits) when amount
of information is varied in three different ways. Data are for Ss G. C , F. K., F. P., and L. S.,
respectively.REACTION TIME 193
variance associated with the remain- series of Exp. II and III (wherein he
ing five degrees of freedom was non- showed no practice effect). Conse-
significant. quently his regression line for Exp. I
The high reaction times for the was displaced slightly upwards on the
three conditions wherein no immedi- ordinate.
ate repetition of a stimulus was allowed The joint regression line.—The joint
raise some interesting questions. On regression line fitted to the combined
the basis of information theory, the points of the three experiments pro-
restriction "no repetition" lowers the duced a linear correlation between
amount of information per stimulus reaction time and amount of informa-
presentation since it effectively de- tion for each of the four Ss of .985,
creases the number of alternatives by .953, .955, and .938, respectively (see
one. Instead of lowering S's reaction Fig. 1). In other words, when we
time, however, this restriction caused vary information in three distinct
his reaction time to be higher than if ways over a limited range of from 0.00
no such restriction had been imposed. to 3.00 bits, a linear regression of
Comparison of the three experiments. reaction time on information accounts
—The second experimental hypothesis for as much as 97.0, 91.1, 91.1, and
stated that the three experiments 88.8% of the total variance among
would produce identical regression mean reaction times for the 24 experi-
lines. In the case of three Ss, the null mental conditions for each of the four
hypothesis that the three regression Ss.
lines do in fact coincide could not be
DISCUSSION
rejected at the 5% level of confidence.
For L. S., however, the null hypothesis So far this paper has presented em-
had to be rejected at the 1% level of pirical relationships which suggest
confidence. This lack of coincidence that reaction time can be considered
could not be attributed to a discrep- a linear function of stimulus informa-
ancy among the three regression co- tion within the range of 0.00 to 3.00
efficients; the difference was due to a bits. More important than the shape
systematic displacement of the regres- of this function are the factors which
sion line for Exp. I upwards on the operate to bring it about. This par-
ordinate relative to the lines for Exp. ticular study was set up to discover
II and III. the type of relationship which exists
This systematic displacement among rather than to delve into the causes of
the regression lines of L. S. can be this relationship. Nevertheless, an
attributed to the relatively large prac- examination of the data suggests some
tice effect which this S displayed on factors which may partially account
Exp. I. Most of the series for Exp. I for the resultant function.
were run during the first six weeks of Nonadditive combination of com-
the experimental period, whereas most ponents within conditions.—The con-
of the series for Exp. II and III were ditions for Exp. II and III can be
run during the latter half of the experi- considered as made up of two or more
mental period. L. S., it will be re- components, each component having
called, showed a practice effect which a different amount of information asso-
accounted for 11.5% of the-variance ciated with its presentation (see
among his series for Exp. I, whereas he Tables 1 and 2). Condition 1 in
presumably had reached a plateau by Table 1, for example, has two com-
the time he participated in most of the ponents, one with 0.15 bits and the194 RAY HYMAN other with 3.32 bits. On the hypoth- 13/16 and 3/16, respectively, our esis that reaction time behaves in a weighted predicted average comes out manner analogous to the measure of to be 363 msec. The observed mean information, we would expect the reaction time for the component with mean reaction time to each of the 0.30 bits was 306 msec, which was 48 components within a condition to fall msec, higher than the predicted value, on the regression line which was fitted and the observed mean reaction time to the over-all means of the conditions. to the component with 4.00 bits was To illustrate, one might expect a con- 585 msec, or 235 msec, lower than the stant mean reaction time to an event predicted value. Yet, when we weight which occurs with probability \ re- these component means by their fre- gardless of how many other elements quency of occurrence, we come up there are in the series. But such was with an observed mean of 361 msec, not the case. In both Exp. II and III agreeing very closely with the pre- the components within a condition dicted mean. Such a situation holds interacted with each other in such a for all the conditions and their com- way that the reaction time to the low ponents in Exp. II and III and for all information component was higher, four Ss. and the reaction time to the high in- These analyses mean that we can- formation component was markedly not predict, on the basis of the regres- lower, than would be predicted on the sion line fitted to the means of the basis of the regression line fitted to conditions, what the mean reaction the means of the conditions. This times will be to the components which effect was very marked and occurred make up a condition. If, however, we without a single exception for all four know what the components of the Ss in both Exp. II and III. condition are, we can predict what the An example will illustrate the nature combined mean for this condition will of this effect. Take the condition in be on the basis of the over-all regres- Table 1 (Cond. 3) which has 0.99 bits sion. The components, of course, do associated with it. For G. C , the not combine additively. But they regression line fitted to the reaction interact in such a manner that the times of the 24 experimental condi- condition means behave as if the tions would predict a mean reaction components combined additively. If time for this condition of 363 msec. we are interested only in the behavior The observed mean reaction time for of the condition means, the assump- this condition was 361 msec, a figure tion of additive combination of the which agrees closely with the expected components will serve our purposes. value. This condition consisted of If, however, we are interested in the two components, one with 0.30 bits of behavior of the components making information and the other with 4.00 up the conditions, we must find differ- bits of information attached to its ent laws and equations. occurrence. On the basis of the over- Reaction time as a junction of the all regression line to G. C.'s points we number of other stimuli intervening would predict mean reaction times for between successive occurrences of a these two conditions of 258 and 824 stimulus.—Another interesting factor msec, respectively. If we weight determining the reaction time was each of these expected values by the first observed during the pilot study. probability of occurrence of the com- The E observed that whenever a ponent with which it is attached, stimulus was immediately followed by
REACTION TIME 195
itself in the series, S seemed to respond ulus in the series. The three param-
unusually fast to it. This effect was eters plotted are the conditions with
apparently independent of S's verbal- two, four, and eight alternatives from
ized expectancy of the stimulus for he Exp. I. Although the data are aver-
reported that in such cases he was not aged over the four Ss, the individual
expecting the stimulus to follow itself. curves differed from each other only
An examination of the data showed in displacement along the ordinate.
that this phenomenon was quite For more than two alternatives the
marked for the situation with four or general trend of the functions seems
more alternatives and steadily de- to be parabolic; the function seems to
clined until it disappeared or became reach a maximum at around a dis-
slightly negative for the case with just placement of one or two stimulus
two alternatives. presentations and then come down
As can be seen in Fig. 2, the experi- again. The effect is more marked the
mental data from the four Ss support greater the number of alternatives.
the observations made from the pilot Presumably two factors are operating
study. In this figure reaction time is to produce this bow-shaped curve.
plotted as a function of the number of One is S's verbalized introspection
stimuli intervening between succes- that a stimulus which has not appeared
sive occurrences of a particular stim- for some time in the series is reacted
to more quickly than ordinarily be-
cause of the greater expectancy now
attached to its appearance. This
"verbal expectancy" apparently ac-
counts for the fact that the reaction
times begin to get lower than the
maximum for large displacements.
The second factor seems to consist of
some sort of residual effect produced
by just having seen and reacted to a
particular stimulus; this effect seems
to facilitate reaction to this stimulus
if it reappears within a finite time
interval. For eight alternatives this
facilitation seems to last for at least a
displacement of one stimulus presen-
tation. For two alternatives this
facilitation does not affect the func-
2 ALTERNATIVES tion; perhaps it is at its maximum
throughout the series and therefore
I I
0 1 2 3 does not show in the function for two
NUMBER OF OTHER STIMULI INTERVENING alternatives.
BETWEEN SUCCESSIVE OCCURRENCES
OF A STIMULUS Evidence for periodicity.—The data
FIG. 2. Reaction time as a function of the suggest a third factor which may have
number of other stimuli intervening between to be taken into account in the final
successive occurrences of a particular stimulus story concerning the role of stimulus
within a series. Each point represents an aver- information as a determinant of reac-
age of the data from four Ss. The three param- tion time. Separate frequency distri-
eters are the conditions with eight, four, and two
alternatives from Ezp. I. butions were made of the reaction196 RAY HYMAN
times in each condition. For the probable alternatives from which it
situations wherein we have two or could be chosen, (b) the proportion of
more alternatives the distributions times it could occur relative to the
tended to be multimodal. In almost other possible alternatives, and (c)
every distribution a peak, clearly dif- the probability of its occurrence as a
ferentiated from the remainder of the function of the immediately preceding
distribution, regularly occurred at stimulus presentation.
approximately S's simple reaction The reaction time to the amount of
time. The remainder of the distribu- information in the stimulus produced
tion in each case, however, did not a linear regression for each of the three
present such a consistently clear pic-
ways in which information was varied.
ture. The variability of the data was
The three regression lines obtained
such that it is impossible to make any
definite conclusions about the number by the three separate ways of varying
of peaks and their location on the the amount of information were found
abscissa. Furthermore, if there is any to coincide for three Ss. In the case
natural periodicity in the distribution of the fourth S, a systematic displace-
it seems to have been confounded with ment of one of his regression lines was
a periodicity suggested by the group- attributed to a relatively large prac-
ing of stimuli on the display. Since tice effect which he showed for that
the distributions seem to support sev- experiment.
eral possible and different models as
to what is happening, further discus- (Received for early publication
November 20, 1952)
sion must be postponed until more
data are available.
REFERENCES
SUMMARY 1. HICK, W. E. On the rate of gain of infor-
mation. Quart. J. exp. Psychol., 1952,
The reaction time to a visual stim- 4, 11-26.
ulus was investigated as a function of 2. MERKEL, J. Die zeithchen Verhaltnisse der
the amount of information conveyed Willensthatigkeit. PMos. St., 1885, 2,
73-127.
by that stimulus. The amount of 3. SHANNON, C. E., & WEAVER, W. The mathe-
information in the stimulus was varied matical theory of communication. Urbana:
by varying (a) the number of equally Univer. of Illinois Press, 1949.You can also read
