Journal of Experimental Psychology:
Human Perception and Performance
1983, Vol. 9, No.2, 299-309
Copyright 1983 by Ibe American Psychological Association, Inc.
0096-1 523/83/0902'()299$OO. 75
Information Integration and the Identification of Stimulus
Noise and Criteria! Noise in Absolute Judgment
Robert M. Nosofsky
Harvard University
Two main classes of theories have been proposed regarding range effects in unidimensional absolute-identification tasks. One class posits that as range is increased, .criterial noise increases but stimulus noise remains constant. Another
class posits increasing stimulus noise but constant criterial noise. In this study,
an effort is made to help decide this issue. Multiple observations are used in
several absolute-identification tasks of varying range. A stimulus integration
model is proposed in which averaging takes place over stimulus internal representations, thereby reducing stimulus variance; on the other hand, it is assumed
that criterial'variance is unaffected by the number of observations. The model
allows one to identify the relative amounts of stimulus noise and criterial noise
inherent in observers' recognition judgments. The model yields good fits to data
in several experiments, and it is concluded that both stimulus noise and criterial
noise increase as range in the absolute-identification task is increased.
Researchers have theorized that the response variance inherent in unidimensional
absolute-judgment tasks is the result of two
underlying factors: stimulus noise and criterial or memory noise (Durlach & Braida,
1969; Gravetter & Lockhead, 1973; Wickelgren, 1968). Each time a stimulus is presented it is assumed to give rise to some internal psychological representation. These internal representations,
like the physical
stimuli, are conceived as lying along some
unidimensional psychological continuum.
Because of noise in the system, a given stimulus will not yield the same internal representation each time it is presented; rather, the
internal representations that arise are assumed to be normally distributed. I This
source of variance in the recognition process
is termed stimulus or sensory noise.
To make a decision regarding the identity
of a presented stimulus, the subject must obviously use some sort of response rule. It is
assumed that the subject partitions the range
As G. A. Miller (1956) made well known,
there are severe limits on the ability of subjects to identify absolutely unidimensional
stimuli. In terms of the Thurstonian framework just presented, errors in absolute identification are due to the overlap that occurs
among the various stimulus and criterial dis-
This work was supported in part by grants from the
Nationat Science Foundation to Harvard University.
I would like to thank R. Duncan Luce for the valuable
suggestions, help, and time he gave me at all stages of
this project.
Requests for reprints should be sent to Robert M.
Nosofsky, Department of Psychology and Social Relations, Harvard University, 33 Kirkland Street, Cambridge, Massachusetts 02138.
solute, of course, it is just the assumption generally made.
Another assumption
sometimes made is that it is the
double exponential. The rationale behind the normality
assumption, both theoretical and empirical, is reviewed
extensively in Green and Swets (1973); the rationale behind the double exponential is treated by Yellott (1977)
and Wandell and Luce (1978).
along which the psychological representations lie into as many intervals as there are
responses. The locations of these partitions,
or category boundaries, are presumably based
on subjects' memory for past presentations
of the stimuli as well as various other judgmental and bias factors. Due to imperfect
memory and other noise factors inherent in
the judgmental process, the locations of the
category boundaries may exhibit variability
over time. Like the stimulus distributions,
they are assumed to be normally distributed,
although there is no very strong reason for
this assumption. This source of variance in
the recognition process is referred to as cri-
299
teria/ or memory noise.
1 The
assumption of normal distributions is not ab-
-
,...
300
ROBERT M. NOSOFSKY
tributions. Two examples of these information-processing limitations and the problems
they pose for the Thurstonian framework are
now briefly reviewed.
Suppose that one holds fixed the number
of equally spaced signals and increases the
range that they occupy. One would expect
that spreading apart the stimuli along the
continuum should greatly facilitate performance, since the amount of overlap among
the various distributions ought to decrease.
The data, however, are otherwise. Pollack
(1952), for instance, had subjects attempt to
identify eight tones separated by equal logfrequency units. In one condition, the tones
occupied a 400-Hz range, whereas in a second condition they occupied an 8000-Hz
range. Pollack found no observable difference
in subjects' ability to identify the tones.
Experiments have also been performed in
which the locations of two stimuli remain
fixed while the locations ofthe other stimulus
set members are varied. In one condition, the
entire stimulus set ensemble encompasses a
narrow range, whereas in a second condition
the range is wide. The result obtained is that
ability to distinguish between the fixed pair
of stimuli is much worse in the wide-range
than in the narrow-range condition (Gravetter & Lockhead, 1973; Hartman, 1954).
Both of these results indicate that the distributions governing the various stimulus internal representations and category boundaries cannot be independent of the experimental context. It has generally been assumed
that if the Thurstonian framework for modeling these types of judgments is essentially
correct, then the variance of at least some of
these distributions increases with increasing
range of the experimental context. Two main
classes of theories have been put forth to explain the range effects in absolute-identification tasks. One class has emphasized the
variance of the criterial distributions (e.g.,
Durlach & Braida, 1969; Gravetter & Lockhead, 1973)2;the other class has emphasized
the variance of the stimulus distributions
(e.g., Luce, Green, & Weber, 1976).3The criterial noise theories stress memory and judgmental limitations in the absolute-identification task. The stimulus noise theories, on
the other hand, stress attentional and perceptual factors.
The main purpose of the current study is
to test experimentally, under the guidance of
a simple mathematical model and what seem
to be intuitively reasonable assumptions,
which of these noise components is actually
responsible. Are the range effects in absoluteidentification tasks due to increased stimulus
noise, criterial noise, or both? In what follows, the design of the experiment and the
assumptions made are outlined in schematic
fashion. Details of the experimental procedure are reported in the Method section.
Experiment I
Design and Assumptions
Design. Two stimulus sets were used, each
consisting of six signals varying only in auditory intensity. In a narrow-range condition,
the signals were located at 63,65,67,69,71,
and 73 dB SPL. In a wide-range condition,
the signals were located at 52,54,67,69,82,
and 84 dB SPL. The signal selected for presentation on a given trial was random in both
conditions. The important thing to note here
is that the center two stimuli (Signals 3 and
4) were the same across conditions. The expectation, of course, was that subjects' ability
to distinguish the center stimuli would be
worse in the wide-range than in the narrowrange condition.
The unique feature of thisabsolute-identification experiment was that instead of a
trial consisting of only a single stimulus presentation, multiple observations were used.
2 When formally quantified, Durlach and Braida's
( 1969) preliminary theory of intensity resolution speaks
only in terms of a single decision variable. The variance
of this decision variable is conceptualized,
however, as
consisting of two underlying
components:
sensation
noise and memory noise. Sensation noise is assumed to
be independent of the experimental context, but memory
noise is assumed to be directly proportional
to the
squared stimulus range measured in decibels. Since the
present article conceptualizes all memory noise as being
located in the criteria, Durlach and Braida's theory is
classified as a criterial noise theory.
3 It should be noted that the attention-band
theory of
Luce, Green, and Weber (1976) stresses that increased
stimulus noise is only an indirect consequence
of increasing range. A review of the theory would go beyond
the scope of the present article, however. The interested
reader is referred to Luce et aI. (1976) and to Luce
(I 977).
~
...
STIMULUS AND CRITERIAL
~
l
R
301
NOISE IN ABSOLUTE JUDGMENT
In particular, each trial consisted of independent presentations of the same signal either
I, 2, 3, or 4 times with equal probability.
Subjects made their responses only after all
the observations on a given trial were presented; they were urged to make use of all
the information that accrued during a trial.
To help ensure "independence" of signal presentations, repetitions were spaced by 2-sec
intervals.4
Assumptions. The experimental analysis
compares absolute-identification
performance on Signals 3 and 4 across the two
ranges and the differing number of signal
observations. The crucial assumption made
in the analysis of the experiment IS the following: As the subject hears repeated presentations of the same signal on a given trial, he
or she is gaining more information regarding
its true value, and the variance of the internal
representation is thereby reduced. On the
other hand, presenting repeated samples of
the same signal should not improve the subject's memory for past signal presentations.
In other words, in terms of the Thurstonian
framework, multiple observations should
serve to reduce stimulus noise, not criterial
noise.
This assumption is formalized in terms of
the following mathematical model. The internal representations of Signals 3 and 4 are
assumed to be normally distributed with
means f.L3and f.L4,respectively, and to have
common variance that is a function of both
range (R) and the number of observations
(N), us2(R,N). The category boundary established between the two representations is assumed to be normally distributed with variance that is a function only ofrange, u/(R),
and to be independent of the stimulus variances. The sensitivity measure, d3,4, may
then be expressed as a function of both R
and N as follows:
simple detection and k-alternative forcedchoice procedures. They have received empirical support in a five-alternative forcedchoice experiment (Swets, Shipley, McKey,
& Green, 1959), and in a signal-detection
experiment by Swets and Birdsall (1967). The
final internal representation in this model has
a mean equal to the mean of the internal
representation for a given stimulus (i.e., f.Ls)
but has variance equal to us2lN. (It is assumed
here that each internal representation is independent and identically distributed.) Thus,
d'(R, N) is given by
d' (R N )
3,4,
=
f.L4
-
1/us2(R)IN
f.L3
+ ue2(R) .
Since the unit of measurement is arbitrary,
f.L3 = 1 and rewrite the above
equation as
we may set f.L4-
[
1
2
_ us2(R)
d3,4(R, N) J -
N
2
+ ue (R).
d' f.L4 - f.L3
.
3,4- 1/us2(R, N) + u/(R) .
We are thus led to an experimental test of
whether it is criterial noise, stimulus noise,
or both that are increasing as one increases
range in an absolute-identification task. As
one plots (I Id'i as a function of IIN, it
should be linear with slope us2(R) and have
y intercept ue2(R). The best-fitting lines for
the narrow- and wide-range conditions will
be estimated and a comparison of us2(R) and
u/(R) made for each value of R.
Alternative assumptions. Before proceeding, it is worthwhile to deal with some questions that might arise regarding the assumptions stated earlier. First, although it is intuitively clear that multiple observations
should not reduce memory noise, one might
reasonably hypothesize that memory variance should grow with the number of observations, since more time passes from the last
presentations of the previous stimuli until the
current judgment is made (Kinchla & Smyzer, 1967; Siegel, 1972), This hypothesis,
however, is contrary to the theory of intensity
As a simple working hypothesis, it is assumed that the final internal representation
on a given trial is the average of the internal
representations that arise on each presentation. Similar models have been discussed by
Luce (1963) and Green and Swets (1973) for
prove identification performance. Pilot work performed
prior to the experiment had indicated that the time interval between repetitions was important. This observation is discussed in more detail in the General Discussion section.
4
It was expected that multiple observations
would im-
~
~
302
ROBERT M. NOSOFSKY
resolution developed by Durlach and Braida
(1969), which assumes that memory-noise
effects in absolute-judgment tasks are independent of time. Empirical evidence supporting this aspect of the Durlach and Braida
theory has been reported by Purks, Callahan,
Braida, and Durlach (1980) and by Luce,
Nosofsky, Green, and Smith (1982).
A second question concerns the independence assumption made by the averaging
model. It should be pointed out that to the
extent that there are correlations between
successive internal representations, the averaging model will underestimate the relative
amount of stimulus noise (and overestimate
the relative amount of criterial noise) in observers' recognition judgments. On the other
hand, to the extent that linearly increasing
plots of (1/d')2 are obtained as a function of
I/N, it is presumptive evidence that the independence assumption (and the memorynoise assumption) are approximately correct.
tinue listening to the signal being presented on a given
trial until the asterisks disappeared, after which they were
to enter their response. Subjects were urged to make use
of all the information
that accrued over the course of a
trial. After all the observers had responded on a trial,
feedback was provided and the next signal was presented
following a 500-msec delay. At the beginning of each
block of trials, the ascending sequence of intensities was
played three times. During these presentations, the identity of each
was printed
on the terminal
(I
= soft-
Results and Discussion
The main results of the experiment are
displayed in Figure 1, where (I/d3.4)2 is plotted as a function of 1/N, parametrized by R,
for each of the three subjects. Estimates of
d' for Signal Pair 3-4 for each subject were
.
1
Method
Subjects. Three subjects, two males and one female,
were hired. The subjects were undergraduates at Harvard
University and were paid $3.50 per hour for participating. All subjects had normal hearing.
Apparatus. The signals (wide-band noise gated on for
500 msec) were presented binaurally in quiet, via TDH39 headphones. The observers were tested in single-wall
sound-treated chambers (IAC-402A). The experiment
was controlled by a PDP-15 computer, and subjects entered their responses in terminals that were converted
to response boxes.
Procedure. Subjects participated in the narrow- and
wide-range conditions on alternating days to as large an
extent as possible over a period of about 2 months. Midway through collection of the data it was realized that
the wide-range results exhibited quite a bit more variability than did the narrow range. The remainder of the
data collection therefore consisted of wide-range testing.
Blocks of 100 trials were run, with rests between
blocks. Due to the use of multiple observations (with 2see intervals between each observation), the data collection was generally slow. Typically, five blocks of trials
were run in a daily 2-hour session. Approximately 3,300
total responses were obtained for each subject in the
narrow condition, and about 6,850 total responses were
obtained in the wide condition. (This means that for
each subject, about 140 responses were collected per
stimulus per number of observations in the narrow-range
condition, and about 285 responses were collected per
stimulus per number of observations in the wide-range
condition.) In addition, each subject received about 3
days of practice that were not included in the analyses.
At the beginning of each trial, a set of asterisks appeared on the terminal. Subjects were instructed to con-
signal
est, 6 = loudest). Following each block, subjects were
presented with a summary of their overall performance
on each signal.
3
21
or
..
5
... NARROW
I
..
C\2/",,\
''0
3
.........
.--t
'-/
2
III
1
i
1
i
1
2
l/N
Figure 1. Plots of (1Id3.4)2as a function of IIN for individual subjects in the narrow- and wide-range conditions.
11III
..,
STIMULUS AND CRITERIAL
'1
.1
303
NOISE IN ABSOLUTE JUDGMENT
obtained as follows: Whenever Stimulus 4
was presented and a subject responded 4 or
greater, it was considered a "hit," whereas a
response of 3 or less was considered a "miss."
Similarly, when Stimulus 3 was presented, a
response of 3 or less was considered a "correct rejection," whereas a response of 4 or
greater was a "false alarm." The data obtained for each subject were partitioned into
four stimulus-response (S-R) matrices contingent on the number of observations for a
given trial. Maximum-likelihood estimates of
d3.4were computed for each number of observations using the above definitions of hits
and false alarms.
The lines yielding a least-squared fit for
each data set were computed and are displayed along with the obtained data in Figure
1(except for the case of Subject 3, wide range,
whose data are obviously not in accord with
the mpdel). The linear approximations appear to give a fairly good description of the
data. The y intercepts, slopes, and correlations for each data set are summarized in
Table 1.
Restricting attention to Subjects 1 and 2,
the data seem to indicate both increased
slopes and intercepts for the wide- over the
narrow-range condition, implying that both
stimulus noise and criterial noise increase in
the wide-range condition. Unfortunately, it
is difficult to make statistical inferences on
the basis of these data. The fact that only four
data points are used to estimate each line
results in little statistical power. Furthermore,
several of the underlying assumptions that
one would make in a simple linear regression
analysis are not met.5 It is convenient at present to postpone any statements regarding statistical significance and instead to conclude
simply that these results give a preliminary
indication of both increasing stimulus noise
and criterial noise as range in the absoluteidentification task is increased. This hypothesis will be tested in more detail in Experiment 2.
Table I
Summary of the Intercepts, Slopes, and
Correlations for the Regression Lines
Displayed in Figure J
~
Condition
Yo
m
r
Narrow
Wide
.098
1.031
1.160
2.503
.942
.981
2
Narrow
Wide
.146
.956
.543
4.732
.997
.987
3
Narrow
Wide
.363
1.481
Subject
-
-
.992
-.218
Note. Yo = Y intercept; m = slope; and r = correlation.
the pattern of results obtained in these data.
The model used in this article assumed that
the multiple observations were averaged to
a final representation that formed a single
basis for decision. A plausible set of alternative models are those that view each observation as leading to a separate response.
These individual responses are then combined in some fashion to yield a final decision.
To simplify the discussion, attention is restricted to the wide-range condition. Here it
can be safely assumed that presentations of
Stimuli 3 and 4 lead only to responses of
either 3 or 4. (Other responses to these stimuli
actually occurred in the data about 2% of the
time.) The multisignal absolute-identification
task may thereby be conceptualized as a twoalternative situation for which the various
response-model predictions are well known
(Green & Swets, 1973; Luce, 1963).
Perhaps the most plausible response model
assumes that the final response is the one
chosen most frequently over the course of a
trial. hi the case of ties, the response is selected randomly from among those responses
chosen most frequently. It should be noted
that for the case of two possible responses,
the model discussed is equivalent to a model
in which the responses yielded on each observation are averaged. The final response
Response Models
The conclusions that one is able to reach
on the basis of these results are clearly modeldependent. It is pertinent, therefore, to consider other models that may be able to explain
S
In particular,
assumptions
regarding
homogeneity
of
variance and normality of the underlying error distributions are violated. Points higher up in the ( 1/d')2 space
have larger variances than those points lower down. In
addition, the (J/d')2 statistic is positively skewed.
ROBERT M. NOSOFSKY
304
-
selected is the one closest to this averaged data more efficiently. This task was accomresponse. If an averaged response of 3.5 is plished by making the following major
obtained, a response of either 3 or 4 is chosen changes in the experimental procedure:
1. All trials consisted of four stimulus obat random. Although plausible, this response
model is unable to account for the results servations. Instead of responding after all obobtained in the experiment. In particular, this servations on a trial had been completed, submodel predicts identical values of d' for one jects now responded after each stimulus oband two observations, as well as for three and servation. Thus, four responses were obtained
four observations. This is true whether or not per trial, one for each number of observathe criterion upon which each response is tions. Subjects were urged again to make use
of all the information that accrued over the
based varies independently from observation
to observation or remains fixed over the course of a trial in making their decisions.
course of a trial.
2. The narrow- and wide-range conditions
A second response model that might be were modified to contain four signals each
considered is the classic decision threshold
instead of six. In the wide-range condition
model. When applied to a multiple-obser- the signals were located at 53, 67, 69, and 83
vation signal-detection task, this model as- dB; in the narrow-range condition, they were
sumes that if any observation yields a detec- located at 65,67,69, and 71 dB. The reduction, then a positive response is made. This tion in stimulus set size allowed for a higher
model may be applied to the wide-range con- proportion of signal presentations that were
dition of the present experiment by defining relevant to the present analysis. Again, it
arbitrarily either Stimulus 3 or 4 to be the should be noted that the center two stimuli
"signal," and then by assuming that if any were identical across conditions.
3. Stimulus durations were reduced from
observation leads to the response associated
with the signal, this is the final response 500 to 100 msec.
Additional minor changes in the procedure
made. The decision threshold model, however, is unable to account for the pattern of are discussed below; in all other respects, the
results obtained it) this experiment. For ex- procedure was the same as in Experiment 1.
ample, tlie decision threshold model makes
the rather strong prediction that subjects' hit Method
rates and false-alarm rates will steadily inSubjects. Sixteen male and female subjects were
crease as the number of observations on a
hired. Eight subjects were assigned to the wide-range
given trial increases. This pattern of results condition,
and eight were assigned to the narrow-range
was not evident in the data of any of the sub- condition. All subjects were affiliated with Harvard Unijects except for the case of Subject 3 in the versity, most of them being undergraduates. All claimed
wide-range condition. (Unfortunately, it can- to have normal hearing. They were paid a minimum of
not be argued that Subject 3 was actually $6 plus small bonuses for good performances.
Procedure. All subjects were tested individually using
using this response strategy in the wide-range the same apparatus as in Experiment I. Each subject
condition, since it would in fact predict in- participated in a single 2-hour session. The experiment
creasing d' values with number of observa- was organized into blocks of 50 trials each, plus a beginning practice block of 20 trials (80 observations) that
tions. )
Experiment 2
The main purpose of Experiment 2 was to
collect more data to further validate the stimulus integration model and to test the hypothesis that both stimulus noise and criterial
noise increase as range in the absolute-identification task is increased. As mentioned
previously, the data-collection process in Experiment 1 was extremely slow. An effort was
made in the present experiment to collect
was not included in the analysis. At the start of each
block, the ascending sequence of intensities was played
twice, with the identity of each signal printed on the
terminal (I = softest, 4 = loudest). Following each block,
subjects were presented with a summary of their overall
performance
on each signal.
On each trial, the same randomly selected intensity
was played four times. Subjects entered a response for
each stimulus observation; following each response there
was a 5OO-msec delay prior to the presentation
of the
next stimulus observation. After the fourth and final response, the correct answer for the trial was printed on
the terminal screen for 500 msec.
An average of 187.5 responses was collected per stimulus per number of observations for subjects in the wide-
"
...
STIMULUS AND CRITERIAL NOISE IN ABSOLUTE JUDGMENT
range condition, and an average of 150 responses was
collected per stimulus per number of observations for
subjects in the narrow-range condition.
305
4 ~. VIDE
..NARROV
Results and Discussion
,
~
The relevant stimulus pair in the present
experiment consisted of Signals 2 and 3. An
analogous procedure was used to estimate
(l/d2,3)2 in this experiment as was used to
3
estimate (l/dJ,4)2 in Experiment l. Values of
(l/db)2 were computed for each number of
stimulus observations for each subject. The
averaged (I /db)2 values are plotted as a function of l/N (where N is the number of stim<:\1"
ulus observations) for both the narrow- and
'res 2
the wide-range conditions in Figure 2. The
least-square lines for each data set are dis"played as well.
......-t
'-/
As is evident from the figure, the data are
again well described by the hypothesized
straight-line fit. For the wide-range condition,
the correlation is .996 with an intercept of
.748 and a slope of 2.962; for the narrow1
range condition, the correlation is .997 with
an intercept of .120 and a slope of .377.
Equally regular results are obtained if the individual subjects' d' values are first averaged
and then transformed to (l/d')2.
The individual (l/d2,3)2 values obtained
for each subject are presented in Table 2,
I2J
along with the intercepts, slopes, and correlations of the least-square lines. The results
11
1
1
4j 2
;
are exceedingly regular for the individual
subjects in the narrow-range condition. The
results for the subjects in the wide-range condition exhibit quite a bit more variability. In Figure 2. Plots of the averaged (l/d'z.3)2 values as a funcpart, this difference might be expected, since tion of I/N for both the narrow- and wide-range conmore variable quantities are being estimated. ditions.
Nevertheless, it is extremely likely that there
are large individual differences in the true
amounts of stimulus noise and criterial noise both significantly larger intercepts, t*(7) =
2.576, P < .05 (directional; i.e., a one-sided
for subjects in the wide-range condition.
The overall results of this experiment ex- t test), and slopes, t*(7) = 2.26, p < .05 (dihibit a similar pattern to that found in Ex- rectional), for the wide- over the narrowperiment 1, and they lead to a similar con- range condition.
Finally, it should be pointed out that the
clusion: Both stimulus noise and criterial
theoretical
predictions made by the stimulus
noise seem to increase as range in the absolute-identification task is increased. This ob- integration model regarding the cumulative
servation can now be corroborated by a sta- S-R matrices and the estimates of u/(R) and
tistical test. Using the individual intercepts u/(R) are identical under the following two
and slopes obtained for each subject as data,
Satterthwaite's approximation for a t test
6 The asterisk signifies that this is an approximation
with unequal population variances reveals to a t test.
l/N
.J
~
-"
306
ROBERT M. NOSOFSKY
Table 2
Values of (lld'l as a Function of IIN. and the Intercepts. Slopes. and Correlations of the
Least-Square Lines for Individual Subjects in the Narrow- and Wide-Range Conditions
Subject
1/4
1/3
1/2
1/1
Yo
m
~
r
Narrow range
I
2
3
4
5
6
7
8
.1947
.3222
.2948
.1547
.2124
.2167
.2017
.2022
.2106
.3835
.2795
.1342
.2410
.2160
.2187
.2438
.2515
.4280
.3107
.2144
.2759
.3188
.2363
.3441
.5427
.5183
.6284
.3318
.5246
.5196
.4553
.4854
.050
.289
.129
.074
.094
.098
.097
.127
.480
.237
.480
.258
.422
.423
.347
.369
.986
.965
.964
.977
.991
.994
.980
.984
Average
.2249
.2409
.2975
.5008
.120
.377
.997
Wide range
I
2
3
4
5
6
7
8
1.8622
.9180
2.9411
1.9205
2.2039
1.0309
.5675
.9938
1.6559
.9776
2.9411
2.6954
2.0223
1.0113
.6898
.9580
1.9457
1.3702
6.6873
2.1418
2.7594
1.4058
.8178
1.1466
6.1027
1.5317
9.8578
2.9321
3.9840
2.5732
1.5223
1.1310
-.291
.779
.628
1.907
1.396
.375
.239
.951
6.111
.808
9.559
.989
2.586
2.171
1.268
.205
.957
.908
.962
.706
.981
.993
.996
.721
Average
1.5547
1.6189
2.2843
3.7044
.748
2.962
.996
Note. Yo = Y intercept; m = slope; and r = correlation.
realizations of the model: (a) The criterion
varies independently on each observation,
and (b) the criterion varies independently
between trials but remains fixed over the
course of a given trial. Although it might be
possible to distinguish these two versions of
the model by examining subjects' response
sequences within trials, such an analysis has
no bearing on the main issue of concern in
this study.
General Discussion
Utility of Multiple Observations
An initial conclusion that may be reached
is that multiple observations in the present
absolute-identification experiments led to
improved identification performance. Although this result might not be of much surprise to a number of investigators, it is an
important finding because it helps clarify previous conclusions that have been reached regarding the processing of redundant stimulus
information. Garner (1972, 1974), for example, has reviewed and organized a large
number of results regarding the role of stimulus redundancy in perceptual discrimination. An initial conclusion that Garner (1972)
reached was that simple repetition of a stimulus (either spatial or temporal) will improve
discrimination performance only if the original performance limitation is due to inadequate stimulus energy. That is, repetition
redundancy was thought only to improve
discrimination performance indirectly by increasing detection opportunity. This view was
later modified (Garner, 1974) to include the
possibility that some sort of averaging process
could take place over time in cases in which
the performance limitation was not due
solely to inadequate stimulus energy. Clearly,
the performance limitation in the present
absolute-identification task was not a detection problem. Multiple observations served
instead to improve the fine gradedness of the
representation on the informational continuum, leading to improved discrimination
performance. This finding lends further support to the latter conclusion reached by
Garner.
Caution should be expressed, however, in
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STIMULUS AND CRITERIAL
..
~
... ,
NOISE IN ABSOLUTE JUDGMENT
how these results might generalize to other
absolute-identification experiments. Even in
the present study, multiple observations failed
to improve Subject 3's identification performance in the wide-range condition of Experiment I and Subject 8's performance in
the wide-range condition of Experiment 2.
Pilot work conducted prior to the actual experiment indicated that the time interval between successive presentations was a crucial
factor. Simply increasing the duration of the
signal presentations or using short interobservation intervals was far less successful than
the 2-sec interobservation intervals eventually u~d. (In Experiment 2, subjects' responses served to lengthen the interobservation intervals.) Garner and Creelman (1964)
found no improvement in subjects' absolute
identification of a set of visual stimuli when
stimulus duration was increased from 40 to
100 msec. On the other hand, Lockhead
(1966) and Keeley and Doherty (1968) found
substantially improved identification performance using multiple observations with relatively long interobservation intervals. It is
likely that Garner and Creelman's (1964; p.
169) argument that "an increase in duration
is essentially the repetition of the same stimulus" is incorrect. Perhaps it is important in
these experiments that the subject be enabled
to sample independent presentations of the
stimulus in order to gain an improved representation. Separating the stimulus observations further apart in time may allow the
independence criterion to be more closely
met. In any case, the usefulness of multiple
observations in improving identification performance will almost certainly depend on the
type of stimuli used and the underlying processing limitations in the actual task (Garner,
1972, 1974), the time intervals used between
observations, and the ability and willingness
of subjects to use efficiently the information
that accrues over the course of a given trial.
Stimulus Integration Model
The results of this experiment also provided support for a particular model of information integration for multiple stimulus
observations. The model assumed that the
final stimulus internal representation was
simply the average of the representations
307
yielded on each observation. It was argued,
however, that criterial variance should be independent of the number of stimulus observations on a given trial.
It should be pointed out that although the
model was specifically used to test certain
hypotheses regarding the multisignal absolute-identification paradigm, it might also be
applicable to simpler two-alternative absolute-identification designs or signal-detection
tasks that use multiple observations. As an
example, the model is applied to the results
of a study performed by Ulehla, Halpern, and
Cerf (1968). These researchers conducted an
experiment requiring subjects to identify the
direction of tilt of a line (either left or right).
Multiple observations were used in an attempt to test the integration of information
model of signal-detection theory that was
presented in Green and Swets (1973). This
model, like the one used in the present study,
assumes that the final internal representation
is the average of the representations yielded
on each trial. Because it is a traditional signal-detection model, however, it effectively
assumes that there is zero criterial variance.
The Ulehla et al. (1968) study (Experiment
2) used five observation intervals, with subjects making a response on each interval. It
was correctly concluded that each observation past the second observation yielded successively less mean improvement in d'than
predicted in the integration model of signal
detection theory.
The results of the Ulehla et al. study exhibit a high degree of regularity, however,
when viewed within the framework of the
stimulus integration model used in the current study. In Figure 3, diamonds are plotted
to represent values of(lld')2 computed from
the d' values presented in Experiment 2 of
Ulehla et al. (1968).7 These values are plotted
as a function of IIN, where N is the number
of stimulus observations on which each d'
value is based. As is evident from the figure,
the data are extremely well described by a
straight line function (r = .997) with a slope
7
The (I/d')2 values were computed by transforming
each of the individual subjects' d' values to (l/d'f,
and
then averaging these values. Equally regular results are
obtained if the mean d' values reported are transformed
directly to (1/ d12.
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j
308
C\Z""
''0
".......
'-/
ROBERT M. NOSOFSKY
of noise in recognition processes. A logical
analysis seems to indicate that multiple observations should only serve to reduce stimulus noise, not criterial noise. The traditional
signal-detection information integration
model fails to make this distinction.
1.5
1.4
1.3
12
1.1
12
.9
The Range Effect in AbsoluteJudgment Tasks
.8
.7
.6
.5
.4
.3
2
.1 I
;;4 i3
is
1
2
1
1
l/N
Figure 3. Application of stimulus integration model to
the multiple observation data of Ulehla et aI. (1968).
(Diamonds are the averaged [1/d12 values from their
Experiment 2, and triangles are the averaged [1/d12 values from their Experiment 1.)
of 1.28 and an intercept of .09. According to
the present model then, the stimulus noise
in their experiment was 1.28 and the criterial
noise, which was unaffected by the number
of stimulus observations, was .09.
Also plotted in Figure 3 are triangles that
represent the transformed data from Ulehla
et al.'s Experiment 1.8This study was similar
to their Experiment 2; some of the differences
were that only three observation intervals
were used as well as a longer stimulus exposure duration. The results are again well
described by a straight line function (albeit
only three data points) with a correlation of
.988, a slope of .32, and an intercept of .07.
The reduced stimulus noise in this experiment relative to that in Experiment 2 is consistent with the fact that longer stimulus exposure durations were used. The virtually
identical amounts of criterial noise obtained
in the two experiments is also an intuitively
reasonable finding.
The theoretical advance made with the
present model involves the realization that
there are two conceptually distinct sources
A final conclusion that may be reached is
that if the underlying assumptions of the
stimulus integration model are correct, then
both the stimulus noise and the criterial noise
associated with the center signals increased
as range in the present absolute-identification
tasks was increased. One can almost certainly
infer from this conclusion that the range effects for absolute-identification tasks using a
larger number of interior signals are also best
explained by a combination of increasing
stimulus and criterial noise. Luce et al. (1982)
concluded that sequential effects in absolute
identification are best explained in terms of
both stimulus and response factors. Since
these researchers viewed range effects and sequential effects in absolute identification as
being intimately connected, both studies conclude that a full explanation of the range effect in absolute identification will require recourse to both stimulus- and criterial-noise
factors.
8 I deleted Ulehla et aI.'s (1968) Subject 2 from this
analysis (a policy that the original experimenters followed as well). This subject obtained an average d' value
of .20, whereas the other seven subjects' average d' values
ranged from 2.0 to 2.5.
References
Durlach, N. I., & Braida, L. D. Intensity perception. I.
Preliminary theory of intensity resolution. Journal of
the Acoustical Society of America, 1969,46, 372-383.
Gamer, W. R. Information integration and form of encoding. In A. W. Melton & E. Martin (Eds.), Coding
processes in human memory. Washington, D.C.: V. H.
Winston, 1972.
Gamer, W. R. The processing of information and structure. Potomac, Md.: Erlbaum, 1974.
Gamer, W. R., & Creelman, C. D. Effect of redundancy
and duration on absolute judgments of visual stimuli.
Journal of Experimental Psychology, 1964,67, 168172.
Gravetter, F., & Lockhead, G. R. Criterial range as a
frame of reference for stimulus judgment. PsychologicalReview, 1973,80,203-216.
-
STIMULUS AND CRITERIAL NOISE IN ABSOLUTE JUDGMENT
Green, D. M., & Swets, J. A. Signal detection theory and
psychophysics. New York: Wiley, 1973.
Hartman, E. B. The influence of practice and pitch-distance between tones on the absolute identification of
pitch. American Journal of Psychology, 1954,67, 114.
Keeley, S. M., & Doherty, M. E. Simultaneous and successive presentations of single-featured and multi-featured visual forms: Implications for the parallel processing hypothesis. Perception & Psychophysics, 1968,
4, 296-298.
Kinchla, R. A., & Smyzer, F. A diffusion model of perceptual memory. Perception & Psychophysics, 1967,
2,219-229.
Lockhead, G. R. Visual discrimination and methods of
presenting redundant stimuli. Proceedings of the 74th
Annual Convention of the American Psychological Association, 1966,67-68.
Luce, R. D. Detection and recognition. In R. D. Luce,
R. R. Bush, & E. Galanter (Eds.), Handbook of mathematical psychology (Vol. 1). New York: Wiley, 1963.
Luce, R. D. Thurstone's discriminal processes fifty years
later. Psychometrika, 1977,42,461-489.
Luce, R. D., Green, D. M., & Weber, D. L. Attention
bands in absolute identification. Perception & Psychophysics, 1976,20,49-54.
Luce, R. D., Nosofsky, R. M., Green, D. M., & Smith,
A. F. The bow and sequential effects in absolute identification. Perception & Psychophysics, 1982,32,397408.
Miller, G. A. The magical :mber seven, plus or minus
two: Some limits on our capacity for processing information. Psychological Review, 1956,63,81-97.
Pollack, I. The information of elementary auditory dis-
309
plays. I. Journal of the Acoustical Society of America,
1952,24, 745-749.
Purks, S. R., Callahan, D. J., Braida, L. D., & Durlach,
N. I. Intensity perception. X. Effect of preceding stimulus on identification performance. Journal of the
Acoustical Society of America, 1980,67,634-637.
Siegel, W. Memory effects in the method of absolute
judgment. Journal of Experimental Psychology, 1972,
94, 121-131.
Swets, J. A., & Birdsall, T. G. Deferred decision in human signal detection: A preliminary experiment. Perception & Psychophysics, 1967,2, 15-24.
Swets, J. A., Shipley, E. F., McKey, M. J., & Green,
D. M. Multiple observations of signals in noise. Journal of the Acoustical Society of America, 1959, 31,
514-521.
Ulehla, Z. J., Halpern, J., & Cerf, A. Integration of information in a visual discrimination task. Perception
& Psychophysics, 1968,4, 1-4.
Wandell, B., & Luce, R. D. Pooling peripheral information: Average versus extreme values. Journal of
Mathematical Psychology, 1978, 17, 220-235.
Wickelgren, W. A. Unidimensional strength theory and
component analysis of noise in absolute and comparative judgments. Journal of Mathematical Psychology,
1968,5, 102-122.
Yellott, J. I., Jr. The relationship between Luce's choice
axiom, Thurstone's theory of comparative judgment,
and the double exponential distribution. Journal of
Mathematical Psychology, 1977,15, 109-144.
Received June 8, 1982
Revision received September 30, 1982 .
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