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THE AUTOMATIZATION OF VISUAL-MEMORY SEARCH
Denis Cousineau and Serge Larochelle
Université de Montréal
Running head: THE AUTOMATIZATION OF SEARCH
Correspondence: Serge LarochelleDépartement de PsychologieUniversité de MontréalP.O. Box 6128, Station Centre-villeMontréal, Québec Canada, H3C 3J7
E-Mail: [email protected] or [email protected].
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Abstract
In this article, we examine cross-sectional and longitudinal aspects of performance in the
single-frame, visual-memory search paradigm in order to assess the validity of Schneider and
Shiffrin’s (1977) claims, also present in Logan’s (1988) instance theory, that the mapping
between individual stimuli and responses must be consistent for automatization to occur and that
automatic processing is fundamentally different from controlled processing. In addition to
consistent mapping (CM) and varied mapping conditions (VM), the Experiment reported
involved a categorical mapping condition (CVM) in which different sets of stimuli switched roles
as targets and distractors over trials. The stimuli were either all digits or all letters
(HOMOgeneous condition) or mixed digits and letters (HETEROgeneous condition). Among the
main findings of this study was the fact that the memory and display load effects obtained in
condition CVM-HETERO were small and additive, which satisfies Schneider and Shiffrin’s main
criterion of automaticity. Logan’s criterion of automatization was also satisfied, both the mean
response times and their standard deviations decreasing at a similar rate with practice. These
results suggest that consistent stimulus-response mapping is not necessary to achieve automaticity
and that automatization of visual-memory search does not result from the storage and retrieval of
S-R associations. A simple feature-based model is described. In the model, the same learning and
search processes operate throughout learning in all mapping and stimulus conditions. The model
called CL because it captures the main aspects of cross-sectional and longitudinal performance
shows that it is not necessary to postulate qualitatively different processes to account for the
automatization of visual-memory search.
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The goal of the present study is to better specify the processes involved in the
automatization of performance in a joint visual and memory search task. Performance in such a
task has often been shown to depend on the mapping of stimuli to responses. The Experiment
reported here shows that the existence of categorical distinctions among stimuli is as critical. By
contrast with much prior research devoted to visual-memory search tasks, the present study is
not only concerned with cross-sectional aspects of performance e.g., with the properties of
performance obtained after extensive training. We also focus on the longitudinal aspects of
performance i.e., on the evolution of performance with practice, in an attempt to specify how
stimulus composition and mapping affect the dynamics of learning. The general question
underlying this research is whether automatic processing is fundamentally different from limited-
capacity, controlled processing, with the former gradually replacing the latter through training, or
whether there is only one type of processing which becomes increasingly efficient with practice.
The present study addresses three important theories of automaticity, two of which are
the automatic attention attraction theory proposed by Schneider and Shiffrin (1977; Shiffrin &
Schneider, 1977), and Logan's (1988, 1992) instance theory. These two theories do not have the
same focus. The theory put forth by Schneider and his colleagues aims at differentiating
automatic and controlled processing and is therefore concerned with the characteristics of
asymptotic performance. By contrast, Logan's theory is primarily concerned with the dynamics
of automatization, the goal being to characterize and explain the transition from controlled to
automatic performance. However, both theories assume that there is a fundamental, qualitative
difference between automatic and controlled processing and that a consistent mapping of stimuli
to responses is critical for achieving automaticity.
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By contrast with the above two theories, the third view of automatization does not
attribute any specific role to stimulus-response mapping. Search is not even assumed to rely on a
unitized representation of the stimuli. It is thought to proceed instead on a featural basis. Fisher
(1986) has described a single-process, feature comparison model, which he claims can account
for both controlled and automatic performance in a visual search task. According to the model,
the advantage of automatic over controlled performance simply arises from the smaller number
of feature tests required to locate the target. In the present manuscript, we describe a feature
comparison model, whose aim is to account for performance obtained throughout learning in a
single-frame, visual-memory search task under all kinds of mapping conditions and with
different sorts of stimuli.
Stimulus-response mapping
In the single-frame task, subjects have to commit to memory a set of one or more items
and to search for the presence of any of these potential targets in a single visual display
containing one or more elements, some of which serve as distractors. The number of items in
memory (called the memory or M set) and on the display (called the display or D set) is rarely
greater than seven plus or minus two (Miller, 1956), and usually smaller, so that error rates in the
task are low and response times serve as the major dependent variable. Schneider and Shiffrin's
(1977; Shiffrin &Schneider, 1977) seminal study also involved a multiple-frame task in which
subjects had to detect the presence of one or more targets in a series of multi-element displays
presented in rapid succession, the measure of performance being the percentage of correct
responses.
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In Schneider and Shiffrin's (1977) experiments, some subjects had to search for one or
more digits among a set of consonants. So, whenever a digit was present in the display, it was
also a member of the memory set and the correct response was 'yes'. For these subjects, digits
were consistently mapped onto positive responses over trials, as were consonants for the subjects
who had to search for consonants among digits. The basic finding, which was replicated often
since Schneider and Shiffrin's study, is that subjects in consistent mapping conditions (labeled
CM) come to detect the target very rapidly and accurately. Moreover, with practice, performance
becomes relatively independent of the number of items in memory and the display set.
In a sense, the absence of a memory set size effect is hardly surprising. As Schneider and
Shiffrin noted, subjects searching for digits among consonants can ignore totally the items in the
memory set since the mere presence of a digit on the display is sufficient to signal a positive
response. A similar situation prevails for subjects searching for consonants among digits. The
absence of display size effects in CM conditions is more surprising because it suggests that the
presence of a target can be detected without a limited-capacity search. Schneider and Shiffrin
argued that, with sufficient practice, targets come to automatically attract attention.
In order to demonstrate that consistent mapping is necessary for automatization,
Schneider and Shiffrin (1977) contrasted performance obtained in CM conditions to that
obtained in conditions where stimulus-response mapping was varied. The stimuli used in the
varied mapping conditions (labeled VM) were either all digits or all consonants, depending on
the subjects. The targets and distractors were chosen randomly over trials, so that a given
stimulus was associated to a positive response on some trials and to a negative response on
others. The performance obtained in VM conditions showed little improvement in the sense that
the detection rates and search times remained largely dependent on both the number of potential
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targets (i.e., memory set size), and the number of characters on the display (i.e., display size).
Schneider and Shiffrin attributed the results obtained in VM conditions to a limited-capacity
search process consisting in sequentially comparing the memory and display items.
Category distinctions
As Cheng (1985) pointed out, the experiments described contain two confounds of a
categorical nature. First, for any given subject, the targets and distractors used in the CM
conditions belonged to two distinct and well-known categories: digits and consonants, whereas
the stimuli used in the VM condition belonged to only one category: digits or consonants. So, the
advantage of the CM condition can be attributed to this categorical distinction (which we will
refer to as heterogeneity among the stimuli) as much as it can be attributed to consistent
mapping. Schneider and Shiffrin were aware of this confound and countered the argument by
presenting the results of an earlier study by Briggs and Johnsen's (1972). In this study, the
stimuli were homogeneous; i.e. they were all letters. In one condition, the VM condition, all
stimuli served equally often as targets and as distractors whereas, in two other conditions, the
CM conditions, the targets and distractors were chosen among two separate sets of letters. The
results obtained by Briggs and Johnsen in the VM condition showed the same interaction pattern
found in Schneider and Shiffrin's experiment. The combined effects of memory and display size
were much reduced but not eliminated from the CM conditions. In order to account for this small
load effect, Schneider and Shiffrin argued that Briggs and Johnsen's subjects did not have
enough practice to fully automatize the task.
Shiffrin and Schneider (1977) also performed an experiment (Experiment 1) using
homogeneous stimuli, i.e. consonants, in a CM condition. Like Schneider and Shiffrin's (1977)
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first experiment, this experiment involved a multiple-frame task. However, memory size was
fixed at 4 (labeled M4) and display size at 2 (labeled D2) for the entire experiment. Performance
in terms of hit rates (82%) failed to reach the level obtained with heterogeneous stimuli (92%) in
the M4D2 condition of Schneider and Shiffrin's first experiment. Although quite comparable for
the M4D2 condition, amount of practice was greater in Schneider and Shiffrin's experiment,
since it involved other memory and display sizes. So, the differences observed across
experiments could be due to a differential amount of practice. However, the presence vs. absence
of a pre-established categorical distinction between targets and distractors could also have
contributed to the results. Since memory and display size were fixed in Shiffrin and Schneider's
experiment, it is difficult to determine whether memory search or visual search or both would be
affected by pre-established categorical distinctions. One goal of the present Experiment was to
investigate the effects of such distinctions on automatization of visual and memory search, under
comparable amounts of practice.
The second confound of a categorical nature in Schneider and Shiffrin's (1977)
experiments is the following: Even if stimuli are homogeneous, they nonetheless form two
disjoint sets in CM conditions: a set of targets and a set of distractors. This is not the case in the
VM condition. Shiffrin and Schneider (1977) were also aware of this second confound and they
designed a critical experimental condition to investigate it. In this condition, called categorical
varied mapping (labeled CVM), the stimuli are divided in two sets as in CM conditions.
However, the two sets switch roles over trials. If, on a given trial, the potential targets are chosen
from one set, the distractors are picked from the other, and vice versa. So, the stimulus-response
mapping is not consistent, but the stimuli behave categorically. If, on a given trial, a member of a
set is a target, then the other members of the same set will not be distractors.
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Shiffrin and Schneider tested this condition with homogeneous stimuli, i.e. consonants,
in a multiple-frame task (Shiffrin and Schneider, 1977, Experiment 3). Performance was found
to be much better in the CVM condition than in the VM condition. Moreover, with practice, the
effect of memory set size disappeared suggesting that, in the CVM condition, subjects proceeded
by determining to which set the display items belonged instead of comparing the display items to
those in memory. Unfortunately, display size was not varied in the experiment. Hence, it is not
known whether search in the display can proceed automatically in CVM conditions.
Nonetheless, Shiffrin and Schneider argued that only consistent mapping could produce
automaticity. Their conclusion was based on the rapid improvement of performance observed
when subjects were transferred to a CM condition after extensive initial training in VM and
CVM conditions.
The only single-frame experiment approximating a CVM condition is that of Dumais
(1979, Experiment 3; also described in Shiffrin & Dumais, 1980; and in Shiffrin, Dumais &
Schneider, 1980). The experiment involved many sets of stimuli (labeled A, B, C), each
comprising a mixture of characters: Roman, Greek and Hebrew letters as well as Arabic digits.
In one condition, the A stimuli served as targets and the B stimuli as distractors. In another
condition, the B stimuli were targets and the C stimuli, distractors. In a third condition, the C
stimuli served as targets to be found among A stimuli. In the first part of the Experiment, the
different conditions were run in separate blocks of trials so that stimulus-response mapping was
consistent within each block but varied over blocks. In a later part, the three conditions occurred
within blocks, but the set distinctions were preserved. Similar but mixed results were obtained in
both parts of the Experiment. In the best condition, performance was comparable to that
obtained in a control CM condition. At worst, performance was comparable to that obtained in a
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control VM condition. Moreover, the best and worst conditions were not the same across
subjects.
Available evidence concerning CVM performance is therefore quite ambiguous. It is also
incomplete: we do not know which level of performance would be reached in CVM if the two
sets of stimuli were taken from different categories such as digits and letters. One goal of our
Experiment was to compare performance in CVM conditions to that obtained in CM and VM
conditions. The stimuli used in each mapping condition were homogeneous, i.e. composed of
digits or consonants, or heterogeneous, i.e. composed of both digits and consonants. Another
important condition for resolving the debate over mapping vs. categories would involve
consistent S-R mapping but no set distinction between the targets and distractors. Unfortunately,
such a mapping condition is impossible. Our Experiment is therefore limited to the three
realizable mapping conditions.
Training effects
One of the best known learning phenomenons is that performance generally improves as a
power function of practice. The power curve is represented by the following formula
M = a + b N-c
where M is a measure of performance such as response time, and N is the number of practice trials
(or sessions; see Strayer and Kramer, 1990). a represents the asymptote, that is, the best
performance that can be achieved with practice. b represents the difference between initial and
asymptotic performance. At trial (or session) 1, performance is thus a + b. Finally, c is the learning
rate. The larger c is, the more pronounced the improvement observed over successive trials (or
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sessions). Newell and Rosenbloom (1981) found the power curve to be so pervasive over tasks and
performance measures as to christen it the power law of practice.
Strength theories of learning (Anderson, 1982, 1992; Schneider, 1985; Schneider and
Detweiler, 1988; Cohen, Dunbar & McClelland, 1990) account for the power law by assuming that
the strength of the associations linking the stimuli and the responses in a task, or the associations
among intervening representations, increases by a constant proportion of the strength left to be
gained. As a result of these changes in strength, performance improves much more rapidly early in
learning than after extensive training. Technically speaking, strength theories predict an exponential
rather than a power curve. However, such curves are difficult to distinguish empirically. So, the
issue of the best-fitting learning curve will not be at stake here (see Heathcote & Mewhort, 1995).
Strength theories can be used to account for performance obtained in CM conditions.
Consider the simplest, 'no-search' situation in which the memory and the display sets each contain
only one item (M1D1). Suppose further that both sets contain the same item: the target. In such a
situation, response times could decrease as a power function of practice because of the increasing
associative strength linking the stimulus to the positive response. Similar predictions could possibly
still hold with more items in the memory set. Since different stimuli serve as targets and distractors
in CM conditions, subjects can ignore the memory set altogether and proceed by simply
determining which response each displayed stimulus is associated with. In this case, performance
obtained on trials that would otherwise require memory search (such as M4D1 trials) could
resemble that obtained on no-search trials. Finally, performance could also reduce as a power curve
in conditions requiring visual search, such as M1D4 for instance. Dumais (1979, see also Shiffrin
& Dumais, 1981; Shiffrin, Dumais & Schneider, 1980) has indeed proposed a strength model of the
reduction of visual search in CM conditions. According to the model, all stimuli have about the
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same attention attraction power at the start of training. Practice with consistent S-R mapping is
assumed to increase the attentional strength of the stimuli serving as targets and to decrease the
attentional strength of the stimuli serving as distractors. As a result of this strength adjustment, time
to locate a target could reduce as a power function of practice. Such differential attentional strength
cannot develop in VM conditions since the same stimuli serve equally often as targets and as
distractors.
Another theory that purports to account for learning and automatization is Logan's (1988,
1992) instance theory. According to a simple S-R interpretation of Logan’s theory, learning occurs
by storing more and more instances of the stimulus-response associations required by a given task.
Retrieval of these associations is conceived as a competition or race among all the relevant traces
that have been stored. As the number of such traces increases with practice involving a given
stimulus, so does the likelihood that a relevant trace will be accessed rapidly. However, as access
time decreases, so does the number of traces that can be accessed even faster. As a result, Logan’s
theory also accounts for the fact that response times decrease faster during the early stages of
learning. One important prediction of instance-based theory is that both the mean (MN) and the
standard deviation (SD) of RTs should decrease at the same rate, since the same competition
process is responsible for both. So, both the mean RTs and their standard deviations should
decrease as power functions, having the same exponent c. More recently, Logan (1992) has argued
that the entire distribution of RT should change as a power function of practice, with a unique
exponent.
Instance-based learning could be responsible for the performance observed in CM
conditions of visual-memory search tasks. Every correct positive trial would leave a new trace of
the association linking the target presented and the 'yes' response so that, on later trials, the correct
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response could be obtained by accessing these stored associations, in the manner described by
Logan. One would therefore expect predictions derived from Logan's theory to apply to positive
RTs. We will not consider Logan's predictions concerning the distributional aspects of RTs here.
However, we will test whether the MNs and SDs conform to power curves with identical rate
parameters, which we will consider to be Logan's criterion of automatization1.
Since S-R mapping is inconsistent in CVM conditions, Schneider and Shiffrin's theory and
Dumais' model do not make the same predictions for CVM as for CM conditions. Neither does
Logan’s instance theory, when interpreted in strict S-R terms. There is however another
interpretation of Logan’s theory that could allow for automatization to occur in CVM conditions.
This alternative interpretation assumes that two types of associations are learned throughout
practice (Logan, 1990). One type of associations would specify the set membership of each
stimulus. The second type of associations would link the sets to the desired response on a given
trial. Of these two types of associations, the first are consistent in CVM conditions and could lead
to substantial improvement in performance, perhaps to the point of satisfying Logan's
automatization criterion. However, if fully consistent S-R mapping is necessary for automatization,
then the dynamics of performance in CVM conditions should resemble that obtained in VM
conditions.
As previously mentioned S-R associations are totally uninformative about the response
required on a given trial in VM conditions. Moreover, the stimuli do not form distinct subsets in
VM conditions. Therefore, one does not expect Logan's criterion to be satisfied in VM conditions
under any interpretation of instance theory. By contrast, a single-process view leads to expect that
Logan's criterion will either be satisfied under all mapping conditions or under none. Prior to the
current study, we could not tell which mapping or stimulus condition would meet Logan's criterion.
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Fisher's work (1984, 1986; Fisher, Duffy, Young & Pollatsek, 1988) has dealt almost exclusively
with the multiple-frame task; his model concerns only asymptotic performance and only the mean
percent correct is taken into account. Although Schneider and Shiffrin (1977) have been concerned
with the mean and standard deviation of search RTs, they have focused only on the SDs obtained
after extensive practice under VM conditions. Among the few studies that have been concerned
with the longitudinal aspects of performance in search tasks, none have analyzed the joint evolution
of MNs and SDs with practice. One goal of the present study was to fill this void.
METHOD
The Experiment involved the single-frame search task. The main reason for preferring
this task to the multiple-frame search task is that all theories addressed here make predictions
about reaction times, which are the main performance measure in the single-frame task. Three
different mapping conditions were involved: CM, VM and CVM. The stimuli used in each
mapping condition were either homogeneous (labeled HOMO), i.e. composed of digits or
consonants, or heterogeneous (labeled HETERO), i.e. composed of both digits and consonants.
Subjects
Twenty-eight undergraduate students participated to the Experiment. Each received 100
$CAN for completing ten experimental sessions of approximately one and a half hour each.
Duplication of one experimental condition involved four subjects, each of whom could earn an
additional 2.50 $CAN per session if performance exceeded that of a matched subject. In order to
prevent discouragement, subjects were informed of the result of this competition at the end of
the Experiment only.
Stimuli
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The digits used in the Experiment were chosen in such a way that the stimuli serving as
targets and as distractors in the CM condition could not be reliably distinguished on the basis of
a simple perceptual feature such as angular vs. curved shape. Other constraints were that the set
of potential targets and the set of potential distractors in the CM condition contain the same
number of even and odd digits, and of large and small digits (i.e., above and below 4.5). The two
resulting sets of digits were <2, 3, 6, 7> and <1, 4, 5, 8>. The corresponding sets of consonants
were <Z, B, G, F> and <L, H, S, R>. Selection of the consonants in each set was done by
choosing a consonant that resembled each digit in the corresponding set. Although no objective
measure of similarity was used, this procedure was followed to ensure that there would be no
gross difference in the degree of perceptual distinctiveness within or across consonant sets, or
between the consonants and the digits used.
Design
Four different subjects participated in each of the six experimental conditions that result
from crossing the three mapping conditions (CM, CVM and VM) with the two stimulus types
(HOMO and HETERO). Table 1 shows the assignment of the stimuli to the various subjects in
the CM condition. Among the subjects in the HOMO condition, two saw only digits and two
saw only consonants. Each of the four sets of stimuli described previously served as targets for
one of these subjects, the other set of the same category serving as distractors. Each of the four
sets of stimuli also served once as targets and once as distractors over subjects in the HETERO
condition. The assignment of the stimuli to the subjects in the HETERO condition was as
follows: If the targets were taken from one set of digits, for instance, the distractors consisted of
the consonants resembling the other set of digits (i.e. resembling the set of digits used as
distractors for the corresponding subject in the HOMO condition). This procedure was followed
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to maintain similarity of the target and distractor sets as equivalent as possible across the HOMO
and HETERO conditions.
Table 1
Assignment of stimuli to subjects in the CM conditions of the Experiment.
Stimulus condition
Homogeneous Heterogeneous
Subject Targets Distractors Subject Targets Distractors
S1 2,3,6,7 1,4,5,8 S5 2,3,6,7 L,H,S,R
S2 1,4,5,8 2,3,6,7 S6 L,H,S,R 2,3,6,7
S3 L,H,S,R Z,B,G,F S7 1,4,5,8 Z,B,G,F
S4 Z,B,G,F L,H,S,R S8 Z,B,G,F 1,4,5,8
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Assignment of the stimuli to the various subjects in the CVM and VM conditions was
identical to that described for the CM condition. However, in the CVM condition, the two sets of
stimuli assigned to a given subject switched roles randomly over trials, serving sometimes as
targets, sometimes as distractors. In the VM condition, the stimuli serving as targets and
distractors on each trial were chosen among all eight stimuli assigned to the subject, without any
regard to their set of origin.
Four new subjects served in a duplication of condition CVM-HOMO (labeled CVM-
HOMO-I). By contrast with the original CVM-HOMO condition, these new subjects were
informed of the existence of two different sets of stimuli at the onset of the Experiment (thus the I
in the label) and they were reminded at the beginning of every session thereafter. However, they
were not told about the specific composition of each set but were instead asked to recall the
members of the two sets after each session. The first recall test came as a surprise, the others
could be anticipated. All subjects were able to recall correctly the four characters of each set by
the end of the second session. Since the goal of this duplication was to determine the best
performance achievable under CVM-HOMO conditions, subjects were also given the extra
monetary incentive described previously.
Display and memory size varied within subjects, as in Briggs and Johnsen's and
Schneider and Shiffrin's studies. However, in Briggs and Johnsen's experiment, M size was
blocked over a series of consecutive trials and in Schneider and Shiffrin's experiment, both M
and D size were blocked. By contrast, both D and M size varied randomly over trials in the
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present experiment. This reduces the likelihood that subjects develop and rely on specific
strategies for specific set sizes. The possible values that D and M size could take were 1, 2 and
4. The stimuli forming the memory and the display sets varied over trials.
Procedure
Subjects in the CVM and VM conditions spent eight of the ten experimental sessions
practicing the search task. The last two sessions were devoted to a transfer task. For the subjects
in the CM conditions, only the first six sessions were devoted to learning; the last four served for
transfer. For purpose of brevity, the transfer tasks will not be described nor discussed here. Our
presentation will focus mainly on the results obtained during the first six learning sessions,
common to all groups.
Each learning session comprised 864 trials. Although subjects could take a break after
every 108 trials, each session can be viewed as composed of 2 equivalent blocks of 432 trials,
half of which were positive and half negative. All combinations of D and M size were equally
represented within each block. Moreover, every possible target was used equally often on
positive trials in each combination of D and M size. Since there were twice as many potential
targets in the CVM and VM conditions, subjects in these conditions had half as much practice
per target as subjects in the CM conditions (which explains why there were more learning
sessions in CVM and VM conditions).
On each learning trial, an asterisk was presented in the center of a VGA screen for 500
ms before and after the presentation of the memory set. Members of the memory set were
presented for 1 s in a random linear order centered on the position of the asterisk. Following
Schneider and Shiffrin's (1977) procedure, the display set was presented in a square formation
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around the center of the screen. Members of the display set occupied a randomly chosen corner
of the square and a dot was centered in each position left unoccupied when display size was
smaller than four. The visual angle of the display set was about 2 degrees horizontally and
vertically, as in Schneider and Shiffrin's study. However, in contrast with Schneider and Shiffrin
who masked the display set after 160 ms. in their single-frame experiment, our display set
remained visible until the subject responded or until 3 seconds had elapsed.
Subjects responded by pressing the "1" or "2" key on the numeric keypad of the computer
keyboard to indicate a "yes" or "no" response respectively. They were instructed to respond as
fast as possible while maintaining error rate lower than 5%. Subjects got feedback on their
response and reaction time after every trial, plus recapitulative feedback before every rest break
(i.e., after every 108 trials).
In the following, we will first consider the cross-sectional analyses of performance (i.e.,
load effects) before turning to the longitudinal analyses (practice effects). Within each section,
we will start by describing and discussing the experimental results obtained and then show how
a simple feature comparison model can account for these results.
I: CROSS-SECTIONAL ANALYSES
Results
Late Training
Figures 1 to 3 show the RTs obtained on the last block of the sixth session for the six
original Mapping X Stimulus type conditions. The data of one subject are excluded from these
means because this subject's performance was very erratic, exhibiting much larger variations in
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response times and error rates over learning sessions than the other subjects of the same group,
all of which suggests a certain lack of motivation. Therefore, the results of this subject were
excluded from all analyses reported. Unfortunately, this subject had been assigned to a fairly
critical condition, namely: CVM-HETERO.
Average error rates were slightly smaller in CM (3.2%) than in CVM (3.9%) and in VM
(4.1%). Error rates obtained with heterogeneous stimuli (3.1%) were also smaller, on average,
than those obtained with homogeneous stimuli (4.3%). In order to test for the presence of a
speed-accuracy trade-off over the various mapping and stimulus type conditions, a correlation
was computed between the mean error rates and the mean response times of the six subject
groups. The correlation failed to be significant (r (4) = .10). Error rates were affected by the
within-subject factors involved in the experiment. Average error rates increased with memory
and display set size. They were also slightly higher for positive (4.1%) than for negative trials
(3.3%), as is often found in pattern matching and visual search experiments. In order to test for
the presence of trade-off across the various Memory X Display X Response conditions, separate
correlations between mean error rates and response times were computed for each subject group.
Of the six correlations, two were significant but positive (r (16) = .58, p < .02; for both CVM
conditions).
Considering the size of the experiment, we decided to analyze the RTs obtained in each
mapping condition separately. This allows us to focus the description of the results on the
pattern of RTs obtained within each mapping condition, in an attempt to characterize the
processing involved. The factors involved in each of the three ANOVAs performed were
Stimulus type (S: HOMO, HETERO), Memory size (M: 1, 2, 4), Display size (D: 1, 2, 4) and
correct Response (R: Positive, Negative). The data entered in these analyses were the subjects'
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mean RT per condition rather than their median RT (see Miller, 1988). Means were preferred
because of their intrinsic relationship to standard deviations, which are also of concern in this
study. All correct RTs were included in the computation of the subjects' means, RTs longer than
3 s having already been excluded at the data collection stage.
Varied Mapping
Figure 1 shows the results obtained in the least controversial condition, namely VM. As
shown, stimulus composition had little effect on performance. There was no difference in
average response times between the HETERO (547 ms) and the HOMO (563 ms) groups (F (1,
6) < 1., MSe = 62932.), nor was there any interaction involving the stimulus type factor (all p >
.31). However, all the within-subject factors and their interactions were significant (all p < .007).
Decomposition of the M X D X R interaction (F (4, 24) = 6.24, p < .002, MSe = 1780.) showed
the M X D interaction to be significant for both positive (F (4, 24) = 16.0, p < .001, MSe = 658.)
and negative response times (F (4, 24) = 15.7, p < .001, MSe = 3866.). However, Figure 1 shows
the M X D fan to be much more pronounced for negative than positive RTs.
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The results described are very similar to those obtained by Schneider and Shiffrin (1977)
in an HOMO condition. The fact that the same pattern of results was obtained in an HETERO
condition suggests that VM processing is fairly insensitive to the presence of pre-existing
categorical distinction among stimuli. Schneider and Shiffrin (1977) characterized this
processing as a serial self-terminating search in which the memory set items are compared to the
items in the display set.
Consistent Mapping
A comparison of Figure 2 and Figure 1, which have the same scale, shows that the
response times obtained in CM conditions were much smaller that those obtained in VM
conditions. Moreover, within CM conditions, the average RTs were significantly smaller (F (1,
6) = 11.3, p < .02, MSe = 20046.) in the HETERO (390 ms) than in the HOMO (470 ms)
23
condition, and there were many interactions involving Stimulus type. The most general
interaction, which involved M size, D size and R type in addition to S type, was also close to
significant (F (4, 24) = 2.67, p < .06, MSe = 156.). This interaction was decomposed to analyze
the performance of each group separately.
The analyses revealed a marginally significant effect of Response type for both CM
groups (HETERO: F (1, 6) = 5.74, p < .06; HOMO: F (1, 6) = 5.58, p < .06; MSe = 5235.), the
average difference between negative and positive RTs being identical (41 ms.) in the HETERO
and the HOMO conditions. These analyses also revealed significant effects of M size (HETERO:
F (2, 12) = 5.87, p < .02; HOMO: F (2, 12) = 48.7, p < .001, MSe = 329.), and significant
interactions between M size and R type (HETERO: F (1, 6) = 8.58, p < .01; HOMO: F (2, 12) =
6.85, p < .02, MSe = 155.). Decomposition of the interaction obtained in the HETERO condition
showed that M size had an effect on positive RTs (F (2, 12) = 10.6, p < .01, MSe = 276.), the
difference between memory set sizes of four (M4) and one (M1) being 31 ms, but not on
negative RTs (F (2, 12) < 1.0, MSe = 168.), the difference between M4 and M1 being only 3 ms.
By contrast, in the HOMO condition, there were significant M size effects on both positive (F (2,
12) = 36.2, p < .001) and negative RTs (F (2, 12) = 30.8, p < .001), the magnitude of the
difference between M4 and M1 being 54 ms for positive responses and 41 ms for negative
responses.
The analyses also showed D size to have significant effects in both HETERO (F (2, 12) =
20.3, p < .001) and HOMO conditions (F (2, 12) = 51.1, p < .001, MSe = 437.). The average
difference between display sizes of four (D4) and one (D1) was 38 ms in the HETERO condition
and 61 ms in the HOMO condition. D size failed to interact with M size (F (4, 24) < 1.0, MSe =
329.), with R type (F (2, 12) < 1.0, MSe = 336.) and with both (F (4, 24) = 1.72, p < .18, MSe =
24
156.) in the HETERO condition. D size also failed to interact with M size (F (4, 24) < 1) and
with R type (F (2, 12) = 2.33, p < .15) in the HOMO condition. Although M X D X R was not
significant (F (4, 24) = 2.26, p < .10), the data of the HOMO group still show some trend of an
interaction.
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The fact that D size had significant effects, even on the performance of the HETERO
group, forbids us to conclude that the task was performed through a perfectly automatic attention
response to the target, as Schneider and Shiffrin proposed. It could be argued that our subjects
did not have enough practice at the task to achieve full automaticity. However, the longitudinal
results and analyses reported later show that performance of the CM-HETERO group was close
to asymptote on the twelfth block of the experiment.
Other research has also shown display load effects in CM conditions. Using displays of 4
and 8 stimuli, Fisher, Duffy, Young & Pollatsek (1988) obtained D size effects in a multiple-
25
frame, visual search task involving heterogeneous stimuli. These effects could not be attributed
to mere temporal or spatial masking. Dumais (1979) obtained sizeable display load effects in a
single-frame visual search task involving displays of 4 and 16 items. Our results show that D
size effects can also occur with displays containing fewer than four items, in contrast to those of
Schneider and Shiffrin (1977). Factors that are known to affect the rate of visual search, such as
the size and spacing of display items, can hardly account for the discrepancy between the two
experiments since these dimensions were comparable in both studies. Instead, the presence vs.
absence of significant display load effects may be a matter of statistical power, as Anderson
(1992) suggested. (Schneider and Shiffrin did not report any statistical tests of their effects).
Whatever may be the case, the available experimental hardly supports the claim that display load
effects invariably vanish under CM conditions.
Our analyses also revealed significant M size effects. Although subjects in CM
conditions can in principle ignore the memory set, as discussed previously, the results indicate
that our subjects did not. In the HETERO condition, only positive responses were affected by M
size, which suggests that the memory set may have only served a verification function. Upon
encountering a digit among consonants, for instance, subjects may have verified that the digit
was indeed part of the memory set. Such a strategy, composed of a category search followed by
an item verification stage, would not yield an M X D interaction, since search of the display is
limited to one category and subsequent search of memory is for only one item. Accordingly,
there was little of an M X D interaction in either CM conditions, although both M and D had
significant effects in both conditions.
Subjects in condition CM-HOMO may have also relied on a category search strategy
similar to the one described. Since there is a set distinction separating the targets and distractors
26
in condition CM-HOMO, subjects may possibly search for any member of the target set, and
then verify that the item found was specified at trial onset. The fact that the M size effects
obtained with the HOMO group were larger on positive trials than on negative trials suggests
that the memory set did serve a verification purpose. However, this may not have been the sole
function of the memory set, since M size effects were also obtained on negative trials. But, of
course, the properties distinguishing the target from the distractor sets in condition CM-HOMO
were not as overlearned as those distinguishing letters from digits. As a result, subjects probably
still had to rely more heavily on item information. Nonetheless, a comparison of Figures 1 and 2
shows the results obtained in condition CM-HOMO to be much more similar to that obtained in
condition CM-HETERO than to that obtained in the VM conditions.
Categorical Varied Mapping
Figure 3 presents the response times obtained in the CVM conditions. Clearly, the two
original CVM groups behaved very differently. The analyses performed on the results confirm
what is evident in Figure 3, namely that performance of the HOMO group was very similar to
that obtained in VM conditions, whereas performance of the HETERO group was more akin to
that observed in the CM conditions. The overall ANOVA showed all main effects and
interactions to be significant (all p < .03). Decomposition of the analyses over groups revealed
that M size, D size and R type all had significant effects on the performance of the HOMO
group. All interactions involving these factors were also significant (all p < .001). This pattern of
results is similar to the one described for VM conditions. However, response times were even
longer, on average, in CVM-HOMO (607 ms) than in the slowest VM condition (563 ms).
27
By contrast, the results obtained with group CVM-HETERO showed no interaction
involving either M size, D size or R type (all F < 1.0). The difference between negative and
positive RTs was 51 ms, compared to 41 ms in the CM conditions. The D size effect was
comparable in magnitude to that obtained in condition CM-HOMO, the average difference
between D4 and D1 being 56 ms here and 61 ms in CM-HOMO. The magnitude of the M size
effect was about halfway between that obtained in CM-HETERO and CM-HOMO, the
difference between M4 and M1 being 38 ms for positive responses and 23 ms for negative
responses. Finally, the average response time obtained in CVM-HETERO (430 ms) was also
exactly between that obtained in CM-HETERO (390 ms) and CM-HOMO (470 ms).
CVM Positive
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Effects of pre-established categorical distinctions can hardly be more pronounced. At the
same time, the results can hardly be more ambiguous with respect to the role of consistent
28
mapping in automatization. Subjects in condition CVM-HOMO were clearly not on the path to
automaticity. By contrast, subjects in condition CVM-HETERO performed at least as well as
those in condition CM-HOMO, though not as well as in condition CM-HETERO. If one argues
that only condition CM-HETERO led to full automaticity, then one can still maintain that
consistent mapping is necessary for automatization, as Schneider and his colleagues claimed, but
one has to concede that it is not sufficient. A well-established categorical distinction, such as that
between digits and letters, is also needed. Alternatively, if one argues, that subjects in the CM-
HOMO and CVM-HETERO conditions are also in the process of automatizing the task, then
one must conclude that consistent mapping is not necessary for achieving automaticity.
An intriguing possibility that would reconcile both positions would be for consistent
mapping to be involved in category learning. Under this hypothesis, subjects in CVM-HETERO
would not have to form new categories since there is a pre-existing categorical distinction
between the items serving as targets and distractors on any given trial. This is not the case in
condition CM-HOMO, but consistent mapping would allow subjects to form distinct target and
distractor categories and to use such categorical information to improve performance. In the
absence of consistent mapping and of pre-established categorical distinctions, performance in
condition CVM-HOMO could only remain very poor. This suggestion is embodied in the model
described later.
Shiffrin and Schneider (1977) reported that performance in early versions of their
Experiment 3 failed to improve, as it did in our CVM-HOMO condition. If one excludes that
there are fundamental differences between the multiple-frame task used by Shiffrin and
Schneider and the single-frame task used here, then one can hypothesize that the improvements
observed later by Shiffrin and Schneider were due to awareness by the subjects of the set
29
composition of the stimuli. By contrast, our subjects clearly failed to realize the existence of
such a distinction among stimuli, as indicated by informal questioning at the end of the
Experiment.
Condition CVM-HOMO-I
The goal of condition CVM-HOMO-I was to determine the level of performance that can
be achieved when subjects are motivated and aware of the set structure of the stimuli. Figure 4
shows the RTs obtained on the twelfth training block in the two CVM-HOMO conditions.
Performance was clearly better in the informed condition than in the original condition. RTs are
much smaller in CVM-HOMO-I (mean = 495 ms) than in CVM-HOMO (mean = 607 ms). Error
rates were also lower in CVM-HOMO-I (mean = 2.5%) than in CVM-HOMO (mean = 4.0%),
indicating that the gain in RT was not achieved at the cost of increased errors.
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Comparison of Figure 4 with Figure 2 shows that performance in condition CVM-
HOMO-I did not reach the level of proficiency achieved in condition CM-HOMO, which is in
30
agreement with the hypothesis that consistent mapping is necessary for automatization when
there is no preestablished categorical distinction among the stimuli. The interesting question is
whether the differences between conditions CVM-HOMO-I and CM-HOMO are similar to those
obtained between conditions CVM-HETERO and CM-HETERO. Then, according to the logic of
stage additivity (Sternberg, 1966), one would be lead to conclude that the effects of mapping and
of categorical distinctions originate at different levels of processing. Alternatively, the effects of
mapping and stimulus type could interact, thereby suggesting that these two factors affect the
same processes, perhaps those involved in the development of perceptual categories, as suggested
before.
RTs were only 25 ms larger, on average, in CVM-HOMO-I (mean = 495 ms) than in CM-
HOMO (mean = 470 ms). This difference is of the same order as the 40 ms difference separating
the CVM-HETERO (mean = 430 ms) and CM-HETERO (mean = 390 ms) conditions. An
ANOVA comparing these four conditions showed the Mapping X Stimulus type interaction to be
far from significant (F (1, 11) < 1.0, MSe = 26552.). However, Mapping and Stimulus
composition were involved in many interactions with the within-group factors. M size interacted
with Mapping (F (2, 22) = 16.7, p < .001), with Stimulus composition (F (2, 22) = 27.3, p <
.001), and with both (F (2, 22) = 11.3, p < .001, MSe = 1307.). The same was true of D size (all p
< .005, MSe = 684.) and of the D size X M size interaction which varied with Mapping (F (4, 44)
= 2.90, p < .04), with Stimulus composition (F (4, 44) = 5.33, p < .002) and with both (F (4, 44) =
3.70, p < .02, MSe = 493.). Response type failed to interact with Mapping (F (1, 11) = 1.35, p >
.25), Stimulus composition (F (1, 11) < 1.0) or both (F (1, 11) < 1.0, MSe = 3766.). Of all
remaining interactions involving Mapping or Stimulus type, only the M size X R type X Mapping
interaction (F (2, 22) = 4.20, p < .03) and the M size X R type X Stimulus type interaction (F (2,
31
22) = 4.82, p < .02) reached significance, the 4-way interaction involving M size, R type,
Mapping and Stimulus composition failing to be significant (F (2, 22) = 2.00, p < .16, MSe =
484.).
Decomposition of the ANOVA according to Stimulus type showed no Mapping effect
under either the HOMO (F (1, 11) < 1.0) or the HETERO (F (1, 11) = 1.87, p < .20) conditions.
However, for the HOMO groups, Mapping interacted with D size (F (2, 22) = 25.1, p < .001),
with M size (F (2, 22) = 29.5, p < .001) and with both (F (4, 44) = 6.85, p < .001), indicating that
the effects of D size and M size and their interaction were more pronounced under the CVM than
the CM condition. The M size X R type X Mapping interaction was also significant (F (2, 22) =
6.37, p < .01). These results contrast sharply with those obtained in the HETERO conditions
where there was absolutely no interaction involving Mapping (all F < 1.1).
It therefore appears that consistency of mapping has little, if any effect on performance
when there is a pre-existing categorical distinction separating the targets and the distractors. In
such HETERO conditions, the CVM and the CM groups produced very similar results. However,
the CVM and CM groups behaved very differently under HOMO conditions. Subjects in the
CVM group still exhibited a very reliable D size X M size interaction (F (4, 44) = 16.4, p < .001),
even though they knew the composition of the two sets of stimuli serving as targets and
distractors. This result suggests that consistent mapping is involved in the automatization of
search when there is no pre-existing categorical distinction among the stimuli.
It could be argued however, that amount of practice was not properly equated across the
various conditions in the above ANOVA. Although the number of practice trials was the same for
all groups, subjects in CM conditions had half as many targets to learn. They consequently
32
received twice as much practice per target as subjects in CVM conditions. In order to equate
amount of practice per target, we compared performance of the CM groups on the eight block of
practice with that of the CVM groups on the sixteenth block. Performance of the CVM groups
was close to asymptote on the twelfth block of practice, so that it changed very little from the
twelfth to the sixteenth block. The RTs obtained in the CVM-HOMO-I condition still exhibited a
reliable D size X M size interaction (F (4, 44) = 24.3, p < .001) on the sixteenth block. An
interaction was also present in the results obtained on the eight block in the CM-HOMO
condition (F (4, 44) = 6.52, p < .001). However, the D size X M size interaction was more
pronounced for the CVM than for the CM group, resulting in a significant Mapping X D size X
M size interaction (F (4, 44) = 7.63, p < .001) under HOMO conditions. No such interaction was
present under HETERO conditions (F (4, 44) < 1., MSe = 436.).
Early Training
In dual-process theories of automatization, it is assumed that automaticity is achieved by
a decreased reliance on general and relatively inefficient strategies and an increased reliance on
more specific and efficient processes. This replacement of one type of processing by another is
generally assumed to be gradual so that no discontinuity is expected in the learning curves.
However, comparison of performance obtained early and late in training should show sharply
differing patterns of results since early performance is supposed to be dominated by controlled
processing whereas asymptotic performance is assumed to reflect mostly automatic processing.
Since automatic attention attraction theory claims that automaticity can only be achieved
through extended practice under consistent mapping conditions, early CM performance should
resemble that obtained in VM conditions. Another possibility is that subjects in CM and in VM
33
conditions rely on different strategies to perform the task. As discussed previously, subjects in
VM conditions could proceed by comparing items in the memory and display sets as suggested
by Schneider and Shiffrin, whereas subjects in CM conditions would simply categorize the
display items as targets or distractors. In conditions CM-HETERO and CVM-HETERO, where
there is a pre-established categorical distinction separating the targets and distractors, such
category search would be feasible almost from the start of the Experiment, thereby preventing
any form of M X D interaction. By contrast, in condition CM-HOMO, the properties
distinguishing the targets from the distractors have to be learned during the Experiment, so that
early performance would exhibit the type of M X D interaction characteristic of VM and CVM-
HOMO performance.
In order to test these hypotheses, we compared the RTs obtained on the very first block of
trials to those of the twelfth block. It is important to remember that subjects did not have any
practice prior to the first block and that there was no warm-up trial at the beginning of any block.
As before, three separate ANOVAs were performed, one for each Mapping condition. These
ANOVAs were further decomposed to look at each Stimulus condition separately when
necessary. Similar ANOVAs and decompositions were also performed on error rates.
Varied Mapping
According to automatic attention attraction theory, VM performance should not change
much with practice since it is assumed to always involve controlled processing. For group VM-
HETERO, average RT was 717 ms on the first block compared to 547 ms on the twelfth block.
For group VM-HOMO, average RT was 821 ms on the first block and 563 ms on the twelfth (F
(1, 6) = 12.9, p < .02). These differences in RT with practice were significant (F (1, 6) = 17.7, p
34
< .01) and of similar magnitude for both groups (F (1, 6) < 1., MSe = 185645.), representing a
23% gain in speed for group VM-HETERO, and a 31% gain for group VM-HOMO. As will be
seen shortly, these gains are not very different from those obtained in CM conditions. Moreover,
they cannot be attributed to a speed-accuracy trade-off since error rates were also larger on the
first block (5.3% on average over VM groups). It is therefore false to assume that practice has no
effect on performance in VM conditions.
VM Positive
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It is true, however, that practice under VM conditions did not have much influence on the
pattern of interactions obtained. Figure 5 shows the RTs obtained by the VM groups on the first
block of trials under the various M size, D size and R type conditions. Except for M X R, all
effects and interactions involving the within-subject factors were significant on block 1, as they
were on block 12. The M X D X R interaction did not have the exact same size as it did on block
12, resulting in a significant M X D X R X Block interaction (F (4, 24) = 3.62, p < .02, MSe =
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1097.). The only other interactions with Block to be significant or marginally so involved M X R
(F (2,12) = 3.75, p < .06) and M X R X Stimulus composition (F (2,12) = 5.51, p < .02, MSe =
1872.).
Consistent Mapping
Figure 6 presents the RTs obtained on the first block by the subjects in the two CM
conditions. Comparison with Figure 2 shows that the two CM groups differed more on the first
block than on the twelfth. We will therefore consider the performance of each group separately,
starting with CM-HETERO. RTs were longer (F (1, 6) = 17.1, p < .007, MSe = 40165.) on the
first (mean = 527 ms) than the twelfth block (mean = 390 ms). More than 4000 training trials led
to a gain in response time of about 25% (error rates remained about the same at 3.3%). However,
the pattern of RTs obtained on the first block is very similar to that obtained on the twelfth. The
only interaction with Block to approach significance involved D size (F (2, 12) = 2.84, p < .10,
MSe = 2176.). The difference between D4 and D1 was about twice as large on the first block (77
ms) as it was on the last. All other interactions with Block yielded F ratios smaller or equal to
1.0.
36
CM Positive
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The overall decrease in RT with practice observed in CM-HETERO suggests that some
learning took place. One possibility is that the strength of the connections linking the stimuli to
the responses increased with practice, as suggested by instance theory. However, the qualitative
change in performance that was expected on the basis of automatic attention attraction theory
failed to materialize: There was no more D X M or D X M X R interaction on the first than on
the twelfth block. An ANOVA performed on error rates also failed to reveal any effect or
interaction involving Blocks (all p > .10). So, whatever strategy subjects in the CM-HETERO
condition relied on appears to have already been established at the start of the Experiment.
The same cannot be said about performance obtained in the CM-HOMO condition. All
interactions involving Block were significant (all p < .01), except for M X R X Block (F (2, 12)
< 1., MSe = 1092.) and D X M X R X Block (F (4, 24) = 1.50, p < .24, MSe = 890.). Average
RT on the first block was 777 ms, i.e., 300 ms longer than on the twelfth block (F (1, 6) = 84.7,
37
p < .001, MSe = 40165.). This corresponds to a gain in response time of about 40% over the 10
intervening practice blocks.
Categorical Varied Mapping
As Figure 7 shows, the performance of the two original CVM groups differed about as
sharply on the first block as it did on the twelfth. For group CVM-HETERO, average RT was
730 ms on the first block, compared to 430 ms on the twelfth (F (1, 5) = 22.0, p < .006, MSe =
110816.). The difference represents a 41% decrease in response time over 10 intervening
practice blocks. This increase in speed does not seem to have been achieved through a reduction
of load effects. The RTs, obtained on block 1, like those of block 12, show little evidence of a
fanning M X D X R interaction. The only interactions with Block to approach significance in
CVM-HETERO involved M size (F (2, 10) = 3.13, p < .09, MSe = 5659.) and M size and R type
jointly (F (2, 10) = 3.97, p < .06, MSe = 5436.). These interactions suggest that swapping the
digits and consonants as targets may have generated some confusion about the composition of
the memory set during the first block of the Experiment, especially on positive trials. The
ANOVA on error rates revealed no Block effect (F (1, 5) < 1.0) nor any interaction with Block
(all p > .10).
38
CVM Negative
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For group CVM-HOMO, average RT was 881 ms on the first block, compared to 607 ms
on the twelfth (F (1, 5) = 24.3, p < .005, MSe = 110816.), which represents a 31% decrease in
response time with practice. Block interacted with M size (F (2, 10) = 11.4, p < .004, MSe =
5659.) and the Block X D size interaction was also marginally significant (F (2, 10) = 3.79, p <
.06, MSe = 4878.). All other interactions with Block yielded F ratios smaller than 1.0.
39
CVM Positive
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The block 1 RTs obtained with group CVM-HOMO-I are shown in Figure 8, along with
those of group CVM-HOMO. For group CVM-HOMO-I, average RT was 778 ms on the first
block, compared to 495 ms on the twelfth, which represents a 36% decrease in response time
with practice. Note that the 283 ms decrease in average RT obtained with group CVM-HOMO-I
is almost identical to the 274 ms difference obtained with the original CVM-HOMO group. An
ANOVA performed on the results of these two groups showed no significant interaction
involving Block (all p > .10). Although one cannot conclude much from a lack of effect, these
results suggest that the advantage that group CVM-HOMO-I had over group CVM-HOMO was
present very early in the Experiment, stemming either from the monetary incentive or from
knowledge of the set composition of the stimuli, but not from practice.
RT means and standard deviations
The results described so far concerned the effects of load on mean RTs. The main
findings are that a very similar pattern of load effects, characterized by a lack of M X D X R
40
interaction, was obtained at the end of training in both CM-HETERO and CVM-HETERO
conditions and that, despite much slower performance, this pattern was already present at the
beginning of the Experiment. Both of these results suggest that the best performance obtained,
namely that of group CM-HETERO, had little to do with practice under consistent S-R mapping.
A similar pattern also characterized late but not early performance in condition CM-HOMO,
suggesting a possible role for consistent mapping when there is no pre-established categorical
distinction among stimuli. Converging evidence is provided by the fact a very different pattern
of load effects was obtained after extensive training in condition CVM-HOMO, even when
subjects were informed of the set composition of the stimuli (group CVM-HOMO-I). Apart from
a large increase in speed, training did not drastically change the pattern of load effects obtained
by the two CVM-HOMO and the two VM groups. This pattern, which is characterized by
sizeable M X D X R interactions, has been traditionally interpreted as indicative of a serial self-
terminating item search (SSTS). In this section, we analyze further the predictions of SSTS
models concerning load effects on RT means (MN) and standard deviations (SD).
In a SSTS model, the expected RT for a given load condition E(L) can be conceived as
being equal to E(K) x E(T) + E(I), where K is the number of comparisons required, T is the time
needed for a single comparison and I the time related to the intercept processes. In the following,
we will concentrate on the comparison processes and ignore E(I). Search has been traditionally
assumed to be exhaustive on negative trials so that the total number of comparisons required
corresponds to the product of M and D. On positive trials, the average number of comparisons
required corresponds to (MD + 1) / 2. Assuming no gross difference in E(T) across response types,
traditional SSTS models therefore predict negative trial MNs to increase about twice as fast as
41
positive trial MNs, as originally noted by Sternberg (1966). More recently, Townsend and Colonius
(1997) have shown this two-to-one ratio to be one of the signatures of self-terminating processing.
Table 2
Regressions of the negative trial MNs on the positive trial MNs
obtained on block 12 of the Experiment.
Condition Intercept Slope r2 rmsd
CM-Hetero 181.9 0.62 .495 8.0
CM-Homo 83.2 0.90 .759 8.2
CVM-Hetero 107.6 0.86 .795 12.5
CVM-Homo-I - 93.1 1.34 .989 13.9
CVM-Homo -390.9 2.01 .967 20.0
VM-Hetero -286.2 1.84 .954 35.4
VM-Homo -296.1 1.89 .978 19.4
Table 2 shows the results of regressions of the negatives trial MNs on the positives trial
MNs obtained with the various groups of the Experiment on Block 12. A value of r2 larger than
.444 indicates that the linear trend was significant at the .05 level (d.f. = 7), which was the case for
all groups. The root mean square deviations (rmsd) show that the linear fits were quite good, except
perhaps for group VM-HETERO. The two VM groups and group CVM-HOMO have similar
intercepts and a slope that is close to 2.0, as predicted by SSTS models. The slopes of the two CM
groups and that of group CVM-HETERO are smaller than 1.0, which suggests quite different
processing. Performance of group CVM-HOMO-I stands somewhere in between with a slope of
1.34.
42
In a SSTS, the variance of comparison times for a given load condition, Var(L), can be
conceived (Townsend and Ashby, 1983) as being equal to E(K) Var(T) + Var(K) E2(T). When
search is exhaustive, as is often assumed to be the case for negative trials, Var(K) = 0 within each
load condition. The variances of comparison times should therefore increase linearly with load on
negative trials. By contrast, when search is self-terminating, as is assumed by SSTS models to be
the case for positive trials, Var(K) equals (MD + 1) (MD -1) / 12 within each load condition.
Therefore, the variances of the positive comparison times should increase faster than linearly with
load, as noted previously by Schneider and Shiffrin (1977). Consequently, the variance in positive
RTs can come to exceed the variance of negative RTs, as was observed by Schneider and Shiffrin
(1977, Experiment 2) in condition M4D4.
VM Positive
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Figure 9 shows, not the variances, but the standard deviations obtained on the twelfth block
of practice under our VM-HETERO and VM-HOMO conditions. The variability illustrated is not
43
to be confused with the between-subject variability used in the ANOVAs. Instead, the data points
represent the means of the within-subject SDs for every positive and negative M X D condition. As
can be seen, the negative trial SDs failed to exceed the positive trial SDs even with a load of
M4D4. Instead, both positive and negative trial standard deviations tend to increase linearly with
load, the latter increasing faster than the former. It is worth noting that a similar pattern of effects
was obtained by Ward and McClelland (1989) in a conjunctive, visual search task. They found
variances to increase faster than linearly with load on both positive and negative trials, the latter
exhibiting a larger increase than the former. Can a SSTS model accommodate such results?
Returning to the SSTS equation for variances, let us consider the limiting case in which the
variance of individual comparison times (Var(T) in the equation) is assumed to be negligible. Then
Var(L) = Var(K) E2(T), and SD(L) = SD(K) E(T). On positive trials, SD(K) = SQRT ((MD + 1)
(MD -1) / 12), which is closely approximated by MD / (SQRT 12). For a large range of M X D
values, every increase of 1 in MD leads to an increase of about 0.3 in SD(K). Being equal to (MD +
1) / 2, the equivalent increase in E(K) on positive trials is 0.5. In short, with no variability in
individual comparison times, a SSDS model predicts quasi-linear effects of load on positive trial
SDs which are about 60% as pronounced as those on means.
Table 3
Regressions of the SDs on the MNs
obtained on positive trials of block 12 of the Experiment.
Condition Intercept Slope r2 rmsd
CM-Hetero -200.5 0.67 .749 7.7
CM-Homo - 32.1 0.24 .948 7.1
44
CVM-Hetero -147.6 0.52 .798 7.4
CVM-Homo-I -184.9 0.63 .975 7.7
CVM-Homo -151.3 0.55 .981 7.6
VM-Hetero -202.1 0.64 .967 10.7
VM-Homo -190.2 0.64 .990 6.5
Table 3 shows the results of regressions of the positive trial SDs on the positive trial MNs.
The linear trend is significant for all groups and rmsd is also small for all groups. Moreover, the
slopes obtained all hover around the .60 value predicted, except that of group CM-HOMO. When
viewed in the serial perspective described, these results suggest a self-terminating component in the
processing of all groups on positive trials.
Table 4
Regressions of the SDs on the MNs
obtained on negative trials of block 12 of the Experiment.
Condition Intercept Slope r2 rmsd
CM-Hetero - 89.5 0.36 .603 5.1
CM-Homo - 54.5 0.25 .538 7.7
CVM-Hetero -106.4 0.39 .472 11.1
CVM-Homo-I - 80.1 0.35 .899 11.7
CVM-Homo - 98.8 0.37 .960 15.1
VM-Hetero -148.7 0.49 .871 32.2
VM-Homo -152.0 0.49 .996 6.1
45
Let us now turn to the negative trial SDs. Table 4 shows the results of regressions of these
SDs on the negative trial MNs. The linear trends are again significant for all groups although fits
are not equally good for all groups. The slopes are generally within +/- .10 of 0.40, except that of
group CM-HOMO which equals 0.247. Such results are difficult to explain within SSTS models,
especially if one assumes, as we have done, that the variability of individual comparison times is
negligible. With exhaustive search, the number of comparisons required in any load condition is
constant and equal to MD, so there should no load effect on SDs.
This need not be true, however, if search and comparisons are assumed to operate on
features instead of whole characters. Although correct rejection of distractors on negative trials
requires that all characters be processed, within-character feature comparisons can stop as soon as a
mismatching feature is found. So, the search process can be considered to have a self-terminating,
within-character component on negative trials. This within-character, feature comparison process is
affected by the number of features to process in exactly the same way an item-based SSTS model is
affected by the number of items to process. To illustrate, let us suppose that the characters are
composed of only three features each. Then, in condition M1D1, processing can terminate after
either 1, 2 or 3 feature tests, depending on how early a mismatching feature is found. If these three
cases are equally likely, then the number of feature tests will have a MN of 2.0 and a SD of 1.0.
With four-feature characters, the number of feature tests will range from 1 to 4 in condition M1D1,
with an expected MN of 2.5 and an expected SD of 1.29. With five-feature characters, the expected
MN is 3.0 and the expected SD is 1.58. In short, with every added feature, MNs increase by 0.50
and SDs by about 0.30, for a ratio of about 0.60.
Now, let us consider the effect of number of items on MNs and SDs, starting with condition
M1D2, for instance. With three-feature characters, the total number of feature tests will range from
46
a minimum of 2 (1 feature test is sufficient to reject each item in D) to a maximum of 6 (3 feature
tests are needed to reject each item in D). The expected MN is 4.0 and the expected SD is 1.22.
With four-feature characters, the expected MN is 5.0 and the expected SD is 1.63. With five-feature
characters, the corresponding values are 6.0 and 2.04. Note that, for an equivalent level of featural
complexity, the MNs are always twice as large as those obtained in M1D1 as one would expect
from exhaustive processing over items. However, the effect of load on SDs is much smaller. This is
due to the combinatorial over items which make certain numbers of feature tests more likely than
others: For instance, with three-feature characters, there many more ways to make a total of 4
feature tests over the two characters in condition M1D2 (or M2D1) than to make 2 or 6 feature
tests, even if the numbers of within-character feature tests are all equally likely. The probability
distributions of the total numbers of feature tests over items are symmetrical so that the MNs
behave exactly as if all totals were equiprobable. However, the SDs do not. Since the kurtosis of
the distribution increases with the featural complexity of the characters, the load effects on SDs do
not change linearly with featural complexity. With three-feature characters, the effect of load on
SDs is only about 11.0 % as large as that on MNs. With five-feature characters, the effect of load
on SDs is about 14.6 % as large as that on MNs. With seven-feature characters, it is about 16.4% as
large. To obtain a ratio (0.40) approximating the slopes obtained in the Experiment, would require
about 108 features per character. Such featural complexity exceeds by far the number of pixels in
the most complex stimuli used in the Experiment. Of course, it does not exceed the complexity of
the analyses that the visual system could perform on pixels and pixel combinations. However, a
vast amount of parallelism would be needed for such low-level explanation to account for the
results (see next section). If the load effects on SDs obtained on negative trials are to be explained
by a serial feature-based comparison process, then the assumption of exhaustive processing over
items will have to be abandoned.
47
In the next section, we describe a serial feature-based comparison model. The model
accounts for the pattern of load effects on the block 12 MNs obtained in the various conditions of
the Experiment. The model also accounts fairly well for the effects of load on the positive SDs,
since processing is self-terminating on positive trials. Unfortunately, the model involves exhaustive
search over items on negative trials. So, the model fails to provide as good an account of negative
SDs. Our only excuse is that our ambitions did not encompass the SDs at time the model was
designed and implemented. Nonetheless, we will briefly describe how we intend to modify the
model to account for negative SDs.
Model
Our model is based on four basic principles. These principles were incorporated in a
simple computer simulation. As we will show, the simulation captures the main features of the
MNs obtained in the various mapping by stimulus type conditions. Our model differs from dual-
process theories of automatization, including that of Schneider and Shiffrin, in that the same
learning and comparison processes are assumed to be involved in all conditions.
The first postulate is that the search and comparison processes operate on a featural basis.
We therefore assume that each character is represented as a conjunction of simple features, such
as line segments. Although convenient, this assumption is probably an oversimplification since
more global visual aspects of the stimuli may also be represented (von Grünau, Dubé & Galera,
1994). Even under this simplified assumption, it is no easy task to determine the exact nature of
the features composing alphanumerical characters. The dot matrix representation of the characters
48
used in the Experiments does not make the task any easier. Also, different subjects may parse the
same characters differently.
We avoided the issue of the "true" featural representation by using a schematized
representation similar to that of McClelland and Rumelhart's (1981; Rumelhart & McClelland,
1982) word recognition model. The feature set used to represent our stimuli is shown in Figure
10. It involves only straight lines and is composed of 12 horizontal, vertical or diagonal line
segments, each occupying a specific position within the character matrix. The character set used
in the simulation is also shown in Figure 10. As is shown, each character is represented by six
features or less. Some features are shared by many characters, but each character possesses at
least one feature that allows to discriminate it from the other characters. In other words, no
character is fully included in another one. Some characters may seem strange as a result of this
simplifying constraint (see the representation of the 8 for instance). A larger feature set would
undoubtedly allow to design more realistic-looking characters while still respecting the same
constraint. A more important issue concerns the psychological validity of the constraint: The
work of Schyns and Rodet (1997) has shown that subjects can indeed learn to parse objects so as
to obtain distinguishing features.
49
50
The second postulate of the model is that some features are more important than others,
the important features being those which tend to be present among targets but not among
distractors. In other words, the important features are precisely those that allow to distinguish the
targets from the distractors. In the simulation, the relative importance of the 12 features is
determined by their position in a list. Prior to learning, the order of the features in the list is
random. On every trial, some of features which are present among the characters in the memory
set, i.e. among the potential targets, and which are absent from the distractors in the display set,
are raised one position. So, the features which frequently allow to discriminate the targets form
the distractors will come to dominate the list over trials.
The learning algorithm currently implemented is very rough. Features that are in the
memory set but not in the display set on any given trial are moved up one position in the feature
list. A maximum of one feature per item in the memory set is promoted. Features which are
promoted are those which are already higher in the list. The features promoted on positive trials
may belong to items that were not even considered by the self-terminating comparison process
described shortly. The algorithm used; in fact the whole simulation was deliberately kept simple
to test the power of the underlying assumptions. Whether learning occurs on both positive and
negative trials is a question for further empirical research. Which features are raised on positive
trials is a matter for later adjustments.
The third postulate is that the features of the characters in the memory set and on the
display are not necessarily all considered. Two sorts of features will come to be ignored by the
model: features which have little power to discriminate the targets from the distractors and
features which are so strongly correlated with the diagnostic features as to become redundant. The
result is a more economical coding of stimuli in the memory set and on the display, a
51
consequence of importance to the model as we will see. In the simulation, a threshold in the
ordered feature list limits the features considered. This threshold is set at the bottom of the list
prior to learning. It is raised by one position after every succession of 20 correct positive
responses. The neglect of too many features will inevitably yield some false alarms. To maintain
an acceptable level of false alarms, the threshold is lowered one position after every incorrect
positive response (see Chun & Wolfe, 1996, for a similar mechanism). This procedure maintains
a false-alarm rate of about 5%.
The first postulate dealt with the nature of representation, the second and third with the
learning process. The last postulate deals with the comparison process. It asserts that there is a
limit on the number of features that can be handled together. However, all features within this
limit are processed exhaustively. In the simulation, the comparison process requires that the
featural representation of the characters in the memory set be loaded in a limited-capacity buffer.
The same applies to the characters on the display, which must also be loaded in a buffer. The
capacity limit on these two buffers was very pragmatically set equal to the number of features in
the most complex character (i.e., 6) plus one. This insures that the model will be able to match the
memory and visual representation of any character, an absolute pre-requisite for recognition to
occur. (Number seven has also been considered to have magical properties in the past.)
In the current version of the program, the loading of the character representations in the
buffers is determined by the ordered feature list. The item in the memory set that has the most
dominant feature will be loaded first. However, not all features of the item will be entered in the
buffer, only those which are above the threshold. As a result, there may be some space left in the
buffer for the representation of another character, one which shares the same dominant feature or
which has the next most dominant feature in the ordered list. Loading the featural representation
52
of the display characters is also driven by the ordered feature list and proceeds in exactly the same
fashion. A positive response is emitted if a match is found between an item represented in the
"memory" buffer and one represented in the "visual" buffer. If no match is found, a negative
response is emitted unless there are characters in the memory or display set which remain to be
compared. In this case, the process starts anew with the loading of some of the remaining
characters in the memory and/or visual buffer.
The question arises as to which of the memory or the display buffer is refreshed first: does
the content of the display buffer change more frequently than that the memory buffer or vice-
versa? This question concerns the direction of the comparison process: Subjects can focus on
items in the memory set, comparing them to all items on the display prior to considering the items
remaining in the memory set when no target is found. In this memory-driven case, the memory
buffer would cycle more slowly than the display buffer. Alternatively, subjects can focus on items
on the display, comparing them to all items in memory, prior to considering the items remaining
in the display set. In this display-driven case the display buffer would cycle more slowly than the
memory buffer.
Schneider and Shiffrin (1977) clearly favored the first, memory-driven possibility for
controlled processing. However, their automatic attention attraction mechanism implies that
processing is driven by the display and that all display items are somehow considered in parallel.
We are not committed to any specific possibility. Both yield identical results for negative trials,
processing being assumed to be exhaustive over the items in the memory and display sets. They
also yield similar results for positive trials when there is only one target, as was the case
throughout training in our Experiment. The model proposed here is not very specific either about
the mechanism for comparing the contents of the memory and visual buffers. Since the
53
performance of the model will be evaluated by considering the total number of features entered in
the memory and visual buffers and by comparing this variable to the RTs obtained by the
subjects, all that needs to be assumed is that the features in the buffers are not compared in an
absolutely parallel fashion. The previously reported analyses performed on the SD data of the
subjects suggest that the feature comparison process is, in fact, serial. We are currently attempting
to modify the model proposed here to take the SD results into account.
The goal of the simulation was to determine whether the simple principles just described
are sufficient to reproduce the pattern of MN results obtained in the Experiments. The program
was therefore submitted to the same conditions as the real subjects, using the same sets of stimuli.
In this section, we consider only asymptotic performance of the model, so we defer to a later
section the presentation of the training schedule to which the simulation was submitted. Figures
11 to 13 show the mean number of features considered by the simulated subjects in the various
conditions of the Experiment.
CM Positive
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As shown in Figure 11, there are small M size and D size effects on the number of features
considered in the CM conditions. But there is little evidence of an M X D interaction, except
perhaps on negative trials in the HOMO condition. (Remember that there was a similar trend
54
toward a M size X D size X R type interaction in the RTs of the CM-HOMO group). The CM
pattern of result is explained by the fact that the feature list has come to be dominated by very
discriminating features. The threshold has therefore moved close to the top of the list, so that few
features are used to code each item in the memory set and on the display. The number of features
loaded in the buffers tends to increase slightly with the number of items in memory and on the
display, yielding M size and D size effects, but the amount of information loaded on a given trial
rarely exceeds the limit of the buffers, thereby preventing any M X D interaction.
More generally, the model predicts that the results obtained will depend on the
dissimilarity of the targets and distractors, and on the similarity among targets and among
distractors (Humphreys, Quinlan & Riddoch, 1989; Duncan & Humphreys, 1989). Performance
will be better with distractors that are so similar that only a few (ideally only one) features suffice
to discriminate each target from all distractors. Performance will improve further if many (ideally
all) targets share the same discriminating features. In short, the features which come to dominate
the list tend to be those that are common and unique to targets. This is precisely what categorical
knowledge is about. Features that are common to all members of a category are called necessary
in the literature on concepts and categories, and features that are unique to members of a given
category are called sufficient. The model therefore aims towards categorical representations made
of necessary and sufficient features, as proposed by the classical view of concepts (see Medin &
Smith, 1981). Of course, such ideal categorical representation is not always possible.
55
VM Positive
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The model cannot develop categorical representations in VM conditions for the simple
reason that there are no distinct target and distractor sets, the targets and distractors being selected
randomly over trials. The best strategy therefore consists in learning to discriminate each stimulus
from all others. Each such discrimination will generally require a larger number of features than
in CM conditions where fewer stimuli serve as distractors. But, even if a subset of discriminating
features can be found for a given target, the same set of features will belong to a distractor on
another trial when the same stimulus serves as distractor. As a result, the threshold cannot change
much with practice: only the features shared by all stimuli can be ignored. The coding of the
items in the memory set and on the display therefore remains fairly extensive, with the
consequence that the buffers can rarely handle more than one character at a time. The model then
behaves in a manner analogous to the item-comparison process described by Schneider and
Shiffrin. As shown in Figure 12, it produces a fanning M size X D size interaction and the
interaction is twice as pronounced for negative as for positive trials.
Figure 13 shows the performance of the model in CVM conditions. The results shown in
the top panel are fairly similar to those obtained in condition CVM-HOMO-I. They still exhibit an
M size X D size interaction, but one that is much less pronounced than in VM conditions. The
56
advantage of CVM over VM performance is due to the subset composition of the stimuli. Since
each stimulus must be distinguished from fewer stimuli than in VM conditions, a smaller number
of discriminating features is required in CVM conditions. Some of these discriminating features
may also be shared by other stimuli in the same set, all of which facilitates performance in CVM
conditions. However, performance cannot reach the level obtained in CM conditions because the
two sets of stimuli switch roles as targets and distractors. The same conclusion holds for the
HETERO as well as the HOMO condition. So, the model, as described so far, cannot account for
the much more efficient performance obtained in the CVM-HETERO condition.
CVM Negative
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The solution, adopted in the simulation, consists in assuming that there are two distinct
ordered feature lists, one for digits and one for letters. The two lists are composed of the same
features but their order can differ. When digits have to be found among letters, the digit feature
list is activated and updated in the manner described previously. Similarly, the letter feature list is
activated and updated when the targets are letters. Since different lists are involved on different
trials, performance is no longer affected by switching the target and distractor sets. The digit
feature lists comes to be dominated by features which tend to be shared by digits but not by
letters, and vice-versa for the letter feature list. This modification to the model allows the
57
simulation to produce a pattern of results very similar to that obtained in the CVM-HETERO
condition, as the bottom part of Figure 13 illustrates
One may view the two-list hypothesis just outlined as post-hoc and very implausible. We
view it, on the contrary, as quite plausible. As we have already noted, an ordered feature list can
represent categorical knowledge, the order of the features in the list corresponding to the
importance or salience of the features among the members of a category. Inasmuch as digits and
letters form two distinct categories, it is normal that each has a distinct categorical representation
(i.e., ordered feature list). Although our simulation formed such category representations during
the course of the experiments, it is likely that our educated subjects had long acquired such
representations for letters and digits. This explains why performance in the CVM and CM
HETERO conditions was very efficient right from the beginning. If this explanation is correct,
then training in our VM-HETERO condition must have blurred the category distinctions between
digits and letters that were present in our subjects at the beginning of the Experiment. Finally,
note that this modification to the model does not change anything for the HOMO conditions since
these conditions involved only letters or only digits.
The reader may wonder why the model does not simply update the featural representation
of every stimulus instead of categorical feature lists. The reason is simple: the model would have
identical performance in CVM and in CM conditions, which is contrary to results obtained.
Imagine that, on every trial, the learning mechanism reorders and eventually reduces the featural
representation of the items in the memory set (i.e., the potential targets). Then, with practice, the
featural representation of each stimulus in the memory set will come to be dominated by the
features with best discriminate it from the set of distractors. So, for a specific set of targets and
distractors, the discriminations required are the same in CVM and in CM conditions. Switching
58
the target and distractor sets over trials in CVM conditions optimizes the featural representation
of the stimuli in both sets, which is irrelevant for the subjects in CM conditions since the set of
potential targets remains constant throughout practice. Varying the target and distractor sets over
subjects in CM conditions further insures that the discriminability level was the same over
subjects in CM and in CVM conditions (before eliminating one subject). The fact that the CVM
groups did not perform as well as the CM groups therefore constitutes strong evidence in favor of
the category-based representations and processes involved in the model.
y = 64.10x - 44.80R2 = 0.84
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Mean numbe r of fe ature comparisons
Homogeneous
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y = 60.98x - 45.56R2 = 0.83
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4 6 8 10 12 14 16 18Mean numbe r of feature comparisons
Positive NegativeHeterogeneous
The preceding discussion shows that our model provides a good qualitative fit for the
59
results obtained in various Mapping X Stimulus type conditions. Figure 14 illustrates the
goodness of the quantitative fits. In Figure 14, the mean RTs obtained in the different M size X D
size conditions have been plotted as a function of the number of features considered by the model,
along with the best-fitting lines. The top part shows the MNs obtained in the three HETERO
conditions. If, as we have argued, the same mechanism underlies performance in all conditions,
then the mean RTs should all fall on the same line. A regression performed on positive trial MNs
accounted for 90% of the variance and another performed on negative trial MNs accounted for
94% of the variance. The amount of variance explained dropped to 88% when both positive and
negative trial MNs were considered together. Note however, that the separate regressions
performed on the positive and negative trail MNs yielded very similar slopes (about 9 ms per
feature considered), but different intercepts. This 9 ms figure is plausible. However, an increase in
the featural complexity of the stimuli would soon produce slopes exceeding the physiological
refractory period, thereby forcing any theory to abandon the assumption that features are
processed serially, as discussed previously.
The bottom part of Figure 14 shows the MNs obtained in the CM and VM HOMO
conditions as well as in condition CVM-HOMO-I. Separate regressions performed on the positive
and negative trial MNs accounted for 82% and 92% of the variance, respectively. The amount of
variance accounted for was 87% when both positive and negative trial MNs were considered
together, and it raised to 91% when a binary variable was introduced to account for the intercept
difference between positive and negative RTs. Positive and negative trial slopes again failed to
differ much (about 11 ms per feature considered) and they were also similar to those obtained for
the HETERO conditions. An overall regression involving all the means shown in Figure 16
accounted for 87% of the variance. The introduction of two binary variables, one for the positive-
60
negative distinction and one for the HOMO-HETERO distinction, raised the percentage of
variance accounted for to 92%. The fact that the model does almost as well without these binary
variables is evidence that the same mechanism captures most of the variance in all conditions.
Let us now turn to the SDs produced by the model. Figure 15 shows the positive and
negative trial SDs obtained in VM conditions. Note that the scale of Figure 15 is the same as that
used for the MNs in Figure 12. The SDs produced by the model are therefore in the same global
range as the MNs, which is in clear conflict with the empirical results. However, the empirical
MNs include E(I) for which there is no provision in the model. A more important flaw of the
model is that the effects of load are more pronounced on positive trial SDs than on the negative
trials SDs, as expected from the self-terminating vs. exhaustive nature of the search over items on
positive vs. negative trials. Nonetheless, load effects on positive and negative trial SDs appear
quite linear in both VM conditions.
61
Table 5
Regressions of the SDs on the MNs
obtained on positive trials of block 12 of the simulation.
Condition Intercept Slope r2 rmsd
CM-Hetero -1.21 0.22 .14 0.1
CM-Homo -1.05 0.48 .69 0.2
CVM-Hetero -0.69 0.48 .62 0.2
CVM-Homo -0.88 0.53 .88 1.0
VM-Hetero -5.03 0.79 .93 4.7
VM-Homo -6.53 0.88 .96 5.6
Table 5 shows the results of regressions performed on the positive trial SDs and MNs
produced by the model in all conditions of the Experiment. The linear trends are significant for all
conditions, except CM-HETERO. However, the slopes obtained tend to be larger than those
obtained with the subjects, the overshoot being especially pronounced in VM conditions. As
shown in Table 6, the opposite occurs with negative trial SDs: the slopes obtained with the model
are generally much smaller than those obtained with the subjects, except in condition CVM-
HETERO. The linear trends are significant in all but the two CM conditions.
62
Table 6
Regressions of the SDs on the MNs
obtained on negative trials of block 12 of the simulation.
Condition Intercept Slope r2 rmsd
CM-Hetero 0.7 -0.12 .11 0.09
CM-Homo 0.4 -0.05 .21 0.24
CVM-Hetero -0.2 0.46 .89 0.54
CVM-Homo -0.3 0.20 .83 0.76
VM-Hetero 0.4 0.15 .81 2.99
VM-Homo -0.1 0.20 .90 3.34
In short, the model described is about as unsuccessful in accounting for the pattern of SDs
obtained as it is successful in accounting for the MNs. We do not believe, however, that the flaws
of the current model are fatal to the hypothesis that a single-process, feature-based comparison
process can ultimately account for the MNs and SDs obtained in all mapping conditions. The
slopes of positive SDs on positive MNs can be adjusted by better specifying the nature of the
feature comparison process, which remained largely unspecified in the model described, due to
the buffers postulated. The feature comparison process, we are testing at the time of writing is
inspired by feature integration theory (Treisman & Gelade, 1980), the presence or absence of a
feature being tested in parallel over all items on the display. Each item in the memory set is
considered in turn, the order of successive feature tests being determined by the categorical
feature list described here. We have already implemented and tested this process and found the
63
slopes of positive trial SDs on positive trial MNs to match much more closely those obtained with
empirical data.
The approach we are currently exploring to account for the negative trial SDs is based on
the assumption that the feature comparison process is fallible, so that targets sometimes fail to be
detected. This assumption is consistent with the relatively large number of misses obtained in
search tasks. The other assumption is that subjects are aware of their fallibility, which is more
than likely considering the presence of feedback after every trial. Consequently, after failing to
find a target, subjects may proceed to execute a second pass to verify than no target was indeed
present. This second, verification stage cannot be exhaustive: in VM conditions, this would
increase to about 4.0 the slopes of negative trial MNs on positive trial MNs while failing to
improve the slopes of negative trial SDs on negative trial MNs. Therefore, some form of self-
terminating rule operating on both positive and negative trials must be found. This is the avenue
we are currently exploring.
We admit that the model described here does not yet make a very strong case in favor of
our single-process, feature-based account of load effects on RTs, and against Schneider and
Shiffrin's dual-process, item-based account. Our model accounts for the MNs obtained in all
conditions, except those obtained the original CVM-HOMO condition which are easily explained
by Schneider and Shiffrin's model. However, their model cannot account for the MNs obtained in
condition CVM-HETERO, which our model easily explains. Both models are therefore even with
respect to the means. The slopes of the positive trial SDs to the positive trial MNs find a natural
explanation in traditional, item-based SSTS models of the type proposed by Schneider and
Shiffrin to account for VM performance. With extraneous assumptions concerning item-switching
time, Schneider and Shiffrin (1977) were also able to account for the negative SDs obtained in
64
their VM condition. The model described here did not provide a very good account of the SDs
obtained on positive or negative trials. Reasons to still favor a single-process, feature-based
account are 1) parsimony, 2) the effects of practice which failed to reveal the qualitative
differences between early and late performance predicted by a dual-process theory, except in
condition CM-HOMO and 3) hope: there is no principled argument that the model cannot be
improved to account for load effects on SDs.
II: LONGITUDINAL ANALYSES
In section II, we adopt a longitudinal perspective on performance, the goal being to test
whether the MNs and SDs obtained in the various conditions of the Experiment satisfy Logan's
criterion for automatization. In the Introduction, we have discussed how this criterion could be
satisfied in CM conditions, under both Schneider and Shiffrin's and Logan's theory. The discussion
was limited to positive trials, the case of negative trials being more complex. The predictions
concerning the CM conditions were also based on the assumption that performance in such
conditions is determined by the same process throughout learning, be it an attention attraction
device or a race for identification. Schneider and Shiffrin's theory and Logan's instance theory
suppose instead that early performance is controlled by processes of the type involved in conditions
which forbid automatization, such as VM conditions.
Logan (1988) performed some simulations to determine whether the influence of controlled
processing during the early stages of practice masked the dynamics of automatization and found
performance to be little affected by the competing presence of such processes: the simulated MNs
and SDs still followed power curves with identical rate parameters, in agreement with the
automatization criterion. However, the tasks used in Logan's study were quite different from the
65
task involved in the present study. Since little is known about the evolution of mean RTs with
practice in visual-memory search tasks, even less about the evolution of standard deviations,
satisfaction of Logan's criterion remains quite uncertain, even under CM conditions.
The cross-sectional analyses reported in the previous section showed performance in
condition CM-HOMO to be similar to that obtained in VM conditions at the beginning of training,
but not at the end. Such results can be interpreted as indicative of a qualitative change in processing
from controlled to automatic. However, the performance obtained in condition CM-HETERO
failed to show evidence of controlled processing even at early stages of practice, which suggests
that performance was determined by the same processes throughout training. So, if the predictions
concerning the dynamics of instance learning or the development of attention attraction have any
validity, they should be especially manifest in condition CM-HETERO.
Due to a total lack of stimulus-response consistency, automatization cannot occur in any
VM condition, under either instance or attention attraction theory. Therefore Logan's criterion
should not be satisfied in any VM condition, unless controlled processes also satisfy the criterion.
This cannot happen on positive trials if the controlled processes consist in item-based, self-
terminating search. As previously discussed, in traditional SSTS models, the expected comparison
time for any given load condition E(L)= E(K) E(T) and Var(L) = E(K) Var(T) + Var(K) E2(T), on
positive trials. If the search process remains self-terminating from the beginning to the end of the
Experiment, then the expected number of comparisons for a given load condition, E(K), will
remain constant throughout training, and so will Var(K). A power speed-up in E(L) can therefore
only result from a power speed-up in individual comparison time E(T). The equivalent decrease in
Var(L) will depend only on the evolution of Var(T) + E2(T) with practice. The square root of this
expression cannot decrease at the same rate as E(T). Therefore, SD(L) cannot change at the same
66
rate as E(L). A reduction in number of comparisons, E(K), could occur on positive trials, in
conditions other than M1D1, if subjects gradually switched from exhaustive to self-terminating
search. Such a switch would cause a decrease in E(L) over practice but, as discussed in the context
of load effects on SDs, it would cause an increase in SD(L), a prediction that clearly contradicts
Logan's criterion.
Logan's criterion could be satisfied by serial, item-based search on negative trials. If search
remains exhaustive throughout practice, then E (K) will remain constant and Var(K) will be null for
any given load condition. A power decrease in Var(L) can therefore only result from a decrease in
Var(T). For certain distributions of T, the square root of Var(T) can have the requisite relation to
E(T) for SD(L) to decrease at the same rate as E(L). Although such an outcome is coherent with
serial item-based search, it is by no means a necessary consequence of such processes.
By contrast, feature-based SSTS models predict that Logan's criterion will be satisfied on
positive trials provided that E(T) remains fairly constant and that Var(T) is negligible, as we have
assumed so far. Then, E(L) = E(K) E(T) and SD(L) = SD(K) E(T). Since E(K) = (MD +1) / 2 and
since SD(K) is approximated by MD / SQRT (12), a power decrease in E(L) will necessarily be
accompanied by a power decrease in SD(L) with identical rate. The relationship between E(K) and
SD(K) allows to further predict that the amplitude of the power decrease in SD(L) will have a 0.60
ratio with that of the power decrease in E(L), provided that there is no other source of variability
apart from variations in the number of comparisons.
The predictions just outlined concern the effects of practice on comparison times. However,
the observed MNs and SDs do not depend only on the comparison processes but also on the
processes contributing to the intercepts. Practice can of course affect the intercept processes. If
67
practice effects were restricted to such processes, Logan's criterion could be satisfied in all
Mapping X Stimulus type conditions on both positive and negative trials. However, this possibility
seems unlikely, considering the interactions involving Block, M size, D size and R type revealed by
the cross-sectional analyses makes. Predictions that take into account potential effects of practice
on both the comparison and the intercept processes become quite complex. Therefore, we will
discuss this possibility only if the results warrant it.
Before turning to the results, we briefly describe the nature of the analyses performed.
Two complementary approaches were used. The first one consisted in fitting power functions to
the RTs obtained on positive and negative trials. Within each response type, distinct power
curves were fit to the MNs and SDs. This yields a six-parameter description of the RTs, whether
positive or negative (aMN, bMN, cMN, and aSD, bSD, cSD). Logan's (1988) test of instance
theory consisted in comparing such six-parameter solutions to five-parameter solutions,
containing a single c parameter. Since the five-parameter solutions did not cause a significant
loss in explanatory power, Logan was led to conclude that MNs and SDs decreased at the same
rate. Note, however, that this test bypasses an important prerequisite of instance theory, namely
that the MNs and the SDs must each behave according to a power function. Logan did not report
the goodness-of-fit of the separate three-parameter solutions computed on the MNs and on the
SDs. Our results show that the joint fits on MNs and SDs (labeled MN&SD fits hereafter) can
provide a very good account of the data, irrespective of the number of c parameters, even when
the SDs or the MNs fail to show conformity to a power curve. Therefore Logan's (1988)
approach constitutes a weak and potentially biased test of instance theory.
68
Simulated learning curves
0100200300400500600700
1 2 3 4 5 6 7 8 9 10 11 12
Session number
Tim
e (m
s)MN1MN2SD
SD plotted against MN1
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SD plotted against MN2
8595
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250 450 650
r2 = .975D = .947, p < .05
r2 = 1.000D = 1.634
An alternative approach, limited to the significant three-parameter solutions, would consist
in comparing the estimated cMN and cSD with some statistical test such as a t-test or a binomial
sign test (see Rickard, 1997). However, this approach is still dependent on the capabilities of the
minimization program2. Instead, we set out to test the equality of the curvature of the empirical
MNs and SDs. It can be shown (see Appendix 1) that, given two power curves, one is a linear
function of the other if and only if the rate parameters of the two curves are equal. According to
instance theory, it should therefore be possible to find k and h such that SD = k MN + h.. Figure 16
69
illustrates this point using hypothetical results. The top part of the Figure shows three learning
curves, one of which is thought to represent SD data, and the other two, MN data. The parameters
of the various curves have been chosen arbitrarily, with the restriction that one learning curve
(MN1) had the same c as the SD curve. The bottom part of the Figure 16 plots the standard
deviations against the means. The result is a straight line when the SDs and the MNs share the same
rate parameter. Otherwise, the result is curvilinear. Attempts to fit a straight line to curved data
yield systematic deviations: the beginning and end data will be under (or over) the line while the
middle data will be over (or under) the line. To check for the presence of systematic deviation to
linearity, we used an autocorrelation test, the Durbin-Watson (DW) test (1951, also see
Wesolowski, 1976), which determines whether successive observations are on the same side of the
regression line or not.
Results
By contrast with Logan's (1988) results, which concerned the evolution of performance over
successive trials, all results reported here are based on successive blocks of trials. Analyses based
on successive trials were impossible, due to the variability of load conditions over trials in the
Experiment. The main disadvantage of block analyses is that some precision is lost about the exact
course of learning. However, block analyses have the advantage of providing enough observations
to consider the results of each subject individually, which is important since the shape of the
individual learning curves need not match that of the groups (Estes, 1956). Not to mention that,
when trying to account for learning and automatization, one is essentially concerned with the
memory representations and processes of individual subjects. In the following, we will therefore
consider both group and individual results, although only the former will be illustrated graphically.
70
Power-curve analyses
Figures 17 to 20 show the MNs and SDs obtained on correct positive and negative trials
during the first twelve blocks of the Experiment by the various groups. Each point in Figures 17 to
20 summarizes a maximum of 216 observations per subject (minus the errors). For the CM
conditions, the positive RTs obtained on the six successive occurrences of each of the four different
targets were pooled before computing the MNs and SDs for each load condition within a block. A
similar procedure was followed for the CVM and VM groups, except that there were eight different
targets occurring only three times per block. The negative MNs and SDs were obtained in a like
manner. These MNs and SDs are equivalent to those involved in the cross-sectional analyses
reported. They were then averaged over load conditions and finally, over subjects within each
group3.
VM negative
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72
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Although not shown in the Figures, the corresponding error rates remained fairy stable
throughout learning in most Mapping X Stimulus type conditions. The sole significant exception
was condition CVM-HOMO for which the correlation between the percentage of misses and
positive MNs was positive (r (10) = .81, p < .01), indicating that both measures decreased with
practice. All other correlations yielded p values larger than .10. So, there was no significant
evidence of speed-accuracy trade-off in the group results, either on positive or negative trials.
Figures 17 to 20 show not only the empirical data but also the best fitting power curves.
These power functions were computed using a distribution and trend fitting program called
PASTIS (Cousineau and Larochelle, 1997)4. Table 7 gives the three parameters of the curves fitted
to the MNs (leftmost columns), to the SDs (center columns), as well as the five parameters of the
functions fitted to the MNs and SDs considered jointly. Table 8 presents the r2 and rmsd of these
various fits. Values of r2 larger than .332 are needed for the separate MN and SD fits (d.f. = 10) to
be significant at the .05 level. The corresponding value for the joint MN&SD fits (d.f. = 22) is .163.
73
Table 7
Parameters of the power curves fitted to the means (MN) and standard deviations (SD)
and to the combined means and standard deviations (MN&SD)
obtained on positive and negative trials.
MN SD MN&SD
Condition a b c a b c a b c a b
Positive trials
CM-Hetero 372.9 144.0 1.07 37.8 79.3 0.57 369.5 146.0 0.99 54.5 66.0
CM-Homo 375.9 352.8 0.63 55.5 143.5 0.85 383.3 347.3 0.67 40.7 154.5
CVM-Hetero 402.0 326.7 0.70 70.9 166.3 0.63 398.4 330.1 0.68 76.2 162.0
CVM-Homo-I 432.5 274.7 0.83 79.7 139.3 0.72 430.3 276.0 0.82 86.0 135.2
CVM-Homo 510.6 277.2 0.70 158.5 66.3 1.15 510.2 277.5 0.70 146.5 74.2
VM-Hetero 325.7 330.0 0.27 2.7 181.5 0.14 325.6 330.0 0.27 72.6 112.9
VM-Homo 345.9 414.0 0.40 64.7 169.5 0.37 347.5 412.8 0.40 72.2 162.6
Negative trials
CM-Hetero 388.6 158.0 0.90 40.4 68.4 0.45 384.9 160.5 0.85 58.4 53.2
CM-Homo 379.3 448.5 0.59 53.9 166.9 0.96 401.7 429.3 0.66 28.7 184.7
CVM-Hetero 475.2 329.1 0.85 128.8 157.3 1.95 498.6 312.9 1.06 110.3 161.7
CVM-Homo-I 420.8 425.9 0.52 0.0 215.1 0.28 392.0 450.2 0.45 54.5 165.5
CVM-Homo 627.6 341.7 0.53 133.5 120.5 0.58 615.2 352.8 0.50 123.4 130.3
VM-Hetero 482.1 306.3 0.30 52.3 177.3 0.16 368.2 418.8 0.20 76.2 154.1
VM-Homo 564.7 326.3 0.67 44.6 218.2 0.30 547.2 340.6 0.60 120.7 147.7
74
The r2 for the MNs are all highly significant. Although the fits are slightly poorer for
negative than for positive trial RTs; the MNs obtained in the various Mapping X Stimulus type
conditions of the Experiment all appear to follow the power law of practice (Newell &
Rosenbloom, 1981). A surprising result is that the asymptotes estimated for the VM conditions,
positive trials, are smaller than the asymptotes of the corresponding CM conditions, which
appears implausible under most accounts.
75
Table 8
r2 and rmsd of the power curves fitted to the means (MN) and standard deviations (SD)
and to the combined means and standard deviations (MN&SD)
obtained on positive and negative trials.
MN SD MN&SD
Condition r2 rmsd r2 rmsd r2 rmsd
Positive trials
CM-Hetero 0.858 15.0 0.865 6.6 0.995 11.7
CM-Homo 0.981 10.8 0.973 5.8 0.998 8.9
CVM-Hetero 0.981 10.5 0.897 12.5 0.997 11.6
CVM-Homo-I 0.980 9.0 0.953 6.8 0.998 8.0
CVM-Homo 0.956 13.8 0.712 10.9 0.997 12.5
VM-Hetero 0.949 10.6 0.587 13.3 0.996 12.2
VM-Homo 0.994 5.9 0.944 7.1 0.999 6.5
Negative trials
CM-Hetero 0.868 15.2 0.735 7.9 0.996 12.3
CM-Homo 0.978 14.5 0.947 9.9 0.997 12.9
CVM-Hetero 0.937 20.8 0.808 20.7 0.990 22.4
CVM-Homo-I 0.973 14.1 0.905 10.1 0.997 12.7
CVM-Homo 0.862 28.2 0.802 12.8 0.995 21.9
VM-Hetero 0.805 23.3 0.393 21.7 0.992 22.2
VM-Homo 0.962 14.8 0.951 7.4 0.998 12.3
76
The fits on SDs are generally poorer that the fits on MNs, but the r2 for the SDs are also
all significant. Table 8 confirms the goodness of the SD fits for the two CM conditions, in
agreement with Logan's (1988) theory. However, the r2 obtained in the VM-HOMO condition are
about as large as those obtained in the CM conditions. Neither Schneider and Shiffrin's (1977)
nor Logan's (1988) theory allow automatization to occur in VM conditions. The fits on the SDs
obtained in condition VM-HETERO are noticeably poorer. As illustrated in Figure 17, the SD
data of group VM-HETERO exhibit large non-monotonicities. Surprisingly, this had little effect
on the quality of the joint MN&SD fits. As Table 8 shows under the MN&SD heading, the r2
obtained in condition VM-HETERO are not much smaller than those obtained in the other
conditions of the Experiment. It therefore appears possible to obtain large r2 for joint MN&SD
fits even when the SDs barely conform to a power curve.
The quality of the five-parameter fits cannot be attributed to an improved c estimate with
respect to the estimates of the three-parameter fits computed on the MNs and SDs separately.
Although the five-parameter solutions did not leave much room for improvement, the r2 produced
by six-parameter fits to the MN&SD were slightly larger (at the 3rd or 4th place after the point)
than those reported for the five-parameter fits and the rmsd, slightly smaller.
Joint consideration of Tables 7 and Table 8 further reveals that there is little relationship
between the quality of the MN&SD fits and the similarity of the separate cMN and cSD parameters.
Compare, for instance the cMN and cSD obtained with groups CVM-HETERO and CVM-HOMO
on either positive or negative trials. The cMN and cSD are much more similar for one group than
the other. Nonetheless, both groups have about equal goodness-of-fit for joint MN&SD.
77
VM HETERO Negative
y = 0.99x + 3.60
y = 0.39x + 114.99
y = 0.79x + 141.73
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The goodness of the joint MN&SD fits appears to be related to the range of data considered.
Figure 21 plots the MNs and SDs obtained by group CVM-HETERO on negative trials in each of
the 12 practice blocks against those predicted by the best-fitting power curves. MNs occupy the
upper right corner and SDs, the lower left corner. The two straight lines represent the best fitting
linear trend among the MNs and the SDs, considered separately. The reader simply has to extend
these lines to realize that they do not meet. The dotted line is the best fitting linear regression to the
MNs and SDs considered jointly. As previously mentioned, predicted SDs do not account very well
for the observed SDs (VM-HETERO, Negative trials: r2 = .0.393). However, the SDs form a cloud
of points resting in the projection of the MNs, thereby extending the range of the regression line
78
and improving the relationship between predicted and obtained results when the MNs and SDs are
considered jointly. Joint MN&SD fits are therefore subject to an extended range bias.
79
Table 9
r2 and rmsd of the power curves fitted to the means (MN) and standard deviations (SD)
and to the combined means and standard deviations (MN&SD)
obtained on positive and negative trials.
MN SD MN&SD
Subject r2 rmsd r2 rmsd r2 rmsd
Positive trials
CM-Hetero
s5 0.835 9.4 0.868 4.5 0.998 7.4
s6 0.925 13.5 0.848 7.9 0.996 11.1
s7 0.622 17.2 0.395 15.2 0.988 16.3
s8 0.914 22.8 0.914 9.7 0.993 17.5
CM-Homo
s1 0.961 18.4 0.854 16.0 0.994 17.3
s2 0.941 26.3 0.921 16.4 0.989 22.1
s3 0.897 21.3 0.791 12.7 0.993 17.7
s4 0.935 16.4 0.799 13.0 0.995 14.8
CVM-Hetero
s13 0.983 7.6 0.970 4.9 0.999 6.7
s14 0.829 39.9 0.682 40.7 0.965 40.5
s15 0.995 7.9 0.987 7.8 0.999 7.8
80
CVM-Homo-I
s25 0.865 15.7 0.586 29.7 0.996 23.7
s26 0.902 15.6 0.897 46.1 0.993 34.2
s27 0.911 13.0 0.847 47.2 0.995 34.6
s28 0.967 24.8 0.864 90.0 0.971 65.8
CVM-Homo
s9 0.982 8.4 0.713 12.3 0.998 10.6
s10 0.788 25.6 0.293 22.7 0.988 24.5
s11 0.817 17.4 0.053 18.7 0.991 18.1
s12 0.897 37.3 0.698 21.9 0.987 30.6
VM-Hetero
s21 0.957 14.5 0.426 18.6 0.993 16.8
s22 0.481 17.9 0.262 27.6 0.985 23.2
s23 0.619 16.3 0.000 8.5 0.997 13.0
s24 0.973 15.1 0.815 15.8 0.994 15.5
VM-Homo
s17 0.973 21.7 0.829 26.3 0.992 23.6
s18 0.928 18.3 0.797 14.5 0.992 16.9
s19 0.949 17.0 0.831 15.3 0.992 17.8
s20 0.636 25.8 0.237 14.3 0.991 20.8
Negative trials
CM-Hetero
81
s5 0.923 7.7 0.613 6.7 0.998 7.2
s6 0.909 16.1 0.367 11.7 0.995 13.9
s7 0.783 16.9 0.207 19.0 0.989 18.1
s8 0.929 17.5 0.919 9.2 0.996 14.2
CM-Homo
s1 0.969 20.3 0.958 10.3 0.996 16.4
s2 0.946 29.6 0.858 30.7 0.981 30.7
s3 0.903 23.0 0.746 14.1 0.994 19.3
s4 0.948 20.2 0.809 13.1 0.995 17.1
CVM-Hetero
s13 0.988 7.7 0.990 4.5 0.999 6.3
s14 0.842 41.8 0.779 45.8 0.961 47.1
s15 0.971 14.9 0.947 11.7 0.996 14.1
CVM-Homo-I
s25 0.887 18.1 0.374 45.4 0.996 34.6
s26 0.809 24.7 0.876 108.9 0.983 78.9
s27 0.776 31.9 0.697 84.4 0.986 63.9
s28 0.975 28.3 0.870 103.8 0.963 76.3
CVM-Homo
s9 0.942 17.8 0.789 14.1 0.997 16.8
s10 0.424 84.9 0.556 24.2 0.966 62.4
s11 0.500 34.1 0.052 12.6 0.989 25.9
s12 0.792 62.2 0.641 40.8 0.977 52.4
VM-Hetero
82
s21 0.743 33.6 0.179 26.2 0.983 29.9
s22 0.500 35.3 0.109 62.4 0.958 50.7
s23 0.153 32.4 0.000 20.6 0.990 27.2
s24 0.893 31.6 0.944 10.6 0.990 24.8
VM-Homo
s17 0.952 34.8 0.924 21.9 0.987 31.6
s18 0.849 31.4 0.576 23.3 0.987 27.7
s19 0.728 35.2 0.758 15.0 0.992 27.2
s20 0.219 30.8 0.108 16.5 0.990 24.6
Table 9 gives the r2 and rmsd of the power functions computed for each individual subject.
Table 10 gives the corresponding parameters. As shown in Table 9, the estimated MNs correlated
significantly with those of all but two subjects: s20 and s23, negative trials. The correlations
between estimated and obtained SDs failed to be significant for four subjects on positive trials:
s10, s11, s20 s22 and s23, and for six subjects on negative trials: s7, s11, s20, s21, s22 and s23. If
one excludes such subjects, the fits on SDs now tend to be better in the CM conditions than in the
VM conditions, which is more consistent with Logan's theory than the group results mentioned
previously. As before, the r2 of the joint MN&SD fits were all highly significant. The goodness of
the joint MN&SD fits was unfortunately also fairly insensitive to the quality of the separate fits on
MNs or SDs: for the seven subjects with non-significant fits on MNs, on SDs or on both, r2 for the
joint M&SD fits averaged .986.
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Table 10
Parameters of the power curves fitted to the means (MN) and standard deviations (SD)
and to the combined means and standard deviations (MN&SD)
obtained on positive and negative trials.
MN SD MN&SD
Subject a b c a b c a b c a b
Positive trials
1.00 285.77 480.69 0.45 16.36 184.15 0.56 299.62 469.29 0.47 0.00 198.58
2.00 374.43 403.08 0.82 61.09 200.32 1.06 383.87 395.00 0.87 49.37 208.10
3.00 375.85 308.62 0.52 81.35 98.71 0.96 390.22 296.16 0.57 59.16 115.21
4.00 435.54 253.98 0.87 40.18 115.15 0.67 432.96 255.83 0.84 50.96 106.84
5.00 328.94 100.03 0.57 35.84 50.82 0.70 332.03 97.35 0.60 32.31 53.66
6.00 325.67 221.98 0.49 44.33 90.27 0.46 320.50 227.02 0.47 45.25 89.07
7.00 172.66 260.85 0.14 0.00 111.27 0.18 234.83 198.35 0.19 0.95 110.67
8.00 349.41 311.64 0.62 25.87 121.89 0.78 361.96 299.72 0.68 18.72 127.26
9.00 437.23 286.55 0.61 114.50 81.15 0.79 428.61 294.37 0.58 102.53 90.64
10.00 600.43 183.03 1.84 177.23 52.85 10.00 602.23 182.58 1.99 175.00 50.75
11.00 221.85 368.92 0.17 69.85 67.55 0.10 229.69 360.80 0.17 94.93 42.64
12.00 607.50 464.16 0.77 207.94 133.05 0.96 606.80 465.64 0.77 196.93 141.83
13.00 335.07 249.64 0.71 9.27 147.40 0.45 327.01 255.70 0.66 35.62 124.50
84
14.00 264.23 493.60 0.40 34.65 261.44 0.69 334.82 429.27 0.52 0.00 288.03
15.00 306.60 477.27 0.72 8.47 286.38 0.75 307.36 476.70 0.73 5.54 288.56
16.00 611.89 176.16 1.07 224.90 0.18 0.00 370.35 386.94 0.19 225.08 0.00
17.00 322.77 682.17 0.44 0.00 340.28 0.35 206.50 795.24 0.35 0.00 340.68
18.00 353.15 313.10 0.55 0.00 205.19 0.26 331.99 330.81 0.48 67.12 141.75
19.00 512.40 273.63 1.68 160.90 122.86 5.49 519.67 270.41 2.06 156.06 120.37
20.00 125.48 516.59 0.10 82.76 68.37 0.18 137.75 502.52 0.10 32.47 119.92
21.00 84.11 608.53 0.20 0.00 178.57 0.15 95.75 597.72 0.20 39.83 139.90
22.00 510.39 96.52 0.39 110.75 115.33 0.28 463.48 141.52 0.22 89.45 136.08
23.00 472.11 141.39 0.26 109.81 2.53 0.00 474.01 139.48 0.27 112.34 0.00
24.00 289.28 429.74 0.46 80.06 137.29 0.64 299.68 420.30 0.48 60.24 154.04
25.00 453.54 185.39 0.60 78.78 95.74 0.35 442.15 195.38 0.53 97.72 79.61
26.00 367.00 201.91 0.79 51.52 187.88 0.42 349.18 213.83 0.63 86.14 159.37
27.00 470.11 168.59 1.44 116.05 148.17 0.57 460.66 170.85 1.08 146.73 127.00
28.00 421.47 540.72 0.83 0.00 444.57 0.32 378.25 567.96 0.67 147.93 315.18
Negative trials
1 382.91 522.75 0.61 37.23 199.26 0.87 403.77 504.44 0.66 14.01 215.96
2 362.02 476.11 0.80 64.54 264.47 1.25 384.92 457.81 0.92 42.69 277.80
3 466.86 303.18 0.72 0.01 159.98 0.30 458.29 309.72 0.67 60.51 104.67
4 415.19 388.02 0.65 30.98 125.75 0.58 416.87 386.59 0.65 37.57 120.29
5 315.79 128.18 0.53 15.29 66.09 0.24 304.38 139.11 0.46 39.04 43.41
6 338.29 253.86 0.42 65.31 42.46 0.47 298.48 293.42 0.34 56.00 51.31
85
7 195.36 319.73 0.17 0.04 112.68 0.14 243.40 271.04 0.21 32.27 80.43
8 395.40 248.80 0.75 0.00 141.86 0.51 380.80 261.07 0.66 16.82 127.15
9 529.96 378.56 0.45 119.66 103.35 1.31 562.78 349.60 0.53 82.25 128.30
10 840.64 263.36 10.00 196.67 98.19 10.00 840.63 263.36 10.00 196.66 98.25
11 348.22 338.38 0.17 86.22 34.34 0.14 407.26 276.16 0.21 98.12 21.86
12 564.79 684.16 0.40 88.69 324.99 0.34 456.71 785.81 0.32 65.86 350.80
13 386.67 275.94 0.94 32.74 180.44 0.83 383.71 277.93 0.91 38.49 176.37
14 337.61 500.82 0.46 108.76 317.22 1.99 476.03 384.17 0.92 55.40 337.92
15 251.05 487.92 0.39 0.00 232.26 0.56 332.64 414.37 0.54 0.00 228.32
16 690.75 275.19 1.48 260.27 0.18 0.00 690.73 275.40 1.48 260.45 0.00
17 536.64 654.90 0.77 0.00 461.30 0.34 476.45 701.51 0.63 137.17 336.89
18 475.33 342.43 0.60 81.87 134.08 0.51 470.74 346.47 0.59 90.83 126.32
19 726.41 213.85 1.82 161.61 96.97 2.90 728.06 213.22 1.93 158.36 97.20
20 494.03 164.63 0.15 56.74 96.33 0.09 420.45 239.75 0.10 74.80 77.57
21 443.93 322.62 0.39 62.92 138.09 0.15 356.89 407.13 0.27 122.15 76.94
22 571.01 275.31 0.23 136.80 196.34 0.20 544.47 303.63 0.21 146.01 186.91
23 623.42 71.23 0.41 124.99 0.83 0.00 449.31 242.51 0.08 125.81 0.00
24 387.99 451.64 0.42 118.75 152.99 1.23 409.12 434.05 0.46 52.80 200.00
25 370.81 354.70 0.27 14.77 161.50 0.12 365.89 359.60 0.27 93.05 84.24
26 408.48 250.44 0.57 0.00 332.42 0.20 283.91 356.73 0.27 58.96 277.98
27 545.70 270.55 0.75 6.04 303.36 0.19 454.40 342.19 0.39 124.12 190.15
28 313.37 882.54 0.53 0.00 535.36 0.44 226.43 954.29 0.44 0.00 540.15
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For completeness sake, let us add that we also analyzed the individual subjects' performance
for each target separately. These analyses provide the most adequate test of instance theory, since
the race for identification is assumed to involve different traces of the same S-R association (same
target in the visual-memory search paradigm) rather than traces of different S-R associations
(different targets in the visual-memory search paradigm). These analyses required pooling only the
three (CVM and VM conditions) or six (CM conditions) successive occurrences of a given target
within a given M X D condition prior to computing the MN and SD. These MNs and SDs could
then be averaged over M X D conditions, but not over subjects, since the assignment of targets to
subjects was variable. These analyses could also be performed only for positive trials, since targets
are undefined for negative trials. We will spare the (tired) reader of the results of these analyses.
Suffice it to say that the same anomalous insensitivity of the joint MN&SD fits to the separate MN
and SD fits was also found.
Durbin-Watson tests
As discussed before, an alternative approach to the question of the equality of cMN and cSD
consists in testing whether the SDs are linearly related to the MNs, which should be the case when
the MNs and SDs follow a power curve with identical rate parameters. This approach has the
double advantage of involving only obtained data and of not being subject to the extended range
bias identified. The results of the Durbin-Watson test of linearity are given in Table 12 for the
various groups and subjects in the Experiment. Small values of the DW statistic lead to the
rejection of the hypothesis that the data are on a line. In our context, values smaller than 1.01 lead
to the rejection of the null hypothesis (p < .05) and to the conclusion that the cMN and cSD differ.
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Table 11
Durbin-Watson statistic for the various groups and subjects in the Experiment
Group Subjects
Positive trials
CM-Hetero 1.83 s5-s8 1.63 0.47 1.93 1.30
CM-Homo 1.76 s1-s4 1.92 1.55 1.23 1.48
CVM-Hetero 1.80 s13-s15 1.24 1.76 1.84
CVM-Homo-I 1.83 s25-s28 1.34 1.21 1.07 1.58
CVM-Homo 1.15 s9-s12 1.64 0.62 0.67 1.29
VM-Hetero 1.12 s21-s24 0.97 0.87 0.37 1.08
VM-Homo 1.88 s17-s20 0.70 0.92 1.39 1.67
Negative trials
CM-Hetero 1.48 s5-s8 1.03 1.61 1.97 0.49
CM-Homo 1.59 s1-s4 1.66 1.71 1.63 2.00
CVM-Hetero 0.59 s13-s15 1.87 1.89 1.27
CVM-Homo-I 1.74 s25-s28 1.59 1.65 1.51 1.91
CVM-Homo 1.60 s9-s12 1.67 1.29 1.13 1.71
VM-Hetero 1.25 s21-s24 1.95 1.55 0.96 1.80
VM-Homo 1.06 s17-s20 1.70 1.45 0.69 0.35
Tests performed on positive trial RTs of the individual subjects show eight significant
departures from linearity. Most of these are found in conditions which do not allow performance to
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rely on instance retrieval, namely: VM-HETERO (s21, s22, s23), VM-HOMO (s17, s 18). The SD
power fits computed for two of these subjects (s22, s23) had also failed to be significant (see Table
10). Three other subjects in VM conditions (s19, s20, s24) appear to meet Logan's criterion, but the
SD data of one of these subjects (s20) failed to exhibit a significant power decrease. Other
significant departures from linearity are found in conditions CVM-HOMO (s10, s11) and in
condition CM-HETERO (s6), despite significant power fits to the MNs and SDs in the later case.
The performance of three subjects (s17, s18, and s20) who do not meet Logan's criterion exhibited
a significant speed-accuracy trade-off over blocks on positive trials. There was also a speed
accuracy trade-off in the performance of two other subjects (s3, s9) who appear to meet Logan's
criterion. Therefore, success or failure to meet Logan's criterion does not seem to depend on the
absence or presence of a speed-accuracy trade-off.
The results of the DW tests performed on negative trial RTs show only four significant
departures from linearity, two in condition VM-HOMO (s19, s20), one in condition VM-HETERO
(s23) and one in condition CM-HETERO (s8). However, the power fits to the SD data of three
other subjects (s7, s11, and s21) were not significant. The performance of two subjects (s1, s8)
exhibited a significant speed-accuracy trade-off over blocks on negative trials. Nonetheless, both of
these subjects appear to meet Logan's criterion. The DW tests performed on group results show
only one significant departure from linearity, for negative trials in condition CVM-HETERO. The
discrepancy between the results obtained with the group vs. the individual subjects in this condition
illustrates the distortions that averaging can produce.
To summarize, the DM tests failed to be significant for 18 of the 22 subjects for whom the
power fits to the MNs and SDs obtained on positive trials were significant, which suggests that the
rate parameters cMN and cSD did not differ. For these 18 subjects, the ratio of the amplitude
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parameters bSD on bMN obtained in the joint MN&SD fits range from 0.30 to 0.75 (see Table 10).
The average of these ratios, 0.50, is not far from the 0.60 value expected on the sole basis of a
reduction in the number of feature tests over practice. For negative trial RTs, the DM tests
performed failed to be significant for 20 of the 22 subjects for whom the power fits to the MNs and
SDs were significant, which suggests that the rate parameters cMN and cSD did not differ. For
these 20 subjects, the ratios of the amplitude parameters, bSD on bMN, range from 0.23 to o.88
(see Table 10), with an average of 0.47. For the 15 subjects whose performance meet Logan's
criterion on both positive and negative trials, the ratios of the amplitude parameters, bSD on bMN,
averaged 0.50 for both trial types, which suggest the same processes may be responsible for the
power decrease in MNs and SDs on both positive and negative trials. However, the rate of learning
was not the same for positive and negative trials. For the same15 subjects mentioned above, the c
parameters of the joint MN&SD fits averaged 0.67 on positive trials and 0.48 on negative trials.
Logan's criterion (of the equal-rate, power curves on MNs and SDs) failed to be satisfied by
all but one subject in VM conditions on either positive or negative trials. This finding supports
instance theory since prior S-R associations are totally uninformative in VM conditions. Although
CM conditions are ideal for relying on retrieval of prior S-R associations, Logan's criterion failed to
be met by three of the four subjects in condition CM-HETERO on positive or negative trials. By
contrast, all subjects in condition CM-HOMO appear to satisfy Logan's criterion on both trial types,
which is surprising in view of the results of the cross-sectional analyses reported earlier. Remember
that performance of this group exhibited fanning M X D interactions on the first block of the
Experiment, but not on the twelfth, which can be taken as evidence for a switch from controlled to
automatic processing. If this is the case, then the results of our longitudinal analyses confirm and
extend Logan's simulations in showing that the dynamics of controlled processing do not mask the
90
dynamics of instance retrieval in the visual-memory search task. A simpler interpretation is that the
same processes underlied performance at all stages of learning.
Logan's criterion failed to be met by two of the four subjects in condition CVM-HOMO on
either positive or negative trials. However, no single subject failed to meet Logan's criterion on
either trial type in condition CVM-HOMO-I and in condition CVM-HETERO. These results
suggest that, if performance relies on retrieval of prior associations, these associations specify the
set membership of the stimuli, as discussed in the Introduction. This interpretation accounts nicely
for the generalized failure to meet Logan's criterion in VM conditions since the stimuli did not form
any set, and for the occasional failure to meet the criterion in condition CVM-HOMO since the set
composition of the stimuli was not necessarily perceived. The set composition of the stimuli was
much easier to perceive in CM conditions, especially in condition CM-HETERO where the set
composition of the stimuli matched pre-established categorical distinctions. For this reason,
subjects in condition CM-HETERO may have relied less heavily on stimuli-to-set associations than
subjects in condition CM-HOMO, which would account for the fact that Logan's criterion was
more generally satisfied in the latter condition. So, an interpretation based on stimulus-to-set
associations provides a nice overall account of the results, although admittedly a bit contrived to
exclude the performance of group CM-HETERO. However, the performance of this group also
conflicts with an interpretation based on the retrieval of stimulus-to-response associations.
Model
In this section, we consider the behavior of the model over practice. There is no
comparison time parameter in the model. The only effect of practice is to change the number of
features that are considered on any given trial. As previously described, these changes are
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achieved through two mechanisms. The first consists in ordering the features tests in such a way
that the features which best discriminate the targets from the distractors over trials come to be
considered first. The second consists in setting a threshold of diagnosticity, below which feature
processing stops. As currently implemented, these mechanisms lead to very rapid improvement in
performance. It was not deemed very useful to fine-tune these mechanisms considering the other
weaknesses of the model. For the same reason, we did not implement any forgetting mechanism
and, of course, the model does not warm up or tire, it does not take weekend breaks etc.
Therefore, one should not expect the model to provide a good quantitative fit to the empirical
data. Our goal was only to determine whether, and in which condition, the model yields power
curves for MNs and SDs with the same rate parameter.
The computer simulation was therefore run in the same Mapping X Stimulus type
conditions as the real subjects. Assignment of the simplified stimuli shown in Figure 10 to each
simulated subject was the same as for real subjects. However, the training schedule differed.
Because of the model's rapid rate of learning, amount of practice within each block was reduced
to a minimum while still respecting the constraints of the Experiment's design: Instead of
appearing three (CVM and VM conditions) or six times (CM conditions) per block in each of the
nine M size X D size conditions, each of the eight (CVM and VM conditions) or four possible
targets (CM conditions) was used only once per block on positive trials. Each block was therefore
composed of 72 positive trials for each simulated subject in CVM and VM conditions, and of an
equivalent number of negative trials, for a total of 144 randomly ordered trials. For the simulated
subjects in CM conditions, there were only 36 positive and 36 negative trials per block. Each
simulated subject was run through 12 successive blocks of trials.
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The mean number of features considered by the model in each M size X D size X R type
condition of each block was computed for every simulated subject, and so were the standard
deviations. These MNs and SDs were then averaged over M size X D size conditions and finally
over subjects within each Mapping X Stimulus type condition, these computations being
equivalent to those previously performed on the RTs. PASTIS was used to fit power curves to
these averaged MNs and SDs. We have not attempted to fit separate power curves for each
simulated subject. By contrast with real subjects, whose performance may be very idiosyncratic,
the only 'individual' differences expected from the model arise from the variable stimulus-to-
subject assignment procedure used. These differences are probably not such as to warrant
individual analyses, especially considering the preliminary status of the model.
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Table 12
r2 and rmsd of the power curves fitted to the means (MN) and standard deviations (SD)
and to the combined means and standard deviations (MN&SD)
produced by the simulation on positive and negative trials.
MN SD MN&SD
Condition r2 rmsd r2 rmsd r2 rmsd
Positive trials
CM-Hetero .98 0.21 .97 0.21 .98 0.24
CM-Homo .78 0.45 .83 0.47 .93 0.49
CVM-Hetero .97 0.38 .98 0.29 .98 0.36
CVM-Homo .99 0.03 .99 0.03 .99 0.04
VM-Hetero .41 0.83 .56 0.93 .87 0.93
VM-Homo .56 0.86 .64 0.99 .82 1.00
Negative trials
CM-Hetero .99 0.01 .99 0.01 .99 0.01
CM-Homo .78 0.08 .85 0.08 .99 0.09
CVM-Hetero .99 0.08 .99 0.08 .99 0.12
CVM-Homo .99 0.00 .99 0.01 .99 0.01
VM-Hetero .47 0.10 .64 0.14 .99 0.15
VM-Homo .49 0.15 .67 0.14 .99 0.15
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Table 12 gives the r2 and rmsd of the power curves fitted to the means (MN) and standard
deviations (SD) and to the combined means and standard deviations (MN&SD) produced by the
simulation on positive and negative trials. Although goodness-of-fit is generally poorer in VM
conditions, the separate fits computed on the MNs and on the SDs are significant in all Mapping
X Stimulus type conditions. The five-parameter fits computed on the joint MN&SDs are even
better. The improvement of the joint MN&SD fits is especially pronounced for negative trials in
condition CVM-HETERO. Comparison of Figures 12 and 15 shows that the model may not have
been totally immune to an extended range bias on negative trials.
95
Table 13
Parameters of the power curves fitted to the means (MN) and standard deviations (SD)
produced by the simulation on positive and negative trials,
along with the results of the Durbin-Watson tests.
MN SD
Condition a b c a b c DW
Positive trials
CM-Hetero 0.00 7.68 0.11 0.00 2.07 0.14 1.34
CM-Homo 6.79 0.12 0.00 1.87 0.09 10.00 1.85
CVM-Hetero 3.28 3.18 6.39 1.43 0.86 4.50 1.35
CVM-Homo 5.29 0.78 10.00 1.65 0.32 10.00 1.01
VM-Hetero 6.46 0.75 0.16 1.99 0.14 0.10 1.86
VM-Homo 6.92 0.07 0.00 2.03 0.02 0.00 1.29
Negative trials
CM-Hetero 3.81 0.38 0.21 1.13 0.14 0.37 1.88
CM-Homo 4.21 0.06 10.00 1.25 0.10 3.89 1.86
CVM-Hetero 7.71 0.43 4.79 2.69 0.33 2.78 1.98
CVM-Homo 7.50 1.02 0.18 2.74 0.49 0.54 1.67
VM-Hetero 9.46 0.61 0.13 3.53 0.17 0.12 1.32
VM-Homo 9.49 0.05 0.00 3.48 0.17 1.33 1.99
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The parameters of the separate power fits computed on the MNs and on the SDs are given
in Table 13, along with the result of the Durbin-Watson tests performed on the MN and SD data
produced by the model. As shown, cMN and cSD tend to be similar in all Mapping X Stimulus
type conditions. The Durbin-Watson tests failed to reveal any significant deviation from linearity.
These results suggest that the model meets Logan's criterion in all conditions. Over conditions,
the ratios bSD over bMN average X on positive trials and Y on negative trials.
There is nothing inherent to a serial, feature-based comparison process which forces the
mean number of feature tests to decrease as a power function of practice. It is the reordering and
reduction of feature tests in the model that caused the power reduction in MNs on both positive
and negative trials. However, the equations that characterize serial self-terminating processing
lead to expect that the SDs will decrease at the same rate as the MNs when the MNs obey the
power law of practice. So the success of the model in meeting Logan's criterion is no surprise.
In view of the empirical results discussed previously, the model appears too successful in
meeting Logan's criterion. Although the performance of seven subjects met Logan's criterion on
either positive or negative trials in VM conditions, the performance of only one subject met the
criterion on both trial types. It is difficult to attribute these results to idiosyncratic variations in
performance since the criterion was met by all subjects on both positive and negative trials in some
CVM and CM conditions. The model therefore appears less sensitive to varied mapping than the
real subjects do.
The very insensitivity of our single-process model to VM conditions shows that Logan's
criterion can be satisfied even in conditions, which are thought by dual-process theorists to forbid
automatization. As such, the model invalidates Logan's criterion as an a-priori test of
97
automatization. Note that this conclusion was foreshadowed by Logan's (1988) own simulations.
How can same-rate power curves for MNs and SDs be considered a signature of automatic
processing when the presence of controlled processing does not alter the results? Not to mention
that the tests performed by Logan (1988) could very well have been contaminated. Since Logan did
not compute separate three-parameter fit on the MNs and SDs, it is impossible to tell whether the
MNs and the SDs behaved according to the power law. The quality of the joint MN&SD fits
reported could simply have resulted from an extended range bias, as demonstrated here.
DISCUSSION
On the basis of the overall picture depicted, we wish to argue that it is not necessary to
postulate fundamentally different processes to account for either load or practice effects in CM
and in VM conditions. This does not mean, however, that consistency of mapping is irrelevant.
As noted by Duncan (1980), totally inconsistent mapping is found only in arbitrary tasks. This is
not the case of the visual-memory search task, even in VM conditions. If one considers the
stimulus to encompass both the memory and display sets, then the correct response is fully
determined, even in VM conditions. The important question is what level of consistency affects
processing and performance?
Some of our results strongly suggest that it is not the level of combined memory and
display sets just mentioned. The number of different combinations of memory and display sets to
learn was much smaller in CVM than in VM conditions: over trials, subjects in CVM conditions
were presented with only 12 different memory (or distractor) sets of size 2 and with only 2
different memory sets of size 4, compared to 28 and 70 different sets of size 2 and 4 respectively
in VM conditions. The large load effects obtained in condition CVM-HOMO show clearly that
98
the subjects did not benefit from this reduced combinatorial. A similar case can be made from
the results obtained in CVM vs. CM conditions. Compared to subjects in CVM conditions, those
in CM conditions were presented with half as many different memory sets over trials, receiving
twice as much practice on each. Nonetheless, the load effects obtained in condition CVM-
HETERO were similar, if not smaller than those obtained in condition CM-HOMO.
This last result is very important. First, it clearly contradicts Schneider and Shiffrin's
claim that consistent S-R mapping is necessary and sufficient for automatization. Second, it
shows that the frequency contingencies of the task at the level of individual stimuli are not the
primary cause of improvement either. Since there were half as many targets in CM conditions as
in CVM conditions, amount of practice per target was twice as large in CM conditions.
Nonetheless, subjects in condition CVM-HETERO outperformed those in condition CM-
HOMO. Comparison of these two conditions therefore suggests that it is not at the level of
individual stimuli that mapping and frequency effects occur. The load effects obtained in
condition CVM-HOMO further suggest that the discriminability of individual targets is not
critical either. Although all stimuli served equally often as target and as distractor in the CVM
and the VM conditions and although amount of practice per target was the same across
conditions, subjects in CVM conditions had to discriminate each target form only four other
characters whereas subjects in VM conditions had to discriminate each target from seven other
characters. The greater ease of discrimination involved did not benefit subjects in condition
CVM-HOMO.
The only evidence that consistency of mapping at the level of individual stimuli might be
involved in the automatization of visual-memory search comes from a comparison of the load
effects obtained before and after extensive practice in condition CM-HOMO. Recall that the
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load effects obtained on the first training block were characteristic of controlled processing
whereas those obtained on the last training block were characteristic of automatic processing.
These results contrast sharply with the load effects obtained in condition CM-HETERO which
were characteristic of automatic processing right from the start of the Experiment, though
slightly more pronounced. On the basis of these results, we suggested that consistent S-R
mapping may be involve in the formation of distinct target and distractor categories, such
categorical distinctions being pre-established in condition CM-HETERO. The fact that load
effects remained much more pronounced in condition CVM-HOMO-I than in condition CM-
HOMO, even though subjects were told of the set distinctions among the stimuli, provides
further support to this hypothesis. One way to determine whether consistent mapping is
necessary to the formation of categorical distinctions between targets and distractors would
involve training subjects in a CM-HOMO condition before transferring them to a CVM-HOMO
condition. If the target-distractor distinction achieves the same categorical status as the
distinction between digits and letters, then performance on the previously defined target set
should not suffer from transfer. To our knowledge, this critical test has not yet been performed.
Much of the literature on automaticity in the visual-memory search task deals with the
pattern of load effects obtained after extensive training in different mapping conditions.
However, the general arguments made previously concerning the consequences of mapping on
the combinatorial aspects of the task, as well as on the frequency and discriminability of
individual targets do not only apply to asymptotic performance but also to learning rate. The rate
parameters given in Tables 7 (group data) and 10 (subject data) indicate that performance did not
improve faster in condition CVM-HOMO than in VM conditions despite the reduced
combinatorial and the greater discrimination ease involved. Similar rate parameters were also
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obtained in conditions CM-HOMO and CVM-HETERO despite the reduced number of targets
and the larger amount of practice per target. All these results suggest that it is not at the level of
individual stimuli that consistency of mapping is important.
The same conclusion applies mutatis mutandi to instance theory. As previously
discussed, performance in CM conditions can rely on the storage and retrieval of S-R
associations. These associations would link each target to a positive response and, possibly also,
each distractor to a negative response. According to Logan's original theory, and more recent
extensions (Nosofsky & Palmieri, 1997), one could then expect both MNs and SDs to decrease
as power functions of practice with similar rate parameters, a result which was considered by
Logan (1988) as the criterion of automatization. The results of all subjects in condition CM-
HOMO appeared to meet Logan's criterion on both positive and negative trials. This was a
surprise given the differential load effects obtained at the beginning and end of training
discussed previously. Even more surprising was the fact that the performance of all subjects in
condition CVM-HETERO (with the probable exception of the subject rejected from the
analyses) also met Logan's criterion. Prior S-R associations were totally uninformative in the
CVM and VM conditions of the Experiment. So, inasmuch as Logan's criterion constitutes a
valid test of instance theory, one much reject the 'behaviorist' hypothesis that subjects must rely
on prior S-R associations to automatize performance.
All subjects in condition CVM-HOMO-I also satisfied Logan’s criterion. Failures to meet
the criterion were concentrated in the VM conditions and in the CVM-HOMO condition,
especially on positive trials. It is tempting to attribute the failures obtained in VM conditions to
the fact that there was no set distinction among the stimuli. Although present in CVM
conditions, such a distinction does not seem to have been perceived by the subjects in condition
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CVM-HOMO, thus the differences in performance between conditions CVM-HOMO vs. CVM-
HOMO-I. Although the stimulus-responses associations are uninformative in CVM conditions,
the stimulus to set associations are constant. The results obtained in the two informed CVM
conditions (HETERO and HOMO-I) therefore suggest that performance may have been
mediated by stimulus-to-set associations, in agreement with a less behaviorist interpretation of
instance theory. More generally, the fact that the practice and load effects obtained in some
CVM conditions were so similar to those obtained in CM conditions and so different from those
obtained in VM conditions certainly supports Cheng's (1985) argument that automatization of
performance in the visual-memory search task might have more to do with the set and category
distinctions than with the mapping of individual stimuli to responses.
Our main claim is that consistency of mapping is critical at the featural level. In ideal
circumstances, only one or a few features would allow to discriminate all targets from all
distractors, in which case the mapping of features to responses would be absolutely consistent.
We argued that, through learning, subjects learn which features are more discriminative, search
being guided by these more discriminative features. In the simple model developed, the relative
importance of features is represented by an ordered feature list. The features which allow to
discriminate each target from the distractors move up the list. If these discriminative features are
shared by many targets, they come to dominate the list. In ideal circumstances, the list will be
dominated by features that are both common and unique to targets. This is exactly the nature of
categorical representations proposed in the classical view of concepts. The ideal is not always
achievable, even in CM conditions. Approximation of this ideal depends on the level of
similarity among targets and on their level of dissimilarity with the distractors, as suggested by
the results of Humphreys, Quinlan and Riddoch (1989; Duncan & Humphreys, 1989). So,
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according the vocabulary of the literature on categories and concepts, the knowledge embodied
in the feature list is more of a prototypical nature than of a definitional nature. Even this type of
categorical knowledge in impossible to approximate in CVM and VM conditions since there are
no distinct target and distractor sets. According to our view, this is the cause of the poor
performance obtained in VM and CVM-HOMO conditions.
In order to account for performance in conditions CM-HETERO and CVM-HETERO,
we had to postulate two different feature lists, one for letters and one for digits. This is not
implausible since feature lists are thought to embody categorical knowledge. The features that
discriminate digits from letters had been learned by our subjects, long before the start of the
Experiment. We attribute early performance obtained in the above conditions to this pre-
established categorical knowledge. The existence of different feature lists (weights) for digits
and letters also accounts nicely form the fact that performance in condition CVM-HETERO was
not disturbed by the switching of targets and distractors over trials. Since different feature lists
were updated, performance was little affected compared to that of the other CVM groups.
To summarize: although the mapping of features to responses is central to our account of
the results, the link between the features and responses is by no means direct. Set and category
representations mediate the effects on performance. Given such representations, the model was
able to account for a large array of results using a single comparison process. The feature-based
comparison process we have described was able to account for the pattern of load effects on the
mean RTs obtained after extensive practice in all mapping and stimulus conditions of the
Experiment, except CVM-HOMO. The serial, self-terminating nature of the process predicted
further that the effects of load on SDs would be 60% as large as those on MNs, a prediction
which was confirmed by the positive trial RTs obtained during the last block of training under
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most mapping and stimulus conditions. The success of the model in accounting for the pattern of
load effects on positive trial MNs and SDs resulted from a simple reordering and reduction in
the number of the feature tests performed.
According to the model, the exact same mechanism underlies load and practice effects of
on performance. The mean number of feature tests performed by the model in all conditions of
the Experiment decreased as a power function of practice, which yields credibility to the model
considering the ubiquity of the power law in our Experiment and others. As previously noted,
the serial self-terminating nature of the comparison process involved in the model almost
guaranteed that the SDs would decrease at the same rate as the MNs on positive trials. This
result, which Logan (1988) considered to be the criterion of automatization, was obtained with a
vast majority of subjects. Moreover, for subjects who met the criterion, the amplitude of the
practice effects on the SDs was about 50% as large as that on means, a value which is not far
from the 60% figure expected on the sole basis of the serial self-terminating nature of the
comparison process.
Failures to meet the criterion were concentrated in the conditions that also produced the
largest load effects: VM and CVM-HOMO. It is tempting to attribute these failures to the fact
that there was no set distinction among the stimuli in VM conditions and that, although such a
distinction was present in condition CVM-HOMO, it failed to be perceived by the subjects. In
it's current implementation, the model updates the featural representation of sets of stimuli. The
model could perhaps provide a better account of the practice effects obtained in the VM and
CVM-HOMO conditions by reordering the feature tests for each individual stimulus (or, in other
words, by updating the featural representation of the individual stimuli instead of that of
stimulus sets). Such a possibility would provide a very plausible explanation for the differential
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load effects obtained in conditions CVM-HOMO and CVM-HOMO-I. Unfortunately, this
possibility has just recently dawned on us, so the modification described and the requisite
simulations have not yet been performed. Despite these weaknesses, the model's account of
positive RTs is currently the most encompassing while being at the same time the most
parsimonious.
The model has much more serious drawbacks with respect to the RTs obtained on
negative trials. Search was assumed to be exhaustive over items on negative trials, as in most
traditional, model. This provides a natural account of the 2 to 1 ratio of load effects on the
negative vs. positive MNs obtained in VM conditions. By contrast with traditional item-based
models, our feature-based comparison model involves self-terminating processing within items.
This self-terminating component allowed to account for the ratio of load effects on negative vs.
positive MNs in most mapping and stimulus type conditions of the Experiment. Unfortunately,
the model fails to account for the load effects on the SDs obtained on negative trials: the within-
character variability in the number of feature tests performed is not sufficient to compensate for
the lack of variability of search over items within a given load condition. We have shown that, in
order to account for the load effects on SDs, the featural complexity of the stimuli would have to
be increased to over 100 features per character. However, the size of the load effects on the
positive and negative MNs suggest that, with such featural complexity, successive feature tests
would have to be performed at a rate which exceeds the physiological refractory period. In short,
exhaustive search over items on negative trials is incompatible with the serial, feature-based
account proposed.
We have deferred discussion of the RTs obtained on negative trials until now, because
the case of negative trial RTs is not as simple as it might seem. Schneider and Shiffrin attributed
105
the differences between the positive and negative MNs obtained in VM conditions to the self-
terminating vs. exhaustive nature of item search. With some post-hoc assumptions concerning
the item processing and switching time, their serial model was also able to account for the load
effects on positive and negative trial variances. They did not attempt to model performance in
CM conditions, attributing CM performance to some form of parallel comparison process. Item-
based parallel processing will not account for the load effects on negative trial SDs obtained
here. Error-free performance on negative trials requires that all distractors be processed before
the response can be produced. In such a case, the variance in finishing time tends to decrease
with the number of distractors to process. This decrease in variance should have been especially
pronounced in the CM conditions of our Experiment, since the same four distractors were
repeatedly used when display size was equal to four (different subsets of distractors being used
in conditions of lesser load). This is clearly not what happened: SDs tended to increase with load
on negative as well as positive trials, in CM as in VM conditions.
Although not developed in the context of the visual-memory search task, instance theory
provides another possible mechanism for reaching a negative decision in CM conditions: one can
imagine that negative trials increase the number of associations linking the distractors to the 'no'
response, just like positive trials increase the number of associations between targets and the 'yes'
response. This would allow both types of responses to result from a race for identification among
the display items. Positive and negative RTs should therefore exhibit a very similar dynamic, at
least when separate power curves are computed for each individual target and distractor. The power
curves analyzed here were computed over all targets and distractors. When considered in the
perspective of instance theory, they do not reflect only a race among traces for each item, but they
also a competition between items (when memory or display size is greater than 1). Recent
106
extensions of instance theory (Nosofsky & Palmieri, 1997) take into account the type of
competition and could possibly account for the SDs obtained on negative as well as positive trials.
The fact that Logan's criterion was satisfied by all but one subjects in CM and CVM conditions
suggests that the traces involved specify set information rather the response required. The fact that
Logan's criterion was also satisfied by a majority of subjects in VM conditions suggests that the
traces involve featural information. The feature lists in our model summarize exactly such feature-
to-set associations.
A lot of research has been done and continues to be done to distinguish between instance
and prototype theories of categories and concepts. We do not wish to make a strong claim in
favor of our feature list representations and against instance-based representations and processes.
The list format was adopted mainly for its simplicity, which makes the feasibility of the serial
comparison process proposed more obvious. However, it is possible that the prototypical
representations embodied in our feature lists and that the updating of feature lists results from
underlying instance representations. Arguments derived from rational analysis suggest that, in
order to update a summary representation, such as a prototype, one has to know how much
weight to give to the information provided by a newly encountered instance with respect to the
old information embodied in the prototype. This implies some knowledge about the amount of
information underlying the prototype, knowledge which is derived from instance representations:
For example, one should not reject a prototype built from a million instances on the basis of a
single new instance but, in order to prevent rejection of the prototype, one must have kept at
least a rough count of the number of instances encountered. Our only reply to this argument is
that our model does fine in it's micro-world without keeping such a tab, at least on positive trials.
107
Our current approach to negative trial RTs is based on the fact that performance is not
error-free. Within the context of a feature-based model, this means that some features may be
misperceived. Misperception of features is much more likely to lead to the false identification of
a target as being a distractor than to the false identification of a distractor as being a target.
Accordingly, misses tend to be more frequent than false alarms in search tasks. Consequently,
subjects may proceed to a verification when no target has been found, a verification which can
lead to the correct response on positive trials but which is useless on negative trials. Since the
probability that an item is misperceived increases with the number of feature tests performed, we
are confident that such a search and verify mechanism will be able to account for both load and
practice effects on MNs and SDs obtained on positive and negative trials in all conditions of the
visual-memory search task. All current accounts of performance in the task fall way short of
such a goal.
Whether we will succeed in reaching this goal remains to be seen. As the saying goes, the
proof will be in the pudding. Although our pudding is not cooked yet, the main ingredients are
there: A simple serial feature comparison process which remains unchanged throughout learning,
coupled with just as simple a mechanism for updating the featural representations of items and
sets. What is currently missing is a form of 'self-terminating' rule to operate on both positive and
negative trials. What are not missing are different processes for controlled vs. automatic
processing. The results of our cross-sectional and longitudinal analyses suggest strongly that
there is no qualitative difference between controlled and automatic processing in the recipe.
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Figure Caption
Figure 1. Mean response times obtained on the twelfth block of training under VM-HETERO
and VM-HOMO conditions. Results are presented separately for positive and negative
trials, as a function of memory (M) and display (D) size.
Figure 2. Mean response times obtained on the twelfth block of training under CM-HETERO and
CM-HOMO conditions. Results are presented separately for positive and negative trials,
as a function of memory (M) and display (D) size.
Figure 3. Mean response times obtained on the twelfth block of training under CVM-HETERO
and CVM-HOMO conditions. Results are presented separately for positive and negative
trials, as a function of memory (M) and display (D) size.
Figure 4. Mean response times obtained on the twelfth block of training under CVM-HOMO and
CVM-HOMO-I conditions. Results are presented separately for positive and negative
trials, as a function of memory (M) and display (D) size.
Figure 5. Mean response times obtained on the first block of training under VM-HETERO and
VM-HOMO conditions. Results are presented separately for positive and negative trials,
as a function of memory (M) and display (D) size.
Figure 6. Mean response times obtained on the first block of training under CM-HETERO and
CM-HOMO conditions. Results are presented separately for positive and negative trials,
as a function of memory (M) and display (D) size.
Figure 7. Mean response times obtained on the first block of training under CVM-HETERO and
CVM-HOMO conditions. Results are presented separately for positive and negative trials,
as a function of memory (M) and display (D) size.
115
Figure 8. Mean response times obtained on the first block of training under CVM-HOMO and
CVM-HOMO-I conditions. Results are presented separately for positive and negative
trials, as a function of memory (M) and display (D) size.
Figure 9. Standard deviation of response times obtained on the twelfth block of training under
VM-HETERO and VM-HOMO conditions. Results are presented separately for positive
and negative trials, as a function of memory (M) and display (D) size.
Figure 10. Illustration of the features and characters used in the simulation.
Figure 11. Means and standard deviations of response times obtained during the first twelve
blocks of practice under VM-HETERO and VM-HOMO conditions along with the beset
fitting power curves. Results are presented separately for positive and negative trials.
Figure 12. Plot of the empirical ratios between MN+, MN-, SD+ and SD- obtained in the
Experiment. Squares show MN- as a function of MN+, diamonds show SD+ as a function
of MN+, and crosses show SD- as a function of MN-. The slope of the best fitting line
represents ∆ MN-/∆ MN+ (straight line), ∆ SD+/ ∆ MN+ (dotted line), and ∆ SD-/∆ MN-
(dashed line).
Figure 13. Plot of the ratios between MN+, MN-, SD+ and SD- obtained in the simulations.
Squares show MN- as a function of MN+, diamonds show SD+ as a function of MN+, and
crosses show SD- as a function of MN-. The slope of the best fitting line represents ?
MN-/? MN+ (straight line), ? SD+/ ? MN+ (dotted line), and ? SD /? MN- (dashed
line). D is the difficulty factor averaged over subject for the last trial of the simulation. L
is the position of the threshold on the feature list.
Figure 14. Mean number of feature comparisons obtained by the simulation on the twelfth block
of training under the six conditions of mapping and stimulus type. Results are presented
116
separately for positive and negative trials, as a function of memory (M) and display (D)
size.
Figure 15. Plot of the empirical mean RTs as a function of the mean number of feature
comparisons obtained in the simulation, both on the twelfth block of learning. Squares
represent the means obtained in VM conditions, stars represents the means obtained in
CVM conditions, and squares represent the means obtained in the VM conditions.
Figure 16. Means plotted against standard deviation for two hypothetical learning curves having
different learning rate parameters.
Figure 17. Means and standard deviations of response times obtained during the first twelve
blocks of practice under CM-HETERO and CM-HOMO conditions along with the beset
fitting power curves. Results are presented separately for positive and negative trials.
Figure 18. Means and standard deviations of response times obtained during the first twelve
blocks of practice under CVM-HETERO and CVM-HOMO conditions along with the
beset fitting power curves. Results are presented separately for positive and negative
trials.
Figure 19. Means and standard deviations of response times obtained during the first twelve
blocks of practice under CVM-HOMO and CVM-HOMO-I conditions along with the best
fitting power curves. Results are presented separately for positive and negative trials.
Figure 20. Illustration of the extended-range bias for the twelve blocks of practice under VM
HETERO condition. Only the negative trials are represented. Triangles show the
predicted SD by a power curve as a function of the empirical SD, and circles show
predicted MN by a power curve as a function of the empirical MN. Best-fitting line for the
MN (straight line), SD (bold line) and MN & SD (dashed line) is also shown with the
regression equation.
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Figure 21. Predicted vs. obtained means and standard deviations of response times obtained on
negative trials during the first twelve blocks of practice in condition VM-HETERO.