Full text of DOI:10.3758/BF03194934

Memory & Cognition
2002, 30 (3), 325-339
Multiple attention systems
in perceptual categorization
W. TODD MADDOX
University of Texas, Austin, Texas
and
F. GREGORY ASHBY and ELLIOTT M. WALDRON
University of California, Santa Barbara, California
Five observers categorized inverted L-shaped stimuli according to the length of the horizontal line
segment.A centrallylocated spatialcue precededthe stimulus on eachtrial.On 80%of the trials,the (rel-
evant) horizontal line segmentfell within the cued location, and on 20% of the trials the (irrelevant)ver-
tical line segment fell within the cued location. The empirical results provide support for the hypothesis
that perceptual attention can focus on the stimulus attribute inside the spatially cued location at the
same time that decisionalattentionis focused on the (relevant)horizontal attribute—that is, the results
suggest that perceptual and decisional attention can function independently during categorization. De-
cision bound models and extended generalized context models that assume separate perceptual and
decisional attention systems were fitted to the data. Versions of the models that assume that the spatial
cue affected perceptual attention were superior to versions that assume no effect on perceptual atten-
tion. These theoretical analyses support the functional independence hypothesis and suggest that for-
mal theoriesof categorizationshould model the effectsof perceptualand decisionalattentionseparately.
There is growing consensusthatthehumanattentionsys- Petersen, 1990). Although anatomically separate, the ques-
tem is subserved by separate subsystems, or at least by a tion of whether the systems are functionally separate has
broad anatomical network in which different subtasks are been only recently addressed in the attention literature.
mediated by different brain areas (e.g., Buchel & Friston,
Empiricalevidencefor a functionalindependenceof per-
1997;Knight, 1997;LaBerge, 1997;Olshausen, Anderson, ceptualand decisionalattentionis growing (e.g., Johnston,
& Van Essen, 1993; Posner & Petersen, 1990; Rushworth, McCann, & Remington,1995; Pashler, 1989, 1991, 1993;
Nixon, Renowden,Wade, & Passingham, 1997). Although Posner,1993;Posner, Sandson,Dhawan,& Shulman,1989).
a number of different theories have been proposed, there is Johnston et al. (1995) provided some of the strongest evi-
widespread agreement that visual perceptual attention is dence to date for the functional independence of percep-
mediated by a posterior system that includes the visual tual and decisional attention by showing that perceptual
cortex, much of the posterior parietal cortex, the pulvinar, and decisional attention systems operate at different tem-
and the superior colliculus (e.g., Desimone & Duncan, poral stages of processing during letter identification.
1995; Olshausen et al., 1993;Posner & Petersen, 1990). In Specifically, they showed that a critical reference stage of
contrast, executiveor decisional(i.e., conscious)attention processing (letter identification in their task) operates
is thought to be mediated by an anterior system that in- after the stage of perceptual attention but prior to the stage
cludes theanteriorcingulate,theprefrontal cortex, and per- of decisional attention.
haps the basal ganglia and the pulvinar (Ashby, Alfonso-
Within the perceptual categorization literature, there is
Reese, Turken, & Waldron, 1998; Ashby, Isen, & Turken, widespread agreement that attentional processes play a
1999; Goldman-Rakic, 1995; LaBerge, 1997; Posner & prominent role during normal categorization (e.g., Ashby
& Lee, 1991; Estes, 1994; Goldstone, 1994; Kruschke,
1992; Maddox, 2002; Maddox & Ashby, 1998; Nosofsky,
This research was supported in part by National Science Foundation
1986; Shepard, 1964). However, the question of whether
Grants SBR-9796206 and SBR-9514427 and by NIH Grant R01
separate perceptual and decisional attention systems op-
MH59196. We thank Candace Blair for help with the data collection.
erate during categorization has never been broached. One
We also thank Veronica Black, Evan Heit, Richard Ivry, Robert Nosof-
reason for the lack of data that speaks to this question is
thatnocategorizationstudieshavebeenconductedthathave
placed the goals of the two systems in direct competition.
Rather, the goals of the perceptual and decisional atten-
tion systems are usually the same and so, empirically, the
actions of the two systems are correlated.
sky, Harold Pashler, Jeremy Wolfe, and three anonymous reviewers for
helpful comments on an earlier version of this manuscript. Correspon-
dence should be addressed to W. T. Maddox, Department of Psychol-
ogy, Mezes Hall 330, University of Texas, Austin, TX 78712 (e-mail:
maddox@psy.utexas.edu)or to F. G. Ashby, Department of Psychology,
University of California, Santa Barbara, CA 93106 (e-mail: ashby@
psych.ucsb.edu).
325
Copyright 2002 Psychonomic Society, Inc.

326
MADDOX, ASHBY, AND WALDRON
The goal of this article is twofold. First, we describe the portion of trials, but leads to cooperationbetween the two
results of an experiment in which we investigatedwhether systems on other trials. Because of the popularity of the
perceptual and decisionalattention can function indepen- spatial cuing paradigm for manipulatingperceptual atten-
dently during categorization. The approach combines a tion, we decided to manipulate perceptual attention
traditionalcategorizationtask with a popularspatial cuing processes across trials while holding decisional attention
paradigm (e.g., Eriksen & Hoffman, 1972; Kingstone, processes fixed. Each stimulus consisted of a vertical and
1992;Klein & Hansen, 1987,1990;McCann,Folk,&John- a horizontalline joinedat an upperleft corner. The lengths
ston, 1992; Posner, 1980; Posner, Snyder, & Davidson, of these two line segments varied across trials. The ob-
1980). Second, we applied decision bound(Ashby, 1992a; servers were informed prior to the experiment that their
Maddox & Ashby, 1993) and extended generalized con- task on each trial was to determine whether the horizontal
short
long
(CategoryB)
text models (Lamberts, 1995, 1998) to the data in order to line segment was
determine the locus of the spatial cuing effect. To antici- and that the vertical line length was not relevant. Thus, on
relevant
(CategoryA) or
pate, both the empirical and model-based analyses sup- every trial, the length of the horizontal line was
irrelevant
,
port the hypothesis that perceptual and decisional atten- and the length of the vertical line was
, and the
tion systems operate separatelyduringcategorization.The goal of the decisionalattentionsystem was to place all de-
next (second) section describes the experiment, and the cisional attention on the horizontal line segment in order
third sectionoutlinesthe method. The fourth section is de- to determine whether it was long or short and to place no
voted to the results and theoretical analyses. Finally, we decisionalattentionon the verticalline segment. Trial-by-
conclude with some general comments.
trial feedback was provided to help the observers learn the
criterion length that separated short from long horizontal
lines. Note that this was not a category learning task in the
traditional sense because the observers were told a priori
that they should focus decisional attention on the hori-
SPATIAL CUING IN A PERCEPTUAL
CATEGORIZATION EXPERIMENT
To address the functional independence of perceptual zontal line segment and that short and long segments be-
and decisionalattention in categorization,we combined a longedin CategoriesA and B, respectively.Each category
categorizationtask with a spatial cuingmanipulation(e.g., contained11 unique stimuli, which are depictedschemat-
Eriksen & Hoffman, 1972; McCann et al., 1992; Posner, ically in Figure 1.
1980; Posner et al., 1980). The basic idea was to devise an
In addition to this standard categorizationtask, a circu-
experimental task that leads to competition between the lar spatial cuing paradigm was used to manipulatepercep-
perceptual and decisional attention systems on some pro- tual attentionon each trial. In many attentiontasks that use
Figure 1. Schematic illustration of the stimulusstructure. Solid squares denote
stimuli from Category A, and open circles denote stimuli from Category B.

PERCEPTUAL AND DECISIONAL ATTENTION
327
Figure 2. Hypothetical stimulus display for a valid and an invalid trial. The
circular attention cue is included for illustrative purposes only and was not
present during the stimulus display.
a spatialcue, the cue directs the observer’s attentionto one of the circular region.1 The top panel in Figure 2 depicts a
of several possibletarget locations(e.g., Kingstone,1992; typical valid trial. The circular spatial cue is displayedfor
Klein, 1994; Klein & Hansen, 1987, 1990). We took a 500 msec while the observer allocates perceptual atten-
slightlydifferent approach.On every trial, the circular spa- tion to this region. Immediately following the removal of
tial cue was centered on the computer screen, and the ob- the spatial cue, the stimulus is presented. Because this is
servers were instructed to place all of their perceptual at- a valid trial, the relevant line segment falls within the cir-
tention within this circular region. The observers were cular cued region. The stimulus is presented for 100 msec
informed that on 80% of the trials, the relevant line seg- and is then masked. The mask remains on the screen until
ment (i.e., the horizontalline segment) would be displayed the observerdetermines whetherthe relevantline segment
valid trials
within the circular region. We refer to these as
is short or long. The bottom panel in Figure 2 depicts a
because the relevant dimension is presentedwithin the cir- typical invalid trial. Again the circular spatial cue is dis-
cular region. On the remaining 20% of the trials, the ir- played for 500 msec while the observer allocates percep-
relevant line segment (i.e., the vertical line segment) was tual attention to this region. Immediately following re-
invalid
displayedin the circularregion.We refer to these as
moval of thespatialcue, thestimulusis presented. Because
trials
out-
because the relevant dimension is presented outside this is an invalid trial, the relevant line segment falls

328
MADDOX, ASHBY, AND WALDRON
side
the circular cued region. The stimulusis presented for types that resulted from the combinationof the two dimen-
100 msec and is then masked. The mask remains on the sion judgments [relevant (horizontal) or irrelevant (verti-
screen until the observer determines whether the relevant cal)] with the two types of spatial cues (valid or invalid).
relevant
line segment is short or long.
These included (1) judgments of the
dimension
(i.e., when the relevant di-
valid
when the spatial cue was
mension was in the cued area), (2) judgments of the
Method
rele-
(i.e., when
Observers. Five observers participated in the experiment. Each
reported 20/20 vision or vision corrected to 20/20. The observers
were paid $6.00 per session for their participation.
vant
invalid
dimensionwhen the spatialcue was
the relevant dimension was outside of the cued area), (3)
irrelevant
judgments of the
dimension when the spatial
(i.e., when the irrelevantdimensionwas out-
Stimuli. Each stimulus consisted of a horizontal line and a verti-
cal line connected at the upper left (see Figure 2 for examples). The
stimulus ensemble contained 22 stimuli selected from a larger set of
49 stimuli that were constructed from a factorial combination of
seven horizontal line lengths with seven vertical line lengths. A
schematic of the 22 stimuli is displayed in Figure 1. The seven line
lengths were 111, 114, 117, 120, 123, 126, and 129 pixels. The stim-
uli were computer generated and displayed on a noninterlaced VGA
monitor with 1,024 3 768 resolution in a dimly lit room. Each line
was presented in white on a black background.
valid
cue was
side of the cued area), and (4) judgments of the
irrelevant
invalid
dimension when the spatial cue was
(i.e., when the
irrelevant dimension was in the cued area).
Table 1 displays the proportionof correct responses for
each of these four response types averaged across the 22
3
stimuli separately for each observer. A 2
2 within-
subjectsanalysisof variance was conductedon these data.
F
Procedure. The category assignments for the 22 stimuli are de- There was a main effect of dimension relevance [ (1,4) =
picted in Figure 1. Solid squares denote stimuli from Category A,
and open circles denote stimuli from Category B. Each session con-
sisted of five blocks of 110 trials each, for a total of 550 trials. Each
of the 22 stimuli was presented five times during each block of tri-
als. During one of the five stimulus presentations (22 trials total), the
display of the irrelevant component was centered in the circular cued
region (an invalid trial), and during four presentations (88 trials
total), the display of the relevant component was centered in the cir-
cular cued region (a valid trial). Thus, the spatial cue was 80% valid.
During the final three blocks of trials, some of the categorization
judgments were followed by an irrelevant component judgment, in
which the observer was asked to determine whether the irrelevant
component was short (less than 120 pixels) or long (greater than 120
pixels). The observer was required to make two irrelevant component
judgments for each of the 22 stimuli (for a total of 44 irrelevant com-
ponent judgments per block). One judgment followed a valid trial,
and the other followed an invalid trial. No corrective feedback fol-
lowed the judgments.
p
29.965, < .005], with higher accuracy for the relevant
(.817) than for the irrelevant component (.623), and no
main effect of cue validity. In addition,overallaccuracy on
the irrelevant component (.623) was above chance (
.001). Finally, the interaction between dimension rele-
vance and cue validity was significant [ (1,4) = 226.562,
< .001]. A number of additional analyses were con-
ducted in order to isolate the locus of this interaction.Sev-
eral results stand out. First, accuracy for the relevant di-
mension was higher on valid trials (.856) than on invalid
trials (.778; < .02). Second, relevant dimensionaccuracy
on invalidtrials was significantlyabovechance (i.e., .778;
< .001). Third, relevant dimension accuracy on invalid
trials (.778) was significantly larger than irrelevant di-
mension accuracy on invalid trials (.655; < .02). Fourth,
irrelevant component accuracy was higher on invalid tri-
als (.655) than on valid trials (.591; < .06). Finally, irrel-
evant componentaccuracy on invalidtrials (i.e., .655) was
p
<
F
p
p
p
p
Prior to each session, the observers were reminded that the circular
spatial cue was valid on 80% of the trials and that they should focus
their attention within the circular cued location on each trial. Finally,
p
they were told that they should respond “A” if the horizontal line significantly lower than relevant component accuracy on
2
was shorter than 120 pixels and respond “B” if the horizontal line
was longer than 120 pixels. A typical trial proceeded as follows:
First, the circular spatial cue was presented for 500 msec centered on
the computer screen. The cue was a circle with a diameter of 140 pix-
els. The cue was replaced by the stimulus that was presented for
100 msec followed by a pattern mask that consisted of a 200 3 200
pixel gray square region. The pattern mask remained on the screen
until the observer gave a response. Hypothetical valid and invalid
trials are depicted in Figure 2. The observer provided a categoriza-
tion response, followed by a 500-msec display with corrective feed-
back and a 500-msec intertrial interval (ITI). When an irrelevant
component judgment was required, the 500-msec feedback display
was followed by a display that asked for an irrelevant component
judgment. The observer provided a response that was followed by a
500-msec ITI and the next trial. No feedback was provided follow-
ing the irrelevant component judgments. Each observer completed
five 1-h sessions on consecutive days. The first session for all ob-
servers was considered practice and was excluded from subsequent
analyses. The observers were instructed to emphasize accuracy over
speed of responding.
p
valid trials (i.e., .856; < .005).
Taken together, these results provide initial support for
functional independence of perceptual and decisional at-
tentionin categorizationand suggest that decisionalatten-
tion can make use of information that is not facilitated by
the spatial cue. If the perceptual and decisional attention
systemsare yoked,thenon invalidtrials, when theirrelevant
dimension is in the cued location, no information regard-
ing the relevant dimension should be available for pro-
cessing, and relevant dimensionperformance should be at
Table 1
Overall Proportion Correct
Relevant
Invalid
Irrelevant
Invalid
Observer
Valid
Valid
1
2
3
4
5
.910
.890
.820
.850
.810
.840
.840
.720
.690
.800
.690
.475
.580
.610
.600
.745
.590
.635
.565
.740
Results
All analyseswere performed onthedatacollapsedacross
Sessions2–5. We beginwithan analysisofthefour response
Average
.856
.778
.591
.655

PERCEPTUAL AND DECISIONAL ATTENTION
329
chance.If, on the otherhand, the perceptualand decisional which the observers were asked to judge the length of the
attention systems are functionally independent, the deci- irrelevant component. For both the relevant and irrelevant
sional attentionsystem will be focused on the relevant di- judgments, and for both cue validityconditions,the accu-
mension, even when perceptualattentionis focused on the racy of all responses increased with the distance from the
irrelevantdimension(as is true on an invalidtrial), and per- stimulusto the categorydecisionbound.This findingis es-
formance will be above chance. It is worth mentioningthat pecially informative with regard to the irrelevant compo-
all of these results, based on averaged data, hold for each nent accuracy, because it indicates that the decisional at-
individual observer. Specifically, for every observer, rel- tentionsystemhadsome access to theirrelevantcomponent.
evant component accuracy on valid trials was higher than However, it is impossible to tell from these analyses
relevant component accuracy on invalid trials and higher whether information about the irrelevant component was
than irrelevant component accuracy on invalid trials. For availableat the same time that the decisionalattentionsys-
4 of the 5 observers, irrelevant component accuracy was tem was judging the length of the relevant component, or
higher on invalid trials than on valid trials. Also, overall whether decisional attention was switched to the irrele-
accuracy on the relevant component was significantly vant component after the relevant component judgment
higherthan overallaccuracy on the irrelevant component.3 was completed.
Figure 3 displays the proportion of correct responses
A closer examination of the stimulus-by-stimulus ac-
for the relevant component for each of the 22 stimuli on curacy rates in Figures 3 and 4 suggeststhat the decisional
valid (i.e., top panel) and invalid (i.e., bottom panel) trials attention system was not able to set a criterion perfectly
averaged across the 5 observers using the same spatial alongthe relevant dimension while ignoringthe irrelevant
configurationof stimulidepictedin Figure 1. Figure 4 dis- dimension. Specifically, the relevant dimension accuracy
short
plays the same proportions for the relatively few trials in rates for stimuli from the
category (i.e., with hori-
Figure 3. Correct categorization proportions for the relevant component averaged across
the 5 observers. The top value of each pair denotes the proportion correct on valid trials, and
the bottom value of each pair denotes the proportion correct on invalid trials.

330
MADDOX, ASHBY, AND WALDRON
Figure 4. Correct categorization proportions for the irrelevant component averaged
across the 5 observers. The top value of each pair denotes the proportion correct on valid
trials, and the bottom value of each pair denotes the proportion correct on invalid trials.
zontal lengths less than 120 pixels) generally increased perceptual attention within the cued region. A more rea-
with increasingverticallength,whereas the accuracy rates sonableassumptionis that some perceptualattentionspills
long
for stimuli from the
category (i.e., with horizontal out of the cued circular region, even when the cuing in-
lengths greater than 120 pixels) generally decreased with structions are effective. In this case, testing whether per-
increasing vertical length. A similar result held for the ir- ceptual and decisional attention can function indepen-
relevant dimension judgments. Specifically, the accuracy dently and determining the locus of the attention effect is
short
rates for stimuli from the
category (i.e., with vertical difficult, in the sense that it requires a process of parame-
lengths less than 120 pixels) generally increased with in- ter estimation and model fitting.In this section, we exam-
creasing horizontal length, whereas the accuracy rates for ine the functional independence of perceptual and deci-
long
stimuli from the
category (i.e., with vertical lengths sional attention in two different but successful models of
greater than 120 pixels) generally decreased with increas- categorization: Ashby and Maddox’s (1993; Maddox &
decision bound model
expected since these stimulus dimensions were measured berts’s (1995, 1998)
ing horizontallength. This finding was not completelyun- Ashby, 1993)
(DBM), and Lam-
extended generalized context model
generalized context model
(EGCM). Nosofsky’s (1986)
integral-dimension
in the same units and likely had some
qualities that made it difficult for the decisional attention (GCM) is not examined below, because it does not sepa-
system to ignore completely the irrelevant dimension rate perceptualfrom decisionalattention(instead it assumes
(e.g., Garner, 1974; Maddox, 1992).
a unitary attention system; Maddox & Ashby, 1998), and
because it is rejected in favor of the other modelsfor every
observer.
THEORETICAL ANALYSES
The results so far support the hypothesis that the per- Decision Bound Theory
ceptualand decisionalattentionsystems can function sep-
Decision bound theory takes as its fundamental axiom
arately in perceptual categorization,but this inference re- that all perceptual systems are probabilistic—that is, re-
lies on the assumption that the observers placed all of their peated presentations of the same stimulus yield different

PERCEPTUAL AND DECISIONAL ATTENTION
331
Figure 5. (a) Hypothetical contours of equal likelihood for four stimuli (1–4).
(b) Hypothetical decision bound for a categorization problem in which Stimuli 1 and
3 are members of Category A and Stimuli 2 and 4 are members of Category B. (c)
Hypothetical contours of equal likelihood for a case in which there is perceptual se-
lective attention to dimension x. The solid line decision bound depicts a case in which
decisional selective attention to dimension x is perfect, and the dashed line depicts a
case in which decisional selective attention to dimension x is imperfect. (d) Hypo-
thetical contours of equal likelihood for a case in which there is perceptual selective
attention to dimension y. The solid line decision bound depicts a case in which deci-
sional selective attention to dimension x is perfect, and the dashed line depicts a case
in which decisional selective attention to dimension x is imperfect.
perceptualeffects (e.g., Ashby & Lee, 1993;Geisler, 1989; major axis implies a positivecovariance (correlation), and
perceptual noise
Green & Swets, 1967). The
elicited by a negativeslope implies a negativecovariance.The greater
repeated presentationsof a single multidimensionalstim- the variance along a dimension, the wider the contour in
ulus can be represented by a multivariate probability dis- that direction.
tribution (Ashby & Lee, 1993). For a two-dimensional
In decision bound theory, the experienced observer
stimulus, a bivariate normal distributionis assumed to de- learns to divide the perceptual space into response regions
scribe the set of percepts. A bivariate normal distribution and assigns a response to each region. On each trial, the ob-
is described by a mean and variance along each dimen- server determines the location of the perceptual effect and
sion, as well as a covariance term, mx, my , s2x, s2y , covxy , givesthe responseassociatedwith that region of the percep-
x
y
x
y
where the subscripts and denote dimensions and . tual space. The partitionbetween response regions is called
decision bound
Figure 5a depicts hypothetical equal likelihood contours the
. Figure 5b displays a hypothetical de-
for four stimuli constructed from the factorial combina- cisionboundfor a categorizationtaskinwhichStimuli1 and
x
y
tion of two levels along two dimensions and . With bi- 3 are placed in Category A, and Stimuli 2 and 4 are placed
variate normal distributions,the equal likelihoodcontours in Category B. Note that the parameters that define the
are always circularor elliptical.When the major and minor perceptual representation are separate from the parame-
axes of the contour are parallel to the coordinate axes, the ters that define the decision bound (Ashby, 1992a).
covariance (correlation) is zero. All four distributions in
In decision bound theory, perceptual attention is as-
Figure 5a have zero covariance. A positive slope for the sumed to affect the perceptual variances, and decisional

332
MADDOX, ASHBY, AND WALDRON
attention is assumed to affect the decision bounds. In par- can vary. For example, the broken line decision bounds in
ticular, perceptual attentionis assumed to reduce the trial- Figures 5c and 5d depict cases in which there is imperfect
x
by-trial variability in the perceived values of a stimulus decisional selective attention to dimension . Note that in
along the perceptually attended dimension, relative to the Figure 5c both attention systems, perceptual and deci-
x
variability along the perceptually unattended dimension sional, are operating on the same stimulusdimension . In
(Braida & Durlach, 1972; Durlach & Braida, 1969; Luce Figure 5d, on the other hand, there is perceptual selective
y
& Green, 1978; Luce & Nosofsky, 1984; Macmillan, attentionto dimension , but decisionalselectiveattention
x
Goldberg, & Braida, 1988). Figure 5c depicts a situation to dimension . Taken together, panels c and d of Figure 5
in which more perceptual attention is directed to dimen- demonstrate pictorially that perceptual and decisional at-
x
y
sion thantodimension . Thisreducestheperceptualnoise tention processes are separate and thus that a functional
x
along dimension relative to the perceptual noise along independence,if it exists, can be isolated.
y
dimension . Figure 5d depicts a situation in which per-
Decision bound models. To test whether perceptual
y
ceptual attention is directed more to dimension . Thus, and decisionalattentioncan function independently, we fit
decision bound theory can be used to test the hypothesis decisionbound models to the relevant(i.e., horizontal)line
that some perceptual attentionspills out of the cued circu- length judgments for each of the 22 stimuli separately for
lar region. If this is the case, then on valid trials, the per- each individual observer. We did not fit the irrelevant line
ceptual variance of the irrelevant component (which falls lengthjudgmentsbecauseof thesmallnumberofthesejudg-
outsidethe cued circular region) will be some finite value. ments. For each stimulus, we computed the observedprob-
Decisional selectiveattention
results when the decision abilityof responding“short” and the observedprobability
bound is orthogonalto one of the coordinateaxes—that is, of responding“long”for bothvalidand invalidtrials. Thus,
when the observer sets a criterion along one stimulus di- each model was fit to a totalof 88 estimatedresponse prob-
mension and places no decisional attention on the other abilitiesfrom each observer. The model yielded predicted
de-
dimension.This decisionstrategy is also referred to as
cisional separability
probabilitiesof responding“short”and“long”for bothvalid
(see Ashby & Townsend, 1986, and and invalid trials by solving the following equations:
Maddox, 1992, for details). Decisional selective attention
P
P h
(Rshort xi) = [ (xpi) < 0 xi]
|
|
x
to dimension holds in bothFigures 5c and 5d, as denoted
by the solid line decision bound. Like perceptual selective
attention, the magnitude of decisional selective attention
P
2 P
(Rlong xi) = 1
(Rshort xi),
|
|
Figure 6. Schematic illustration of the two hypotheses on the effect of the spatial cue on
perceptual attention. The left column depicts valid trials, and the right column depicts in-
valid trials. The top portion depicts the case in which there is no spatial cue effect on per-
ceptual attention (labeled Spatial Cue Effect Absent), and the bottom portion depicts the
case in which there is a spatial cue effect on perceptual attention (labeled Spatial Cue Ef-
fect Present). (See text for details.)

PERCEPTUAL AND DECISIONAL ATTENTION
333
where xi is a vector that contains the horizontal and verti- represents the perceptual variance along the irrelevant di-
i
cal lengths for stimulus , xpi is the perceptual effect for mension (regardless of cue validity). The second hypoth-
i
stimulus under the assumption that bivariate normal per- esis assumes that the spatial cue had an effect on the per-
h
ceptual noise exists, and is a linear decision function ceptualvariancesand is displayedin the bottomtwo panels
(i.e., the equation for a linear decision bound). Decision of Figure 6 (labeled Spatial Cue Effect Present). This hy-
bound theory also postulates noise in the decision pothesisalso requires two perceptualvariance parameters.
process—that is, criterial noise. However, when the deci- However, in this case, the perceptual parameters are not
sion bound is linear, as in the present application,criterial linked to the relevant and irrelevant dimensions but rather
noise is nonidentifiablewith perceptual noise.
to which dimension was presented inside or outside of the
Four decision bound models were tested. They were spatial cue. Specifically, one perceptual variance was esti-
constructed by combining factorially two hypotheses re- mated for the componentinsidethe spatialcue (i.e., therel-
gardingthe effects of the spatialcue on the perceptualvari- evant dimension on valid trials, and the irrelevant dimen-
ances with two hypotheses regarding the effects of the sion on invalid trials). A second perceptual variance was
spatial cue on the decision bounds. The two hypotheses estimated for the component outside of the spatial cue
regarding the effects of the spatial cue on perceptual at- (i.e., the irrelevant dimension on valid trials, and the rele-
tention are depicted in Figure 6. One hypothesis assumes vant dimension on invalid trials).4
no effect of the spatialcue on the perceptualvariances and
A similar pair of hypotheseswas made about the effects
is displayedin the top two panels of Figure 6 (labeled Spa- of decisionalattentionon the decision bound.The two hy-
tial Cue Effect Absent). This hypothesisrequires that two potheses regarding the effects of the spatial cue on deci-
perceptual variance parameters be estimated from the sional attention are depicted in Figure 7. One hypothesis
data. One represents the perceptualvariance along the rel- assumesno effect ofthespatialcueon thedecisionbound—
evant dimension (regardless of cue validity), and the other that is, that the same (linear) decision bound was used on
Figure 7. Schematic illustration of the two hypotheses on the effect of the spatial cue on deci-
sional attention. The left column depicts valid trials, and the right column depicts invalid trials.
The top portion depicts the case in which there is no spatial cue effect on decisional attention (la-
beled Spatial Cue Effect Absent), and the bottom portion depicts the case in which there is a spa-
tial cue effect on decisional attention (labeled Spatial Cue Effect Present). (See text for details.)

334
MADDOX, ASHBY, AND WALDRON
2
L
L
valid and invalid trials. (Quadratic decision bounds were statistic was ln , where is the likelihoodof the model
also examined but in no case provided a significant im- given the data.
2 L
The goodness-of-fit values ( ln ) for each model and
provement in fit.) This situationis depictedin the top por-
tion of Figure 7 (labeled Spatial Cue Effect Absent). This observer are presented in Table 2. The fit of the most par-
version adds two free decision bound parameters (i.e., the simonious decision bound model for each observer is in
slope and the interceptof the boundused on all trials). The boldtype. The resultscan be summarized as follows: First,
second hypothesiswas that the spatial cue affected the de- the spatial cue had the predicted effect on perceptual at-
cision bound.In this case, different linear decisionbounds tention. For all 5 observers, the model that assumes the
were applied on valid and invalid trials (resulting in four cue affected perceptual attention fit better than the corre-
bound parameters—the slope and the intercept of the sponding model that assumes no effect of the cue on per-
·
bound used on valid trials, and the slope and the intercept ceptual attention [i.e., DBM(P, ) always fit better than
· ·
oftheboundusedon invalidtrials). This situationis depicted DBM( , ), and DBM(P,D) always fit better than
·
in the bottom portion of Figure 7 (labeled Spatial Cue Ef- DBM( ,D)], even though the two models had the same
fect Present). The resulting four models are designated as number of perceptual variance parameters. Second, also
follows.
as predicted,in the best-fittingmodel, the perceptualvari-
( , ). The spatial cue has no effect on per- ance for the component within the spatial cue (average
Model DBM · ·
ceptual variability or on the decision bound (i.e., the cue
SD
= 4.936) was smaller than the perceptual variance for
SD
has no effect on perceptual or decisional attention). This the component outside of the spatial cue (average
=
p
model has four free parameters: two perceptual variance 5.806)for 4 of the 5 observers ( < .05). The exact values
parameters (see Figure 6, top panels), and two decision are displayed in Table 3. This was true regardless of
bound parameters (see Figure 7, top panels).
whether the relevant or irrelevant component was within
(P, ). The spatial cue affects the perceptual the spatial cue. Thus, perceptual attentionwas focused on
Model DBM
·
variances but not the decision bound (i.e., the cue affects the component within the spatial cue. Third, in 9 of 10
perceptual attention but not decisional attention). This comparisons,the model that assumes that the cue affected
model has four free parameters: two perceptual variance decisional attention fit better than the corresponding
parameters (see Figure 6, bottom panels), and two decision model that assumes no effect of the cue on decisional at-
·
· ·
bound parameters (see Figure 7, top panels).
tention [i.e., DBM( ,D) always fit better than DBM( , ),
Model DBM ·
·
( ,D). The spatial cue affects the decision and DBM(P,D) fit better than DBM(P, ) for 4 of the 5 ob-
bound but not the perceptual variances (i.e., the cue af- servers]. To determinethe magnitudeof the spatialcue ef-
fects decisional attention but not perceptual attention). fect on the observer’s ability to apply decisional selective
This model has six free parameters: two perceptual vari- attention, the “weight” given to each component in the
ance parameters (see Figure 6, top panels), and four categorizationdecision was determined by examining the
decision bound parameters (see Figure 7, bottom panels). slope of the best-fitting linear decision bound. A slope of
Model DBM
(P,D). The spatial cue affects the percep- zero implies that all weight was given to the irrelevant
tual variances and the decision bound (i.e., the cue affects componentand that none was give to the relevant compo-
perceptual and decisional attention). This model has six nent (i.e., decisional selective attention to the irrelevant
free parameters: two perceptual variance parameters (see component).A slope of one implies that equal weight was
Figure 6, bottom panels), and four decision bound para- given to both the irrelevant and relevant components, and
meters (see Figure 7, bottom panels).
an infinite slope implies decisional selective attention to
Each of these models was fitted to the relevant compo- the relevant component. Not surprisingly, on invalid tri-
nent data separately for each observer. The model para- als, the irrelevant component was given greater weight in
meters were by estimated using maximum likelihood the categorization decision than it was given on valid tri-
(Ashby, 1992b; Wickens, 1982) and the goodness-of-fit als [i.e., in model DBM(P,D)]. Even so, on both valid and
Table 2
-
Goodness-of-Fit ( ln L) Values for the Decision Bound and Extended Generalized Context Models
Decision bound Models Extended Generalized Context Models
· ·
DBM( , )
·
·
· ·
·
·
Observer
DBM(P, )
DBM( ,D)
DBM(P,D)
EGCM( , )
EGCM(P, )
EGCM( ,D)
EGCM(P,D)
(4 parm)
654.13
764.29
938.09
873.77
978.74
(4 parm)
644.06
754.62
935.87
865.01
978.63
(6 parm)
643.72
702.88
926.10
781.26
974.17
(6 parm)
643.71
702.46
922.31
780.56
974.08
(5 parm)
665.18
761.86
942.46
936.98
988.60
(5 parm)
660.58
756.45
934.94
916.17
988.46
(6 parm)
657.13
757.26
931.21
906.30
988.48
(6 parm)
657.12
756.35
931.11
906.30
988.38
1
2
3
4
5
Average
841.80
835.64
805.63
804.62
859.01
851.32
848.08
847.85
Note—The values in bold type denote the most parsimonious model from each model class (decision bound or extended generalized context).

PERCEPTUAL AND DECISIONAL ATTENTION
335
Table 3
where bshort is the bias toward responding“short” (blong
2 P x
(Rshort i). Because
=
Perceptual Noise Standard Deviation Inside and Outside of the
Spatial Cue for the Best-Fitting Decision Bound Model
2
P
x
1
bshort), and the (Rlong i) = 1
|
|
the inclusion probabilities are binary valued, perceived
similarity changes discretely across time and trial. Since
we are fitting the model to aggregate data, the probability
of each possibleinclusionpattern (i.e., neither component,
horizontalcomponentonly, verticalcomponentonly, both
components) is computed from continuous-valuedinclu-
Spatial Cue
Observer
Inside
Outside
1
2
3
4
5
3.793
4.309
5.712
4.653
6.211
5.389
4.613
7.543
5.312
6.172
i
i
sion probabilities, and 2 , that are estimated from the
1
data and can take on any value between 0 and 1. For each
Average
4.936
5.806
x
stimulus, i , the choiceprobabilityfor each inclusionpat-
tern is computed, and the expected value of these choice
probabilitiesdenotes the model prediction(see Lamberts,
1998, for details).
Four extended generalized context models were tested.
They were constructed by combining factorially two hy-
potheses regarding the effects of the spatial cue on the in-
invalid trials, the decision bounds of all observers
weightedthe relevant componentmuch more heavilythan
the irrelevant component (i.e., the slopes were all much
larger than one). Thus, although the decisional attention
system allocated some attention to the irrelevant compo-
nent (for Observers 2–5), the lion’s share of decisionalat-
tention was focused on the relevant component, regard-
less of whether it was inside or outside of the spatial cue.
This result was expected, since Figures 3 and 4 suggest
that some decisional attention was focused on the irrele-
vant component. Finally, for 4 of the 5 observers, the best
fit was provided by model DBM(P,D), which is strong ev-
idencethat the cue affected bothperceptualand decisional
attention.
i
clusion probabilities, , with two hypothesesregarding the
u
effects of the spatial cue on the utility parameter, .
Model EGCM · ·
( , ). The spatial cue has no effect on the
inclusionprobabilitiesor on the utility(i.e., the cue has no
effect on perceptual or decisional attention). This model
c i i , u
has five free parameters: ,
,
, and b.
h
v
Model EGCM
·
(P, ). The spatial cue affects the inclusion
probabilities with one inclusion probability applying to
the component within the spatially cued location (i.e., the
relevant, horizontalcomponenton validtrials, and the irrel-
evant, vertical component on invalid trials) and a second
inclusion probability applying to the component outside
of the spatiallycued location(i.e., the relevant component
on invalidtrials, and the irrelevantcomponenton validtri-
als). The spatial cue does not affect the utility. This model
Extended Generalized Context Model
extendedgeneralized
(EGCM) assumes no perceptual noise and
Unlike decision bound theory, the
context model
that each stimulus is represented by a point in a multi-
dimensional psychologicalspace. When presented with a
target stimulus, the observer computes the distance from
the target item to each category exemplar stored in mem-
ory. Each distance is then converted into a similarity as
follows:
c i
has five free parameters: ,
i
u
outside, , and b.
,
inside
Model EGCM ·
( ,D). The spatial cue has no effect on the
inclusionprobabilities,but does affect the utilitywith one
utilityfor valid trials and a second utilityfor invalidtrials.
c i
This model has six free parameters: ,
i
u
,
v
u
,
,
,
h
valid invalid
r
r q r
/
2c
u h 2 h
2 u vi 2 vj
+ incv(1 ) ] },
hij = exp{ [inch
and b.
|
i
j
|
|
|
Model EGCM
(P,D). The spatial cue affects the inclu-
sion probabilitiesand the utilities.This model has six free
c i
i
j c
where hij denotes the similarity between stimuli and ,
is a scaling constant, inch is the binary valued (0 or 1) in-
clusion probability for the horizontal component, incv is
the binary valued inclusion probability for the vertical
i
u
u
, invalid, and b.
inside outside valid
parameters: ,
,
,
2
L
The goodness-of-fit values ( ln ) for each model and
observer are presented in Table 2. The fit of the most par-
simonious EGCM is in bold type.5 The results can be
summarized as follows: First, the spatial cue had the pre-
dicted effect on perceptual attention. For all 5 observers,
the model that assumes the cue affected the inclusion
probabilities fit as well or better than the corresponding
model that assumes no effect of the cue on perceptual at-
u
u
component, and is the utility placed on the horizontal
Su
component (0 < < 1;
= 1). Following most appli-
cations of the model to continuous-valuedstimuli, we as-
r
sume Euclideandistance( = 2) and an exponentialdecay
q
similarity function ( = 1). Lamberts (1995, 1998) has
suggested that the inclusion probabilities are affected by
perceptual processes and that the utility value is affected
by the decision process. The probability of responding
“short” for both validand invalidtrials is determinedfrom
the following equation:
·
· ·
tention[i.e., EGCM(P, ) compared with EGCM( , ), and
·
EGCM(P,D) compared with EGCM( ,D)]. Second, also
·
as predicted, in the EGCM(P, ), the inclusion probability
i
for the component within the spatial cue (average
=
.999) was larger than the inclusion probability fionsridtehe
bshort
hij
å
j Î
short
i
component outside of the spatial cue (average
=
outside
P
x =
)
i
(R short
,
|
p
.820) for all 5 observers ( < .05). The exact values are
displayed in Table 4. Thus, perceptual attention was fo-
bshort
hij + blong
hij
å
å
long
j Î
j Î
short

336
MADDOX, ASHBY, AND WALDRON
Table 4
vides a better account of invalid trial data for all 5 ob-
servers.
Inclusion Probabilities Inside and Outside
of the Spatial Cue for the EGCM(P, )
·
Irrelevantcomponent judgments. Neithermodel was
fit to the irrelevant component judgments because of the
small amount of data. Even so, both models provide good
qualitative accounts of these data by assuming that the
perceptual variance for the component inside the spatial
cue was smaller than the perceptual variance for the com-
ponent outside of the spatial cue, for the decision bound
model, and by assuming that the inclusion probabilities
inside the spatial cue were larger than those outside of the
spatialcue, for theEGCM. Of course, the accuracy of quan-
titative fits of these models awaits further research.
Spatial Cue
Observer
Inside
Outside
1
2
3
4
5
1.000
.999
.999
.998
.999
.889
.875
.749
.607
.982
Average
.999
.820
cused on the component within the spatial cue. Third, in
7 of 10 cases, the model that assumes the cue affected de-
cisional attention fit significantly better (based on likeli-
hood ratio tests) than the corresponding model that as-
sumes no effect of the cue on decisional attention [i.e.,
SUMMARY AND CONCLUSIONS
This article reports the results of an experiment that
provides a test of two hypotheses regarding the nature of
perceptual and decisionalattention during perceptual cat-
egorization. One hypothesis is that perceptual and deci-
sional attention are yoked, and the other is that perceptual
and decisional attention are functionally independent. To
test these hypotheses, we combined a traditional percep-
tual categorizationtask with a spatial cuing manipulation
(e.g., Eriksen & Hoffman, 1972; Posner, 1980). The goal
of the decisional attention system was to judge the length
of a horizontal line segment. On valid trials, the horizon-
tal line segment fell within the spatially cued region, and
on invalidtrials, the horizontalline segment fell outsideof
the spatiallycued region. Thus, on validtrials, the two sys-
tems were able to work in concert, and on invalidtrials, the
two systems competed. If the two attention systems are
yoked, performance should be at chance on invalid trials
and well above chance on valid trials. On the other hand,
if the two attention systems are functionallyindependent,
performance should be abovechance on bothvalid and in-
valid trials, althoughvalid trial performance should be su-
perior.
·
· ·
EGCM( ,D) compared with EGCM( , ), and EGCM(P,D)
·
compared with EGCM(P, )]. To determine the magnitude
of the spatial cue effect on the observer’s ability to apply
decisional selective attention, the utility value from the
EGCM( ,D) was examined. For all 5 observers, the util-
·
ity for the relevant component was larger on valid (aver-
u
u
age valid = .759) than on invalid (average invalid = .436)
p
trials ( < .05). Finally, the best fit was provided by the
EGCM(P, ) for 2 observers and by the EGCM(P,D) for the
·
other 3 observers.
Comparison of Decision Bound and Extended
Generalized Context Models
In 8 of 10 cases, the decision boundmodel that assumes
no effect of the spatial cue on decisional attention [i.e.,
DBM( , ) and DBM(P, )] provideda better accountof the
data than did the analogous extended generalized context
· ·
·
· ·
·
model [i.e., EGCM( , ) and EGCM(P, )]. Similarly, in 10
of 10 cases, the decision bound model that assumes an ef-
fect of the spatial cue on decisional attention [i.e.,
·
DBM( ,D) and DBM(P, D)] provided a better account of
the data than did the analogousextendedgeneralizedcon-
text model [i.e., EGCM( ,D) and EGCM(P, D)]. To shed
The accuracy and theoretical analyses support the hy-
pothesisthat perceptualand decisionalattentioncan func-
tion independentlyin categorization.Specifically, the two
systems can operate with different goals, in which one
system focuses attention on one stimulus component at
the same time the other system is focusing attention on a
·
additionallighton the ability of the two models to account
for the data, we computed the absolute deviation between
the predicted and the observedprobabilitiesof responding
“A” for the relevant segment for each of the 22 stimuli on
both valid and invalid trials. We then computed the aver-
age across the 22 stimuli on valid trials and the average
across the 22 stimuli on invalid trials. We computed these
two values for each observer for the DBM(P,D) and
EGCM(P,D) models. These data are presented in Table 5.
Several comments are in order. First, note that both mod-
els provided a betteraccountof the validtrial data than the
invalid trial data, and the performance of the two models
were more similar for the validtrials. Even so, for valid tri-
als, the DBM model predictionsare closer to the observed
values than are the EGCM model predictionsfor all 5 ob-
servers. Second, note that the decision bound model pro-
Table 5
Average Absolute Deviation Between Predicted and Observed
Response Probabilities for DBM(P,D) and EGCM(P,D)
DBM(P,D)
EGCM(P,D)
Observer
Valid
Invalid
Valid
Invalid
1
2
3
4
5
.016
.029
.037
.028
.027
.047
.048
.059
.039
.055
.029
.034
.042
.087
.042
.058
.151
.081
.186
.089
Average
.027
.050
.047
.113

PERCEPTUAL AND DECISIONAL ATTENTION
337
different component. This conclusion validates current location varies across trials. Third, in the present task, ir-
work in cognitiveneuroscience that has attempted to map relevantinformationwas provided in the spatiallycued lo-
out a variety of separate, but interconnected,attentionsys- cation on invalid trials, whereas in most spatial cuing
tems (e.g., perceptual, decisional,vigilance;Posner & Pe- tasks, no stimulus is presented in the spatially cued loca-
tersen, 1990). It also points to the need to model percep- tion on invalidtrials. Despite these methodologicaldiffer-
tual and decisional attention separately in formal models ences, the basic findingsare the same, thereby suggesting
of categorization.
that a functional independence of perceptual and deci-
Although we argue that the most reasonable interpreta- sional attention is a robust phenomenon.
tion of these results is in support of the functional inde-
One variantof thetraditionalspatialcuingtask is of par-
pendencehypothesis,onemightbe able todevelopa single- ticularrelevanceto the perceptualcategorizationliterature.
system exemplar model that could account for these data. In this variant, the relation between spatial cuing and re-
For example, one could assume that, on every trial, the ob- sponse expectancy is examined (e.g., Kingstone, 1992;
servers distribute their unitary attention to the four fol- Klein, 1994;Klein & Hansen, 1987, 1990). This literature
lowing locations:(1) the likely locationof the endpointof suggests that the spatial cue is less effective when the tar-
the horizontal line on a valid trial, (2) the likely location get is less likely (i.e., has a lower base rate). For example,
of the endpoint of the horizontal line on an invalid trial, when a bright target is more likely than a dim target, the
(3) the likely location of the endpoint of the vertical line brighttarget shows thetraditionalcost–benefit effect of the
on an invalid trial, and (4) the likely location of the end- spatial cue, whereas the dim target does not (e.g., Klein &
point of the vertical line on a valid trial, with the amount Hansen, 1990). Base-rate effects are ubiquitous in per-
of unitaryattentionbeinglargest at Location1, nextlargest ceptualcategorizationand have been found to affect the lo-
at Location2, next largest at Location3, and the least large cation and nature of the decision criterion (e.g., Maddox,
at Location 4. This model would require that each stimu- in press). Future research should examine the influenceof
lus be represented on four dimensions instead of two, base-rate manipulations on performance when a spatial
where two of these dimensions are “invisible” on each cuing manipulationis combined with a perceptual catego-
trial. Although possible, a model of this sort has not been rization task to determine whether the spatial cue and re-
previously proposed in the literature. Like all theoretical sponse expectancyinteractin perceptualcategorizationin
issues, the best approach to the single versus multiple at- the same way as they do in traditional spatial cuing tasks.
tention systems debate is to look at converging evidence
from a variety of different sources. The present study rep- tionalindependenceof perceptual and decisionalattention
resents a first step toward this goal.
during perceptual categorization by combining a percep-
In summary, in the present study, we examinedthe func-
At this point,it is worth mentioningbriefly the relations tual categorizationtask with a spatial cuing manipulation.
between the present task and traditional spatial cuing de- The empirical and model-based analysesstrongly support
signs (e.g., Eriksen & Hoffman, 1972; Posner, 1980). In the hypothesisthat perceptualand decisionalattentioncan
the present task, the location of the spatial cue was fixed function independentlyin perceptual categorization.
across trials, and the observer was instructed to visually
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NOTES
Luce, R. D., & Nosofsky, R. M. (1984). Attention, stimulus range, and
1. Although we structure our investigation in terms of perceptual and
identificationof loudness.In S. Kornblum& J. Requin (Eds.), Prepara- decisional attention, other frameworks have been used in the literature.
tory states and processes (pp. 3-25). Hillsdale, NJ: Erlbaum.
For example, the term spatial attention is often used in the literature
Macmillan, N. A., Goldberg,R. F., & Braida, L. D. (1988). Resolu- (e.g., Maljkovic & Nakayama, 1994, 1996). We deemed the percep-
tion for speech sounds: Basic sensitivity and context memory on
tual/decisional attention distinction more appropriate for the present ap-
vowel and consonant continua. Journal of the Acoustical Society of plication for two reasons. First, most spatial cuing studies vary the at-
America, 84, 1262-1280.
Maddox, W. T. (1992). Perceptual and decisional separability. In
tended location across trials and often manipulate other factors as well
(Kingstone,1992;Klein, 1994;Klein & Hansen, 1987,1990),whereas our
F. G. Ashby (Ed.), Multidimensionalmodels of perception and cogni- task manipulation was much simpler. We used a fixed spatial location
tion (pp. 147-180). Hillsdale, NJ: Erlbaum.
while varying the stimulus information within the cued location. Thus it
was the information that entered the perceptual system for processing
that was manipulated. Second, the terms perceptual and decisional are
more common in the categorization literature.
2. Before continuing, we must address one potential weakness of our
experimental design. Recall that an irrelevant component judgment was
Maddox, W. T. (2002). Learning and attention in multidimensional
identification and categorization: Separating low-level perceptual
processes and high-level decisional processes. Journal of Experimen-
tal Psychology: Learning, Memory, & Cognition, 28, 99-115.
Maddox, W. T. (in press). Toward a unified theory of decision criterion
learning in perceptual categorization. Journal of the Experimental required on some trials during Blocks 3–5, but not during Blocks 1–2.
Analysis of Behavior.
Specifically, duringBlocks 3–5 one-fourthof the valid trials includedir-

PERCEPTUAL AND DECISIONAL ATTENTION
339
relevant component judgments, whereas all of the invalid trials included dicted direction. Taken together, these analyses argue against any strong
irrelevant component judgments (see the Method section). This might effect of eccentricity on the results. Second, it is possible that the circu-
bias the observer to place more importance on storing the irrelevant com-
ponent length on invalid trials duringBlocks 3–5 (when the irrelevant di- the cued location. This would lead to higheraccuracy for the component
mension was always cued) than during Blocks 1–2 (when the irrelevant
within the cued location relative to the componentoutsideof the cued lo-
dimension was never cued). If this hypothesis is correct, relevant di- cation. If this hypothesis is correct, it should be the case that perfor-
lar spatial cue might serve as a reference frame for the component within
mension accuracy on invalid trials should be lower during Blocks 3–5
(when emphasis was placed on storing the irrelevant component) than
mance would be better for long components within the spatial cue than
for short components within the spatial cue, since the endpoints of long
during Blocks 1–2. We tested this hypothesis by computing relevant di- componentswould be closer to the reference frame. To test this, we com-
mension accuracy on invalid trials separately for Blocks 1–2 and Blocks pared accuracy for the relevant component on valid trials at the three
3–5. Contrary to this hypothesis, accuracy was lower duringBlocks 1–2
shortest lengthswith accuracy for the relevant component on valid trials
(76.3%) than during Blocks 3–5 (78.9%), and the difference was non- at the three longest lengths. Averaged across observers, accuracy was
significant ( p > .10). It is important to note, though,that even if this hy- 84.2% for the short and 86.6% for the long components. This difference
pothesis was supported, it does not preclude us from distinguishingbe-
was nonsignificant but is in the direction predicted by the reference
tween yoked and functionally independentattention systems. In a yoked frame hypothesis. We also compared accuracy for the irrelevant compo-
system, irrelevant judgmentson valid trials and relevant judgmentson in- nent on invalid trials at the three shortest lengths with accuracy for the
valid trials would be at chance, regardless of any decision bias. This fol- irrelevant component on invalid trials at the three longest lengths. Aver-
lows because the decisional system has the information only in the cued
aged across observers, accuracy was 62.2% for the short and 56.0% for
location to operate on. When the information in the cued location is dif- the long components. This difference was nonsignificant and was in di-
ferent from the information needed to generate a response, performance
will be at chance regardless of any bias in the decision strategy. This pat-
rection opposite of that predicted by the reference frame hypothesis. Fi-
nally, because the reference frame hypothesispredicts that accuracy will
tern did not hold in the present study and thus provides evidence in sup- be higher when the component is in the spatial cue, it predicts that accu-
port of the functional independence hypothesis.
3. Before we continue, two alternative explanations for the empirical
results need to be ruled out. First, it is well established that resolution de-
racy will be higher for the relevant component on valid trials and for the
irrelevant component on invalid trials than for the irrelevant component
on valid trials and for the relevant component on invalid trials. This pre-
clines with eccentricity from thefovea(e.g., Geisler, 1989).Thus, one pos- dicted ordering of accuracy was not observed in the data. Taken together,
sibility is that performance is superior for the component in the spatial
cue because that component has higher spatial resolution, regardless of
these analyses argue against the reference frame hypothesis.
4. It is important to note that this is a very restricted set of perceptual
whether separate attention systems exist. As a test of this alternative hy- representation assumptionswithin the framework of decision boundthe-
pothesis, we performed two separate analyses. First, we compared rele-
ory. This version of decision bound theory assumes that the mean per-
vant component accuracy on invalid trials when the irrelevant compo- ceptual effects are located at the stimulus coordinates, that the percep-
nent was at its longest length with relevant component accuracy on
invalid trials when the irrelevant component was at its shortest length.In-
valid trials are those in which the irrelevant component is in the spatial
cue. When the irrelevant component is at its shortest length, the relevant
component will be at a smaller eccentricity than when the irrelevant
component is at its longer length and thus should yield higher accuracy.
Averaged across the 5 observers the accuracy rates were 80.5% and
74.3% for the long and short irrelevant components, respectively which
is nonsignificantand in the oppositedirection from that predicted by the
tual noise across all 22 stimuli can be characterized by only two variance
parameters, and that there is no perceptual correlation (i.e., perceptual
independence is assumed; Ashby & Townsend, 1986). It is likely that at
least some of these assumptions are violated with these stimuli. Even so,
they are sufficient for the goals of the present study.
5. A version of the model that assumes a Gaussian similarity function
was also applied. This version fit slightly better than the present version
· ·
[average fit: EGCM( , ) = 855.08;EGCM(P,·) = 846.27;EGCM(·,D) =
843.42;EGCM(P,D) = 842.88].This version is not reported because the
spatial resolution hypothesis. Second, we compared irrelevant compo- exponential similarity function is used in nearly all applications of ex-
nent accuracy on valid trials when the relevant component was at its
longest length with irrelevant component accuracy on valid trials when
the relevant component was at its shortest length. When the relevant
component is at its shortest length, the irrelevant component will be at a
emplar theory. In addition, and perhaps more important, the parameter
values from the Gaussian similarity function models are difficult to in-
terpret. For example, in the Gaussian EGCM(·,D), the utility values are
nearly all less than .5, suggesting more weight is being placed on the ir-
smaller eccentricity than when the relevant component is at its longer relevant dimension.
length and thus should yield higher accuracy. Averaged across the 5 ob-
servers, the accuracy rates were 56.7% and 60.6% for the long and short
relevant components,respectively, which is nonsignificantbutin the pre-
(Manuscript received January 10, 2001;
revision accepted for publication January 11, 2002.)