Response Time Distributions and the Stroop Task: A Test of the Cohen, Dunbar, and McClelland (1990) Model

Abstract

Cohen, Dunbar, and McClelland's (1990) model was tested for Strooplike interference tasks by studying the shape of the distribution of response latencies produced by Ss and by the model. The model correctly anticipates changes in mean response latency (M(RT)) across congruent and incongruent conditions. It does not, however, correctly anticipate changes in the shape of the distributions, even though changes in the shape of the distributions underlie the changes in M(RT). Thus the model predicts M(RT) successfully but for the wrong reason. It is concluded that the model is not an adequate account of Ss' performance in the Stroop task.

Full text

Journal
of
Experimental
Psychology:
Human
Perception
and
Performance
1992.
Vol.
18,
No.
3,872-882
Copyright
1992
by the
American
Psycholc
'ical
Association,
Inc.
0096-1523/92/S3.00
OBSERVATION
Response
Time Distributions
and the
Stroop Task:
A
Test
of the
Cohen,
Dunbar,
and
McClelland
(1990)
Model
D. J. K.
Mewhort,
J. G.
Braun,
and
Andrew
Heathcote
Queen's
University
at
Kingston,
Kingston,
Ontario,
Canada
Cohen, Dunbar,
and
McClelland's
(1990)
model
was
tested
for
Strooplike interference tasks
by
studying
the
shape
of the
distribution
of
response latencies
produced
by Ss and by the
model.
The
model correctly anticipates changes
in
mean
response latency
(AfRT)
across
congruent
and
incongruent
conditions.
It
does
not, however,
correctly
anticipate
changes
in the
shape
of the
distributions,
even though changes
in the
shape
of the
distributions
underlie
the
changes
in
AfRT.
Thus,
the
model predicts
A/RT
successfully
but for the
wrong reason.
It is
concluded that
the
model
is not an
adequate
account
of
Ss'
performance
in the
Stroop
task.
Suppose
that
you are
shown
a
series
of
character strings,
each
printed
in
either
red or
green,
and
that
you are
asked
to
indicate
the
color
of the
print. Your average response time
will
be
longer when
the
character string spells
a
conflicting
color word than
when
it
spells
a
noncolor word
or is
composed
of
Xs. The
interference implied
by the
difference
in
mean
response time
for the
conflicting
and
neutral conditions
is
widely
known
as the
Stroop
effect
(Stroop, 1935),
and a
comprehensive
review
of its
literature
has
been presented
by
MacLeod
(1991).
How
does
a
color word interfere with subjects' ability
to
name
the
color
of its
print? Cohen, Dunbar,
and
McClelland
(1990)
proposed
a
connectionist model
to
answer
the
ques-
tion.
Their account assumes
(a)
that evidence
from
all
sources
of
information accumulates
in
parallel
for
both potential
responses,
(b)
that activation passes through
the
system
on
pathways
that vary
in
strength
and not
speed,
(c)
that attention
modulates
the flow of
activation through
the
system,
and
finally
(d)
that subjects have more experience reading words
than
naming colors. When subjects
are
asked
to
name
the
color
of
print
and the
print spells
a
conflicting
color word,
evidence
for
both potential responses accumulates
in
parallel.
This
work
was
supported
by an
operating grant
from
the
Natural
Science
and
Engineering Research Council
of
Canada (NSERC)
to
D.
J. K.
Mewhort,
by an
NSERC postgraduate
fellowship
to J. G.
Braun.
and by a
Commonwealth Doctoral Fellowship
to
Andrew
Heathcote.
We
thank
E. E.
Johns
for a
careful
reading
of the
manuscript
and
Jonathan
Cohen
for
help
in
defining
the
parameters used
by
Cohen,
Dunbar.
and
McClelland
(1990).
Andrew
Heathcote
is now at the
Department
of
Psychology, Uni-
versity
of
Newcastle,
Newcastle,
Australia.
Correspondence
concerning
this
article should
be
addressed
to D.
J.
K.
Mewhort. Department
of
Psychology, Queen's University,
Kingston,
Ontario. Canada
K7L
3N6. Electronic
mail
may be ad-
dressed
to
Mewhortd@qucdn.queensu.ca
(bitnet)
or to
doug@vip.
psyc.queensu.ca
(internet).
As
a
result, evidence about
the
word's
name—evidence
passed
through
a
strong
pathway—interferes
with
the
evidence about
the
color
of the
print—evidence
passed through
a
weaker
pathway.
In
this way, interference reflects
the
subjects' relative
experience with
the two
tasks.
Cohen
et
al.
(1990)
showed that
the
model
is
able
to
predict
changes
in
mean response latency
(MRT)
in
several variations
of
the
Stroop task (e.g., Dunbar
&
MacLeod, 1984).
In the
present study,
we
test
the
model
by
comparing
the
distribu-
tions
of
response latency generated
by the
model against
distributions produced
by
subjects.
To
foreshadow
our
argu-
ment,
we
show that
the
model does
not
correctly anticipate
changes
in the
shape
of the
latency distributions, even though
the
changes
in
shape underlie
the
changes
in
A/RT.
Thus,
we
contend that
the
model predicts
MRT
successfully
but for the
wrong
reason,
and we
conclude that
it
does
not
account
for
subjects' performance
in the
Stroop task.
The
Cohen, Dunbar,
and
McClelland Model
The
Model's Architecture
The
model consists
of two
evidence accumulators con-
trolled
by a
12-node
encoder network.
The 12
nodes
are
arranged
in
three layers:
6
nodes
in the
input (stimulus) layer,
4
nodes
in the
middle (hidden) layer,
and 2
nodes
in the
output (response) layer.
The six
input nodes represent
two
colors
of
print (red
and
green),
two
color words (RED
and
GREEN),
and two
instructions
to
respond
to the
color
of the
print
or to the
word's meaning.
The
response nodes tally
the
activation
associated
with
each
response
(red
and
green).
Activation
flows
forward
from
the
input layer
to the
hidden
layer
and
from
the
hidden layer
to the
response layer; there
are no
connections
from
one
layer back
to an
earlier layer.
Finally,
there
are no
connections within
a
given layer,
and no
connections skip
a
layer.
872
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This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

OBSERVATION
873
Deriving
the
Weights
Connections among
the
nodes vary
in
strength,
and the
strengths
are
represented
by
weights. Cohen
et
al.
(1990)
used
a
back-propagation algorithm
to
establish appropriate weights
by
training
the
network
to
indicate
the
correct response
to a
color word
or to the
color
of the
print (see
Rumelhart,
Hinton,
&
Williams, 1986).
To
build stronger connections
for
reading
color words
than
for
naming
the
color
of the
print, they gave
the
network
10
times more training
trials
in
reading color
words than
in
naming
the
color
of the
print.
After
training,
the
weights
effectively
split
the
network into
two
subsystems,
a
reading subsystem
and a
color-naming
subsystem.
In the
color-naming subsystem,
the
node that
represents
an
instruction
to
report
the
color
of the
print,
and
the
two
color nodes
feed
activation
to two of the
four
hidden-
layer
nodes.
In the
reading subsystem,
the two
color-name
nodes
and the
corresponding instruction
node
feed
activation
to the
remaining
two
hidden-layer nodes (see Cohen
et
al.,
1990, Figure
3).
Running
the
Model
To
simulate
a
trial with
the
model,
the
network
is first
given
instructions. Next,
it is
given
a
series
of
simulated test stimuli.
The
network responds
to
each test stimulus
in
turn.
Instructions.
In a
Stroop experiment, subjects
are
required
to
report either
the
color word
or the
color
of the
print.
The
corresponding instructions
are
represented
in the
model
by
setting
the
activation
for the
appropriate
instruction node
to
1
(the other stays
at 0) and by
cycling
the
network through
a
few
iterations
to
alter
the
resting activation
of the
hidden
and
response nodes.
After
a
dozen iterations,
the
network reaches
a
stable state
and is
then ready
for the
test stimuli.
The
fact
that
the
model
acknowledges
a
role
for
instructions
is
one of its
strong
points.
Experimenters
routinely
give
hu-
man
subjects
instructions,
but too few
models
acknowledge
that
instructions
permit
subjects
to set the
state
of
inter-
nal
processing
mechanisms
in
preparation
for the
task (cf.
Mewhort,
1987).
Stimuli.
Test stimuli
in the
Stroop task
are
created
by
combining
one of
three possible colors (e.g., red, green,
or
black)
with
one of
three possible character strings (e.g., RED,
GREEN,
or a
series
of
Xs),
subject
to the
constraint that each
stimulus
must include
at
least
one red or
green attribute.
For
a
congruent display,
the
color word
and the
color
of the
print
are the
same;
for an
incongruent
display,
the
color
of the
print
requires
one
response, whereas
the
color word requires
the
other. Finally,
for a
neutral display,
the
stimulus
is a
series
of
colored
Xs or a
color word printed
in
black
(a
neutral color).
The
test stimuli
are
simulated
in the
model
by
setting
the
activation
of the
appropriate input nodes
to
1.
Assuming that
the
network
has
been
given
instructions
to
simulate
a red
congruent
display,
for
example,
the
activation
of
both
the
red-
word
node
and of the
red-print node
is set to
1.
The
activation
of
each
of the
other
input
nodes—except
the
current
instruc-
tion
node—is
set to 0; the
activation
of the
current
instruction
node
(i.e..
the
node that represents
the
task)
remains
at 1.
Once set,
the
activation
of the
input nodes remains constant
throughout
the
trial.
Processing
and
decision.
At the
start
of
each test trial,
activation
from
the
input nodes
feeds
to the
hidden nodes
and
then
to the
response nodes. Changes
in the
activation
at
the
hidden
and
response nodes
are
achieved
in a
series
of
steps
or
cycles
and
depend
on the
running average
of the
node's previous input
and its
current input (cf. McClelland,
1979).
Evidence
for
both
potential
responses
is
derived
on
each
cycle
from
the
difference
in
activation between
the two re-
sponse nodes.
The
evidence
is
tallied
in
evidence accumula-
tors,
and
when enough evidence
has
accumulated
to
trigger
one of the two
responses,
the
trial
is
complete. Response
latency
is a
linear
function
of the
number
of
cycles needed
to
trigger
the
response.
To
simulate
the
variability
of
human performance, Gauss-
ian
noise
is
added independently whenever
the
activation
of
each
hidden-
and
response-layer node
is
changed
and
when-
ever
evidence
for one
response
or the
other
is
added
to the
corresponding
evidence accumulator. Adding
noise
admits
the
possibility
of
response error
and
introduces considerable
uncertainty
about when
the
network
will
respond.
Summary.
At the
start
of
each simulated trial,
the
network
is
given
an
instruction
and
permitted
to
modify
its
internal
state
in
response
to the
instruction.
The
evidence accumula-
tors
are set to 0, and
inputs representing
the
appropriate
stimuli
and
instructions activate
the
corresponding input
nodes.
On
each cycle
of the
trial, activation
from
the
input
nodes
feeds
forward,
and
evidence
for the two
responses
is
tallied
in the
response accumulators. When evidence
in one
of
the two
accumulators reaches threshold,
the
trial
is
com-
plete.
Generality
of
the
Model
To
facilitate
the
exposition,
we
have cast
the
model
in
terms
of
color versus word interference.
In
fact,
the
model provides
a
general framework with
which
to
account
for
performance
in
Strooplike tasks.
In the
color versus color-word example,
the six
input nodes represent
two
colors
of
print (red
and
green),
two
color words (RED
and
GREEN),
and two
instruc-
tions
(one
to
report
the
name
of the
color
and one to
report
the
word).
For
other tasks,
the
input
and
response nodes represent
different
kinds
of
information.
For
example,
consider
the
conflict
between
local
and
global
information
demonstrated
by
Navon
(1977).
He
used small letters
to
construct large
letters
and
found that when subjects were asked
to
report
the
small
letter embedded
in the
large letter,
the
large letter
interfered
with subjects' report
of the
small letter
in
much
the
same
way a
color word interferes with subjects' report
of the
color
of
print.
To
apply
the
model
to
Navon's (1977) stimuli,
the six
input
nodes must
be
relabeled
so
that
the
nodes represent
the two
letters
at the
global level,
the
same letters
at the
local
level,
and
instructions
to
respond
to
information either
at the
global
level
or at the
local
level.
In
addition,
the
asymmetric weights
must
be
mapped
to
acknowledge
the
asymmetric character
of
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874
OBSERVATION
the
two
tasks:
A
color word interferes with naming
the
color
of
print
but not
vice versa,
and
global information interferes
with
local information
but not
vice versa.
As
before, con-
gruent
displays require
the
same response
to
information
at
both
levels,
and
incongruent
displays require conflicting
re-
sponses;
for
neutral displays, subjects
are
required
to
respond
to
information
at one of the two
levels,
and no
relevant
information
is
provided
at the
other.
Performance
of
the
Model
To
study
the
model,
we
implemented
it in a
computer
program. With
the
posttraining weights
and the
biases pro-
vided
by
Cohen
et
al.
(1990, Figure
3), we
simulated 10,000
trials
for
each
of the
congruency
conditions (i.e.,
the
con-
gruent,
neutral,
and
incongruent conditions)
at
each
of 135
combinations
of the
model's parameters.
In
each case,
we set
the
task
so
that
the
nontask information would dominate,
that
is,
color naming
in the
standard Stroop task
or
reading
the
small letters
in
Navon's
(1977)
version
of the
task.
For
each
simulation,
we
generated
a
frequency
distribution
of the
cycles
to
respond
for
correct responses,
and
then
we
charac-
terized
each
of the
distributions
in
terms
of the
ex-Gaussian
distribution
(see Heathcote, Popiel,
&
Mewhort,
1991).
The
ex-Gaussian distribution
is the
convolution
of a
normal
and
an
exponential distribution;
it is
skewed
to the right and
has
three parameters,
n,
a, and r. The first two
parameters
(n
and
a)
describe
the
mean
and
standard deviation
of the
normal
component
of the
distribution;
^
reflects
the
leading
edge
and
mode
of the
ex-Gaussian distribution.
The
third
parameter
(T) is
derived
from
the
exponential distribution
and
is a
measure
of
skew.
The
mean
of the
distribution equals
n
+ r. The
ex-Gaussian distribution provides
a
good
fit to
latency
distributions (see Hockley,
1984;
Ratcliff&
Murdock,
1976);
we
found
that
it
also provides
a
good
fit to the
simu-
lated
cycles-to-respond
distributions (examples
are
shown
in
Figures
1 and 2).
The
135
conditions tested
in our
simulations were derived
from
the
factorial
combination
of 4
parameters:
(a) the
stand-
ard
deviation
of the
Gaussian noise added
to the
evidence
accumulators
(<TD),
with values
of
0.005, [0.01], 0.05,
0.1,
and
0.15;
(b) the
standard deviation
of the
Gaussian noise added
to
the
activation when updating each hidden
and
response
node
(o>),
with
values
of
[0.1],
0.5,
and
1.0;
(c) the
cascade
rate
(called
T by
Cohen
et
al.,
1990), with values
of
0.05,
[0.1],
0.2;
(d) the
rate
of
information accumulation (called
a
by
Cohen
et
al.).
with
values
of
0.05.
[0.1],
and
0.2.
The
values
in
brackets
are the
values
used
by
Cohen
et
al.1
Table
1
summarizes
our
simulations:
For
each simulated
distribution,
the
table
shows
the
mean
number
of
cycles
to
respond,
the
percentage
of
error responses,
the
standard
de-
viation
of the
distribution,
the
maximum
frequency
of the
distribution
(/,,,av).
the
median
of the
distribution,
and the
three
parameters
of the
ex-Gaussian
distribution
(n,
a, T)
fitted
by
maximum
likelihood
estimation.
The
15
sets
of
simulations summarized
in
Table
1 are a
subset
of the 135
that
we
examined.
We
selected
the
subset
of
15
because
it
illustrates
the
fundamental characteristics
of
the
model's performance. Except
as
noted,
the
simulations
in
the
table used
the
same parameter values reported
by
Cohen
et
al.
(1990);
in
particular,
for all the
simulations
in the
table,
the
cascade
rate
was
0.1,
and the
rate
of
information accu-
mulation
was
0.1.
As
is
clear
in
Table
1,
the
means
for the
congruent, neutral,
and
incongruent conditions were remarkably stable across
the
15
combinations
of
noise parameters
at
approximately 30.5,
35.9,
and
49.7, respectively. Clearly, within each congruency
condition,
neither processing noise
nor
decision noise
had
much systematic
effect
on the
mean number
of cy-
cles
to
respond.
The
noise parameters
did
affect
perfor-
mance,
however.
First, they controlled
the
accuracy predicted
by the
model.
The
model
was
error-free when
<TD
was
0.05
or
less.
As CTD
increased,
the
errors increased.
Second, they controlled
the
variance
and the
shape
of the
distribution
of
cycles
to
respond.
When
the
noise parameters
were
small,
the
distributions were very narrow
and
almost
symmetrical.
For
example, when
<rD
=
0.01
and
af
= 0.5
(the
parameters Cohen
et
al.,
1990,
used),
the SD was
less than
10%
of the
mean,
and the
most frequent cycle
to
respond
in
the
congruent case represented 26.4%
of the
whole distribu-
tion.
As the
noise parameters increased, however,
the
variance
increased,
and the
distributions became more skewed.
One
can see the
amount
of
skew
by
examining
^
or the
difference
between
the
mean
and the
median.
Third,
for all
combinations
of
parameters,
r
increased
monotonically
across
the
congruency conditions (i.e.,
from
the
congruent
to the
neutral condition
and
from
the
neutral
to the
incongruent condition).
The
behavior
of
^
depended
on the
<7D:
When
<7D
was
larger
than
about
0.1,
n
decreased
monotonically across
the
congruency conditions,
but
when
OD
was
smaller than
0.1,
n
increased monotonically
across
the
same conditions. Thus,
the
relative contribution
of
n
and T
to
changes
in the
mean depended
on
<TD.
Nevertheless, across
the
congruency conditions,
the
variance always increased
from
the
congruent
to the
neutral conditions
and
from
the
neutral
to the
incongruent
conditions.
1
There
is an
error
in the
Cohen,
Dunbar,
and
McClelland
(1990)
article
concerning
the
parameter
values.
When
describing
how
noise
is
added
to the
evidence accumulators,
they
state that "the amount
added
is
random
and
normally
distributed,
with
mean
n
based
on the
output
of the
network,
and
with
fixed
standard
deviation
a. The
mean
is
proportional
to the
difference
between
the
activation
of the
corresponding
unit
and the
activation
of the
most active alternative:
"M;
=
«(act,
- max
act>.,)"
(p.
338).
In
addition, "throughout
[their]
simulations,
the
value
of a was
0.1,
the
value
of a was
0.1,
and the
value
of the
[evidence] threshold
was
1.0"
(p.
338).
With
two re-
sponses,
the
means
MI
and
MZ
are
^,
=
a(a,
—
a2)
and
MZ
=
«(fl2
-
a,),
where
a,
refers
to the
activation
of one
response node
and
a^
refers
to the
activation
of the
other. Given
the
description
in the
article,
the
amount
added
on
each cycle
to
each
of the two
evidence
accumulators
should
be
[MI
+
N(0,
a)}
and
[/n2
+
N(0,
a)],
respectively,
where
N(0,
a)
is a
random sample
from
a
normal distribution
with
mean
0 and
standard
deviation
a. In
fact,
however, Cohen, Dunbar,
and Mc-
Clelland
(1990)
weighted
the
noise
as
well
as the
difference
in
acti-
vation
by
«
so
that
the
effective
standard deviation
of the
generator
was
n
x
n:
with
a =
0.1,
the
true
value
of
UD
was
0.01
(J. D.
Cohen,
personal
communication,
June
12.
1991).
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

OBSERVATION
875
Table
1
Percentage
Errors
and
Measures
on the
Distribution
of
Cycles
Produced
by the
Model
as a
Function
of
Decision
Noise,
Processing
Noise,
and
Congruency
Condition
Measure
Noise
parameter
<TD
=
0.15,
<Tp
= 1.0
Congruent
Neutral
Incongruent
__
AI
c
n
=
05
Congruent
Neutral
Incongruent
<rD
=
0.15,
CTP
= 0.1
Congruent
Neutral
Incongruent
^
A
i
1 n
OD
—
u.
i
,
(7p
—
i
.u
Congruent
Neutral
Incongruent
Congruent
Neutral
Incongruent
Congruent
Neutral
Incongruent
<rD
=
0.05,
aP=
1.0
Congruent
Neutral
Incongruent
O-D
=
0.05,
<TP
= 0.5
Congruent
Neutral
Incongruent
<rD
=
0.05,
(Tp
= 0.1
Congruent
Neutral
Incongruent
ffD =
0.01,<rP=
1.0
Congruent
Neutral
Incongruent
CTD
~
0.01,
OP
=
U.5
Congruent
Neutral
Incongruent
A
AI
~
A,
i
<JD
—
v.u
i
,
op —
u.i
Congruent
Neutral
Incongruent
<TD
=
0.005,
<rP
=
1.0
Congruent
Neutral
Incongruent
<TD
=
0.005,
ffp = 0.5
Congruent
Neutral
Incongruent
OD
=
0.005,
o-p
=
0.
1
Congruent
Neutral
Incongruent
M
30.5
36.3
50.1
30.3
35.7
49.4
30.6
36.1
49.5
30.6
36.5
51.4
30.5
35.8
50.5
30.6
36.1
49.6
30.7
36.3
51.2
30.5
35.9
49.6
30.5
35.9
49.0
30.5
36.0
50.4
30.3
35.6
48.8
30.3
35.5
48.2
30.5
36.1
50.5
30.3
35.6
48.7
30.2
35.5
48.2
%
error
4.38
6.16
10.34
4.22
5.66
9.63
4.57
5.38
9.94
0.18
0.48
1.50
0.15
0.40
1.12
0.17
0.36
1.01
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
SD
14.6
21.2
39.2
14.8
19.9
38.4
14.6
20.2
38.2
10.0
14.1
28.4
9.7
13.4
27.3
9.8
13.3
26.0
5.4
7.7
16.5
5.0
6.8
14.0
4.9
6.8
13.0
2.5
3.8
9.1
1.5
2.2
4.9
1.0
1.4
2.7
2.3
3.5
8.8
1.3
1.8
4.3
0.6
0.8
1.5
/max
295
244
189
310
240
181
330
267
181
440
343
211
449
353
230
447
361
227
766
574
301
816
617
335
863
621
259
1580
1106
519
2639
1844
857
3690
2689
1430
1712
1151
521
3072
2105
936
6027
4234
2588
Median
28.0
32.0
38.0
28.0
32.0
38.0
28.0
32.0
38.0
30.0
34.0
45.0
30.0
34.0
44.0
30.0
34.0
43.0
30.0
36.0
48.0
30.0
35.0
48.0
30.0
35.0
47.0
30.0
36.0
49.0
30.0
36.0
48.0
30.0
35.0
48.0
30.0
36.0
49.0
30.0
36.0
48.0
30.0
35.0
48.0
M
16.8
14.9
11.3
16.3
15.8
11.7
17.1
16.2
11.4
23.0
24.0
22.4
23.4
24.5
23.0
23.2
24.8
23.6
27.6
31.0
36.1
27.9
31.5
37.4
27.6
31.5
38.5
29.1
33.6
43.0
29.7
34.7
45.6
29.9
34.9
46.9
29.2
33.8
43.2
29.8
34.8
46.0
30.1
35.2
47.6
a
6.9
6.2
4.2
6.7
6.8
4.6
7.2
7.0
4.1
6.6
7.6
7.2
6.7
7.7
7.6
6.6
7.7
7.7
4.4
5.6
7.8
4.2
5.3
7.9
4.0
5.2
8.2
2.1
2.9
5.5
1.4
1.9
3.8
1.0
1.3
2.4
2.0
2.8
5.3
1.2
1.7
3.4
0.6
0.8
1.4
T
13.8
21.5
38.8
14.0
19.8
37.7
13.5
19.9
38.1
7.7
12.4
29.0
7.2
11.4
27.5
7.4
11.4
26.0
3.1
5.3
15.1
2.6
4.4
12.2
2.9
4.4
10.5
1.4
2.4
7.5
0.6
0.9
3.1
0.4
0.6
1.3
1.3
2.3
7.4
0.6
0.8
2.7
0.2
0.3
0.6
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876
OBSERVATION
Across
the
congruency
conditions, there
was
also
a
modest
interaction
of the two
noise parameters. Decreasing
o>
nar-
rowed
the
distribution
of
cycles
to
respond
and
shifted
its
parameters.
The
effect
of
changing
aP,
however,
was
masked
by
decision noise, except when
<TD
was
very
small.
Although
the
interaction
is not
shown
in
Table
1,
the
noise
parameters also interacted with both
the
cascade rate
and the
rate
of
evidence accumulation.
For
example, increasing
the
latter
parameter reduced errors,
but the
same manipulation
also increased
the
relative contribution
of
T
to
changes
in the
mean
across
the
congruency conditions.
To
anticipate
the
argument
to
follow,
changes
in the
cascade rate
and the
rate
of
evidence accumulation
did not
help
the
model
to fit the
empirical
data;
in
particular,
the
monotonic change
in
n
and
T
across
the
congruency conditions
was not
disturbed
by
changes
in
either parameter.
Figures
1 and 2
show
the
distribution
of
cycles
to
respond
across
the
three congruency conditions
for two of the
combi-
nations
of
noise parameters illustrated
in
Table
1.
Both
figures
also
show
the
ex-Gaussian distribution
fitted
by
maximum
likelihood
estimation. Figure
1
shows
the
distribution when
the
decision noise
was
relatively small:
a0
=
0.01
and
<TP
=
0.5.
The
noise parameters
are the
same values used
by
Cohen
et
al.
(1990)
in
their simulations.
As
noted
earlier, most
of
3000
2000
-
1000
-
Congruent
u
c
CD
D
cr
cu
3000
2000
1000
-
r
Neutral
3000
-
2000
~
1000
-
Incongruent
Cycles
Figure
1.
Frequency histograms
of
simulated cycles
to
respond
as a
function
of
congruency
condition.
(The
solid curve shows
the
ex-Gaussian distribution
fitted to the raw
data
by
maximum likelihood
estimation.
Parameters:
CTD
=
0.01
and
af
=
0.5.)
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OBSERVATION
877
u
c
0)
15
cr
Q)
400
300
4-
200
100
-
400
300
-
200
100
Congruent
Neutral
•ncongruent
400
4-
300
-
200
4-
100
-
0 30 60 90 120
150
180 210 240
270
Cycles
Figure
2.
Frequency histograms
of
simulated cycles
to
respond
as a
function
of
congruency condition.
(The
solid
curve shows
the
ex-Gaussian distribution
fitted
to the raw
data
by
maximum likelihood
estimation. Parameters:
aD
=
0.1
and
<TP
=
0.5.)
the
shift
in the
mean across
the
congruency conditions
reflects
an
increase
in
p.
Figure
2
shows
the
distributions when
the
decision noise
was
relatively large:
a0
=
0.1
and
<TP
=
0.5,
the
values
at
which
the
model starts
to
predict errors. Here,
in
contrast
to the
pattern
in
Figure
1,
most
of the
shift
in the
mean across congruency conditions
reflects
an
increase
in
r.
Tests
of the
Model
Color-
Word Interference
Although
a
monotonic
shift
in
both
n
and T
across
the
congruency conditions
is
characteristic
of the
model's behav-
ior,
it is not
consistent
with
subjects' behavior. Heathcote
et
al.
(1991)
provided
one
illustration
of the
point. They
con-
ducted
a
Stroop experiment
with
the
character strings BLUE
and
GREEN printed
in
blue
or
green.
The
neutral condition
involved
a row of
colored
Xs.
They characterized
the
latency
distributions
in
terms
of the
ex-Gaussian distribution,
and the
results
showed that
in
contrast
to the
Cohen
et al.
(1990)
account, changes
in
MRT
were
often
associated with
a
trade-
off
in
n
and T.
Table
2
summarizes
the
Heathcote
et al.
data.
As
is
shown
in
Table
2,
responses
in the
incongruent
condition were,
on
average,
116
ms
slower than
in the
neutral
condition. Analysis
of the
shape
of the
distribution
of
response
times
showed that
the
interference
effect
(i.e.,
the
difference
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878
OBSERVATION
Table
2
Summary
of
the
Heathcote,
Popiel,
and
Mewhort
(1991)
Data
(in
Milliseconds)
for
Each
Congruency
Condition
Measure
Congruency
condition
SDR1
Congruent
Neutral
Incongruent
Empirical
624
617
733
results
136
117
179
497
524
596
55
64
112
127
92
136
Simulated
results:
<rD
=
0.1,
o>
=
0.5"
Congruent
Neutral
Incongruent
608
639
727
58
80
163
565
572
563
40
46
45
43
68
164
<7D
=
0.01.
crP
=
0.5h
Congruent
607 10 603 9 4
Neutral
641 14 635 12 6
Incongruent
726 32 706 24 20
J
Simulated
response
time
=
5.97
(cycles)
+
425.43.
b
Simulated
response
time
=
6.45
(cycles)
+
411.54.
between
the
incongruent
and
neutral conditions) reflected
an
increase
in
^
of 72
ms
plus
an
increase
in T of 44
ms
(see
Heathcote
et
al.,
1991,
for
details
of the
procedure
and of the
statistical
analysis).
On
average, responses
in the
congruent
condition
were
not
significantly
faster
than
in the
neutral
condition.
In
fact,
there
was a
negative advantage
of 7 ms for
congruency;
analysis
of the
shape
of the
latency distributions
showed
that
the
negative advantage
reflected
a
decrease
in
M
of 27 ms
accompanied
by an
increase
in T of 35 ms.
Note
that
the
change
in
shape
of the
latency distribution
suggests
why a
congruency
effect
is
less
frequently
noted
than
the
corresponding
interference
effect
(see MacLeod,
1991).
Most
experimenters report
MRT,
and
that measure averages
M
algebraically
with
T.
A
change
in the
shape
of the
distribution
can
push
^
and r in
opposite directions,
and
because
the
mean
equals
the sum of
^
and T, an
advantage (decrease)
in
n
can be
masked
by an
increase
in T.
Table
2
also shows
data
from
the
model
fit to
Heathcote
et
al.'s
(1991)
results
by
using
a
linear equation
to
convert
from
cycles
to
respond
to
milliseconds.
We fit the
data twice, once
with
ai>
=
0.01
and
c>
= 0.5 and
once with
aD
= 0.1 and
aP
=
0.5,
the
same combinations
of
noise parameters illustrated
in
Figures
1 and 2. We
used
the first
combination because
it
had
been used
by
Cohen
et al.
(1990);
we
used
the
second
because
it
yielded
an
error rate close
to
that
in the
Heathcote
et al.
study
(1.7%).
We
used
the
same procedure
as
Cohen
et al.
(1990)
to
derive
the
linear equation:
We
minimized
the sum
across
congruency
conditions
of the
squared deviation
of the
simu-
lated
mean
and
empirical mean
to
obtain optimal parameters
for
the
slope
and
intercept
of the
equation.
The
equations
are
given
in
Table
2.
Next,
we
generated
distributions
of
simulated
response
times
for
each congruency condition.
Specifically,
we
applied
the
appropriate linear equation
to
each score
in the
corre-
sponding
distribution
of
cycles
to
respond. Finally,
to
consider
the
shape
of the
distribution
of
simulated data
in
relation
to
the
empirical results,
we
characterized
the
simulated distri-
butions
in
terms
of the
ex-Gaussian distribution.
The
means derived with
the two
sets
of
noise parameters
were
very similar,
and the
simulated means
fit the
data
moderately well.
In
particular, they matched
the
large inter-
ference
effect
associated with
the
incongruent condition.
The
simulated mean
did not
match
the
empirical mean
in the
congruent
condition, however:
The
model predicted
a
small
congruent advantage
in the
mean that
did not
appear
in the
empirical
results.
Although
the
predicted means were similar
for
both
sets
of
noise parameters,
the
variance
of the
distribution
that
was
based
on
<TD
=
0.01
and
o>
= 0.5
(the parameters used
by
Cohen
et
al.,
1990)
was
much
too
small,
a
point clear
in SD
in
relation
to the
corresponding empirical value.
The SD
predicted with
<TD
=
0.1
for the
incongruent case
was
close
to
the
empirical value,
but the
corresponding measures
for the
other conditions were much
too
small
and
were ordered
incorrectly.
The
predicted means matched
the
empirical means mod-
erately
well,
but the
model
did not
correctly anticipate
the
shape of the
distributions
on
which
the
means
were
based.
For
example,
the
model predicted
a
congruency
advantage
in
the
mean
on the
basis
of an
advantage
in
either
n
or T,
depending
on
<TD.
The
empirical congruency
effect
(i.e.,
the
difference
between
the
neutral
and
congruent conditions)
involved
a
decrease
in
n
accompanied
by an
increase
in T,
changes
in the
shape
of the
distribution that canceled when
measured
in
mean response time.
No
combination
of the
model's parameters provides
a way of
shifting
^
to the
left
while
shifting
^
to the right
(with
a
large
<TD,
however,
the
model
can
predict
the
reverse
pattern!).
The
model always
predicts monotonically increasing values
for T
across
the
congruent, neutral,
and
incongruent conditions,
and
although
the
model
can
predict
a
wide variety
of
shapes
for the
distri-
bution
of
response times,
it
cannot accommodate
the
empir-
ical
differences
in
shape across conditions.
The
model
can
explain
the
interference
effect
in the
means,
but
it
does
not
correctly predict
the
shape
of the
latency
distributions.
In
particular, because
it
predicts
the
wrong
shape
for the
response
time
distributions
across
the
con-
gruency
conditions,
it
predicts
a
congruency advantage
in the
mean that
is not
found
in the
data.
Local-Global
Interference
To
extend
the
evidence provided
by
Heathcote
et al.
(1991),
we
studied
a
second illustration
of
Strooplike performance.
Instead
of
conflict between
the
color
of
print
and a
color
word,
we
studied conflict between local
and
global informa-
tion obtained
from
the
same stimulus display.
Method
Subjects.
Six
undergraduates
at
Queen's University (Kingston,
Ontario, Canada) served
as
subjects. Participation permitted
the
subjects
to
earn bonus marks
in an
introductory psychology course.
Apparatus
and
stimuli.
The
stimuli
were
presented
on a
Tektro-
nix
608
display monitor driven
by a
high-speed plotter (see Finley,
1985,
for a
description
of the
plotter).
The
plotter
was
controlled
by
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OBSERVATION
879
a
Zenith
Z-241
computer;
the
computer recorded responses
and
calculated
the
latency
for
each response
(see
Heathcote, 1988,
for the
timing
algorithm).
The
stimuli,
generated
by
brightening
dots
on the
display monitor,
involved
letters
of two
sizes. Small uppercase letters
(H
and Z)
were
created
by
brightening
the
appropriate dots
in a
matrix
of 17
rows
and
13
columns.
The dot
matrix subtended
a
visual angle
of
about
0.18°
x
0.14°.
Large examples
of the
same letters were created
by
placing
small letters
at the
appropriate positions
in a
letter matrix
of
seven
rows
and five
columns.
The
matrix subtended
a
visual angle
of
about
1.65°
x
0.72°.
Congruent displays involved
a
large letter constructed
by
using
the
same small letter (i.e.,
H
constructed with small
Hs and Z
constructed
with
small Zs);
incongruent
displays involved
a
large letter constructed
by
using
the
other small letter (i.e.,
H
constructed with small
Zs and
Z
constructed with small
Hs).
In
addition
to the
large
letters,
two
neutral displays were
created
by
placing
the
small letters
in a
diamond:
One
neutral display
was
composed
of
small
Hs, and the
other
was
composed
of
small
Zs.
Procedure.
At the
start
of
each trial,
a
small
fixation
cross
ap-
peared
in the
center
of the
display monitor. Subjects pushed
a
button
to
continue
the
trial. When
the
subject pushed
the
start button,
the
fixation
cross
was
replaced,
after
an
interval
of 200 ms, by a
target
stimulus.
The
target
was
centered
on the
monitor
and
consisted
of a
set of
small letters (either
Hs or Zs)
arranged
to
form
a
large
H, a
large
Z,
or a
diamond.
The
subjects were required
to
identify
the
small
letter.
Subjects
responded
by
pressing
one of two
buttons. Subjects
1,3,
and 5
used
the
index
finger of
their dominant hand
to
indicate
H and
the
index
finger of the
nondominant hand
to
indicate
Z.
Subjects
2,
4,
and 6
used
the
index
finger
of
their dominant hand
to
indicate
Z
and the
index
finger of
their nondominant hand
to
indicate
H.
If
the
subject
pressed
the
wrong
button
(or did not
respond within
5 s), the
response
was
considered
to be an
error. Response latency
was
calculated
from
the
onset
of the
target,
and the
target remained
on the
display monitor until
the
subject responded
(or
until
the
trial
was
declared
to be an
error).
Error trials were replaced later
in the
session.
In
addition,
to
eliminate slow
posterror
responses,
the
trials
following
an
error trial
were
ignored until
the
subject made
a
correct response;
data
were
taken
following
that response
(see
Rabbitt
&
Rogers,
1977).
Before
starting
the
experiment proper, subjects received
20
practice
trials
to
introduce them
to the
task
and to the
stimuli.
When
the
subjects
had
completed half
of the
experimental trials, they were
given
a
short rest.
No
feedback
on
performance
was
provided.
Design.
Each
subject
received
480
trials
arranged
in 8
blocks
of
60
trials.
Within
each block,
the
subject
received
20
congruent
displays,
20
incongruent
displays,
and 20
neutral
displays.
For
half
of
the
trials
of
each
display
type,
the
displays
were
constructed
with
small
Zs; the
remaining
displays
were constructed
with
small
Hs. The
order
in
which
the
displays
were
shown
was
randomized independ-
ently
within
each
block.
Error
trials
and
posterror
dummy
trials
were
replaced
within
the
same block.
Results
About
2.1%
of the
congruent
trials,
2.4%
of the
neutral
trials,
and
6.7%
of the
incongruent trials were
in
error.
Each
subject
completed
160
trials
for
each
congruency
condition,
and for
each subject
the
ex-Gaussian distribution
was
fitted to the
resulting distributions through maximum
likelihood
estimation. Table
3
summarizes
the
results;
the
table presents
MRT,
SDR-r,
and the
three ex-Gaussian param-
eters
for
each subject
and
congruency condition.
Figure
3
presents
a
graphical summary
of the
empirical
latency
distributions.
The
figure
was
derived through Vincent
averaging,
a
technique that permits
one to
obtain
the
average
shape
of a
distribution across subjects (see
Ratcliff,
1979).
For
each congruency condition, each subject's distribution
was
divided into
16
quantiles,
with
each quantile holding 6.25%
of
the
cases.
The
mean latency within each quantile
was
calculated,
and the
mean across subjects
was
calculated
for
corresponding quantiles. Figure
3
presents equal-area histo-
grams that
are
based
on the
Vincent averages.
The
figure
also shows
the
ex-Gaussian distribution
fitted
to the
average
Table
3
Results
(in
Milliseconds)
for
Each Congruency Condition
and
Subject
Congruency
condition
Congruent
Type
of
result
Empirical
Subject
1
Subject
2
Subject
3
Subject
4
Subject
5
Subject
6
M
Simulated
<TD
=
0.01"
<7D
=
0.10"
<TD
=
0.15C
A/RT
597
432
523
562
505
444
510
506
507
506
SDRT
154
91
114
146
95
127
121
6
36
59
M
465
347
425
424
409
343
402
504
480
451
a
40
45
37
49
34
36
40
6
25
27
T
132
85
99
138
95
101
108
3
27
55
MRT
603
449
517
569
531
463
522
528
527
528
Neutral
SDRJ
129
101
89
147
101
123
115
9
50
79
M
481
371
433
444
435
361
421
524
488
449
a
48
56
29
66
48
37
47
8
29
27
T
121
78
84
125
96
102
101
4
43
78
MR,
625
488
586
675
608
518
583
582
582
582
Incongruent
SDRJ
103
100
117
167
92
100
113
20
103
152
n
542
438
482
527
534
435
493
569
479
433
(T
56
86
43
55
56
54
58
15
29
18
T
83
50
103
148
73
83
90
13
103
149
(cycles)
+
386.57.
1
Simulated
response time
=
3.95
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

880
OBSERVATION
c
O
>~
!Q
o
n
o
c_
Incongruent
30C
700
900
Response
Latency
(rns)
Figure
3.
Probability density obtained
by
Vincent averaging across subjects
as a
function
of
congruency
condition.
(The solid curve shows
the
ex-Gaussian distribution
fitted
by
maximum likelihood estima-
tion.)
curve.
2
As is
clear
in the
figure,
the
ex-Gaussian
distribution
provides
a
good
fit to the
empirical
latency
distributions.
Ana/vsis
of
MRI.
As
Table
3
shows,
in
relation
to the
neutral
condition,
MRT
increased
by
about
61
ms
in the
incongruent condition,
HI,
5) =
26.04.
p <
.01.
In
contrast,
mean
reaction
time
decreased
by
about
11
ms in the
con-
gruent
condition,
/•'(!,
5) =
5.79,
.05 <p<
.10.
The
data
are
similar
to
those
reported
by
Heathcote
et
al.
(1991).
In
partic-
ular,
note that
the
A/RT
data
exhibit strong interference
in the
incongruent
condition
and
weak facilitation
in the
congru-
ent
condition.
MRT
is a
summary
of the
data.
When
the
underlying
distri-
bution
is
symmetrical,
the
mean
is an
adequate
measure.
When
the
underlying
distribution
is
skewed,
however,
the
mean
is
ambiguous
and is
therefore
not an
adequate
measure
2
The
ex-Gaussian parameters obtained
by
fitting
the
Vincent
average
shown
in the figure are
close,
but not
identical,
to the
parameters obtained
by
averaging
the
parameters
in
Table
3. The
difference
reflects inaccuracy
in
Vincent averaging introduced
by
forcing
the
data into
16
quantiles.
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OBSERVATION
881
by
itself.
The
ambiguity arises because
two
distributions
can
generate
the
same
mean even
if
they take
different
shapes
and
are
caused
by
different
underlying processes. Hence,
to un-
derstand performance when
the
underlying distribution
is
skewed,
one
must examine
the
shape
of the
distribution
as
well
as its
mean.
Interference,
facilitation,
and the
shape
of
the
latency distri-
butions.
The
61
-ms
interference
effect
in
MRT
was
generated
by
a
72-ms increase
in
/*,
F(I,
5) =
102.94,
p <
.001,
accompanied
by a
modest
11-ms
decrease
in
r,
F(l,
5) =
1.09,
p >
.30. Thus,
in
contrast
to
Heathcote
et
al.
(1991),
most
of the
interference reflects
an
increase
in
/t.
Next,
consider
the
weak
(11-ms)
facilitation
effect
in
MRT.
The
effect
reflects
a
19-ms
decrease
in
n,
F(1,
5) =
52.98,
p
<
.01, accompanied
by an
8-ms increase
in T,
F(1,
5) =
6.87,
p
<
.05. Again,
as in the
Heathcote
et al.
(1991)
study,
the
congruency
advantage
in
n
was
offset
by a
loss
in T.
Although
it is
modest when measured
in
A/RT,
note
that
the
congruency
effect
is not a
weak
effect
when considered
on a
subject-by-
subject
basis:
All 6
subjects showed
the
decrease
in
ju,
and 4
of the 6
showed
the
increase
in T. The
congruency
effect
is
weak
when measured
in
terms
of
MRT,
because
AfRT
averages
^
and T.
We
do not
contend, however, that
the
change
in
shape
associated with
the
congruent
condition
reflects
two
inde-
pendent factors that cancel each
other
out, although
we
leave
that possibility open.
The
shape
of the
latency distribution
is
different
across
the
congruency
conditions.
We
have used
two
parameters
of the
ex-Gaussian distribution
to
characterize
the
change
in
shape,
but it is not
clear which factors
will
be
needed
to
explain
the
difference.
Our
point
is
methodological:
Because
the
change
of
shape
is not
reflected
in
MRT,
the
mean
can be a
misleading measure
for
response time distributions.
Predictions
from
the
model.
To
apply
the
model
to our
task,
we
assume that global information interferes with local
information
in
much
the
same
way
reading interferes with
naming
the
color
of
print.
In
terms
of the
model,
our
assump-
tion
is
that
global information
is
carried
on
stronger pathways
than local information;
it is
parallel
to
Cohen
et
al.'s
(1990)
assumption that information about color names
is
carried
on
stronger pathways than information about
the
color
of
print.
We
fit the
model
to the new
data
by
applying
the
same
procedures
as
before,
and as
before
we
characterized
the
resulting
distributions
in
terms
of the
ex-Gaussian distribu-
tion.
To fit the
model,
we
used results
from
the
same combi-
nations
of
noise parameters
as
before (i.e.,
the
cases illustrated
in
Figures
1 and 2) and
from
a
third combination selected
to
fit the
error
data
from
the
experiment.
Table
3
also shows
the
predicted means,
the
SDs,
and the
corresponding ex-Gaussian
parameters.
The
linear equations
are
presented
as
well.
Comparison
with
the
model.
As
before,
the
means pre-
dicted with
the
three sets
of
noise parameters were very
similar,
and the
simulated means
fit the
data very well: They
matched both
the
large interference
effect
associated with
the
incongruent
condition
and the
modest facilitation
effect
as-
sociated
with
the
congruent condition. Because there
was an
advantage
for
congruency
in the
local-global
means,
the
model provided
a
better
fit to the
local-global
experiment
than
to the
color-word experiment.
Although
the
predicted means were similar
for all
sets
of
noise parameters,
the
variance
of the
distribution that
was
based
on
aD
=
0.01
and
<TP
= 0.5
(the values used
by
Cohen
et
al.,
1990)
was
much
too
small,
a
point clear
in the
SDs
in
relation
to the
corresponding empirical values. Moreover,
performance with Cohen
et
al.'s parameters
was
error-free.
When
the
decision noise
was
increased,
the
variance
of the
simulated distributions increased.
(Of
course, variance
can be
adjusted
by
altering
the
slope parameter when mapping cycles
to
milliseconds.)
With
<TD
=
0.15
and
aP
=
0.5,
the
model predicted
the
correct pattern
and
roughly
the right
number
of
errors
as
well
as
the
correct
mean latency.
The SDs
and, more important,
the
pattern
of SDs
across
the
congruency conditions
did not
match
the
empirical results. Whereas
the
empirical values
were
roughly
the
same across conditions,
the
model predicted
an
increase
from
the
congruent
to the
neutral condition
and
from
the
neutral
to the
incongruent condition.
The
reason
is
clear:
The
model does
not
correctly anticipate
changes
in the
shape
of the
distributions across conditions.
For
example, when
<FD
=
0.01
and
o>
=
0.5,
the
model
predicted that both
the
congruency advantage
and the
inter-
ference
effect
would
reflect
a
change
in
p.
By
contrast, when
<7D
=
0.15
and
crP
=
0.5—parameters
that provide
a
good
fit
to the
error
data—the
model assigned both
the
congruency
advantage
and the
interference
effect
to
changes
in T. The
empirical interference
effect,
however,
reflected
an
increase
in
/*.,
whereas
the
empirical congruency
effect
involved
a
decrease
in
^
offset
by an
increase
in
T.
Note that
SD for the
empirical distributions
was
roughly
constant across conditions;
the
model
can
hold
the SD
con-
stant,
but
only with very small values
of
<TD.
Such values
yield
unrealistically
narrow distributions
and
unrealistically good
accuracy. When
the
noise parameters
are
adjusted
to
yield
realistic variance
and
accuracy,
the
model yields unrealistic
response time distributions:
It
changes mean response time
by
shifting
the
tail
of the
distribution.
The
model
can
predict
a
wide variety
of
shapes
for the
distribution
of
response times, shapes that
are
based
on a
shift
in
the
whole distribution
or a
shift
in the
tail. When
it is
constrained
to
match accuracy,
it
cannot accommodate
the
empirical
differences
in
shape across conditions.
Discussion
Our
argument
may be
summarized
as
follows:
The
Cohen
et
al.
(1990)
model
is
able
to
account
for the
MRT
data quite
well.
The
mean, however,
is an
ambiguous score:
Two
distri-
butions
can
generate
the
same mean even
if
they take
different
shapes
and are
caused
by
different
underlying processes. Close
examination
of the
distribution predicted
by the
model sug-
gests
that
it
does
not
account
for
subjects' performance.
The
model assigns changes
in
mean across
the
congruency condi-
tions
to
monotonic changes
in
either
n
or T,
depending
on
the
decision noise. Subjects alter
the
shape
of the
distribution
in
more complicated ways. Thus, although
the
model
can
account
for
mean performance,
it
does
so for the
wrong
reasons,
and we
conclude that
the
model
is not an
adequate
account
of
subjects' behavior.
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882
OBSERVATION
We
find
many aspects
of the
model attractive.
In
particular,
we
like
the
idea that information
is
carried
on
pathways that
vary
in
strength.
The
main
difficulty
with
the
model
is
that
its
decision component
is too
separate
from
the
processing
component.
The
thrust
of our
empirical work
is
that process-
ing
is
intimately associated with
the
shape
of the
response
time
distribution.
Yet in the
model,
we
could obtain
the
full
range
of
distribution shapes
by
manipulating
the
decision
noise
alone.
We
think that processing
and
decision
are
more
intimately
linked than
the
model allows.
To
illustrate
our
point, consider
the
shape
of the
distribu-
tions
in the
Heathcote
et
al.
(1991)
experiment.
The
neutral
condition
involved
a
series
of
colored
Xs and
yielded
the
most
symmetrical
of the
three distributions.
One
possible reason
is
that
Xs are
very easy
to
discriminate
from
color words. Given
that
subjects
can
discriminate
the
neutral stimulus early
enough,
we
presume that they
can
alter processing
to
take
advantage
of the
discriminability.
To
fix
the
model,
we
need
a
modification
that
will
allow discriminability factors
to
influ-
ence
the
decision
at an
early point
in
processing.
Finally,
although
we
have pointed repeatedly
to
difficulties
in
using
the
mean
with
skewed distributions,
we do not
wish
to
banish
it
from
the
response time literature. Instead,
our
point
is
that
the
mean
can
mislead when
the
underlying
distributions
change shape.
We
recommend checking
the
shape
of the
distributions
before
calculating
the
mean:
If the
shape
is
stable across conditions,
the
mean
is an
adequate
measure.
If the
shape changes across conditions,
the
mean
is
dangerous
and
should
be
supported
by an
analysis
of the
change
in
shape.
A
null
difference
in the
means
is
particularly
dangerous
because distributions
of
widely
different
shape
can
yield
the
same mean value. Hence,
an
experimental manip-
ulation
may
have
a
large
effect
on the
shape
of the
distribution
without
affecting
its
mean. Likewise, because
an
interaction
involves
a
comparison
of two
differences,
its
interpretation
is
ambiguous
unless
the
shapes
of
underlying distributions
re-
main
constant.
References
Cohen,
J. D.,
Dunbar,
K., &
McClelland,
J. L.
(1990).
On the
control
of
automatic processes:
A
parallel
distributed
processing account
of
the
Stroop
effect.
Psychological
Review,
97,
332-361.
Dunbar,
K.,
&
MacLeod,
C. M.
(1984).
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different
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Experimental
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Finley,
G.
(1985).
A
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A.
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Screen control
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Methods, Instruments,
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A.,
Popiel,
S., &
Mewhort,
D. J. K.
(1991). Analysis
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An
example using
the
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Hockley,
W. E.
(1984).
Analysis
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cognitive
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Journal
of
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Learning, Memory,
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598-615.
MacLeod,
C. M.
(1991).
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An
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Psychological
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J. L.
(1979).
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Psychological
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287-330.
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D. J. K.
(1987).
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