Group Process

SDE Modulates Stroop Interference *

Journal of Experimental Psychology: Human Perception and Performance

(in press)

Symbolic Distance Between Numerosity and Identity

Modulates Stroop-Like Interference

Antonella Pavese Carlo Umilt

University of Oregon University of Padua

Thirty undergraduates participated in an experiment investigating the effect of the arithmetic difference

between stimulus identity and stimulus numerosity in a numerical version of the Stroop task. It was found

that digits symbolically close to the enumeration response reliably produced larger interference than digits

that were farther from the enumeration response. This semantic distance effect (SDE) was found with differ-

ent numerosities (1 9) and different enumeration processes (counting and subitizing), and it increased as a

function of numerosity in the subitizing range. These findings suggest that digit identity autonomously

activates a magnitude representation organized as a compressed number line.

Interference paradigms have been widely used dence that the semantic representation of irrel-

to investigate which representations are automati- evant words is activated in the Stroop task comes

cally activated when nonrelevant or interfering from experiments that have shown a semantic

visual objects are displayed. Among the most gradient of interference. These studies showed

important interference paradigms is the Stroop that interference in the color-naming task in-

task (Stroop, 1935; see MacLeod, 1991, for a com- creases as a function of the semantic association

prehensive review). In Stroop s original work, between the word and the concept of color (e.g.,

participants named the ink color of incongruous Klein, 1964).

color-word stimuli. Relative to control stimuli Comparison judgment is another task in which

consisting of color patches, slower response times the degree of symbolic similarity between stimuli

(RTs) were reported when the word (the affects performance. The symbolic distance ef-

nonrelevant dimension) was the name of a differ- fect (SDE; Moyer & Bayer, 1976) is a general

ent color than that of the ink (the relevant dimen- phenomenon that has been found when individu-

sion). These results showed that, when partici- als compare numbers or other symbols that can

pants were required to name the color, the be associated with continuous object dimensions.

nonrelevant word was processed and interfered Typically, the time required to compare two sym-

with the production of the correct response. Evi- bols on a given dimension varies inversely with

the distance between their referents. When num-

bers are used, the latency of the comparative judg-

We thank Steven Keele and Michael Posner for the use of ment is an inverse function of the arithmetic dif-

the laboratories and for their helpful comments. We are

ference between the two numbers (Moyer &

indebted to Amy Hayes and Scott Doran for editing sug-

Landauer, 1967; Parkman, 1971). Although the

gestions. We would also like to thank Stan Dehaene, Lana

SDE was originally found in comparison tasks,

Trick, Raymond Klein, and an anonymous reviewer for their

several studies have shown that this effect is a

helpful comments and suggestions on earlier drafts of this

article This research was supported by grants from the Ital- more general property of number representation

ian Consiglio Nazionale delle Ricerche.

and is also found in tasks in which no compari-

son is required (Brysbaert, 1995; Dehaene &

Correspondence concerning this article should be addressed

to Antonella Pavese, Department of Psychology, College Akhavein, 1995). It has been suggested that the

of Arts and Sciences, 1227 University of Oregon, Eugene,

SDE is the result of the activation of a magnitude

Oregon 97403-1227. Electronic mail may be sent to

representation associated with numerals and

******@********.*******.***.

SDE Modulates Stroop Interference 2

analogous to a compressed number line (Moyer In his review on the Stroop effect, MacLeod

& Landauer, 1967; Restle, 1970). (1991) concluded that: Compared with naming

In the present study, we wanted to replicate the ink color alone, irrelevant verbal stimuli un-

the effect of symbolic distance between stimulus related to the concept of color interfere only mini-

dimensions on Stroop interference. Previous stud- mally with color naming. However, as the word s

ies (Hock & Petraseck, 1973; Pavese & Umilt, semantic association to the concept of color in-

1997) have found that, when participants are asked creases, so does its potential to interfere. (p. 173).

to enumerate inconsistent digits in a display, the According to this view, interference depends on

amount of Stroop-like interference depends on the the strength of the association between the cat-

arithmetic difference between the identity of the egory of the nonrelevant dimension (colors) and

irrelevant digits and the number of items in the the category of the response (color names). How-

display (e.g., the enumeration response). Our main ever, it is also possible that the degree of associa-

purpose was to investigate whether the modula- tion between the particular values of relevant and

tion of the interference effect would be consis- nonrelevant dimensions in a certain trial might

tent with the activation of a magnitude represen- determine the amount of Stroop interference. This

tation organized as a compressed number line. hypothesis is supported by recent evidence show-

ing that perceptual similarity between the color

Stroop Interference and of the ink and the color designated by the word

Semantic Association affects the amount of Stroop interference. Klopfer

Klein (1964, Experiment 1) measured Stroop (1996) has shown that words that denote a color

interference in six conditions that differed in the that is highly similar to the color-naming response

semantic association between nonrelevant words (e.g., the word GREEN in blue) yield more inter-

and the relevant color dimension: (a) color words ference than words that denote a color that is dis-

included in the response set (the standard incon- similar from the color-naming response (e.g., the

gruent condition); (b) color words not included word ORANGE in blue).

in the response set; (c) common English words

Numerical Variations of the Stroop Task

semantically associated with the colors; (d) com-

Windes (1968) first reported that performance

mon English words not associated with the col-

in an enumeration task was slower when the

ors; (e) rare English words; (f) nonsense syllables;

stimuli being counted were incompatible Arabic

and (g) groups of asterisks. The results revealed a

numerals, and several studies have replicated these

continuum of interference from nonsense syl-

results (Shor, 1971; Flowers, Warner, and

lables, which produced a small but reliable delay

Polansky, 1979). Using a card-sorting task in

in the color-naming latency, to the standard in-

which participants were required to order a group

congruent condition, which showed the strongest

of cards according to the number of symbols

interference effect. Klein concluded that the

printed on them, Morton (1969) found that num-

amount of interference was influenced by the fre-

ber words and digits caused interference and noted

quency of the word as well as its relatedness to

that this interference effect was larger when the

the concept of color.

nonrelevant digits belonged to the response set.

Several studies have confirmed this semantic

Fox et al. (1971) found that an interference

gradient effect and have shown that interference

gradient similar to the semantic gradient found

increases as a function of the strength of the asso-

by Klein (1964) in the domain of color also oc-

ciation between irrelevant words and the concept

curred in the domain of numerosity. They reported

of color (Fox, Shor, & Steinman, 1971; Proctor,

increasing interference as the semantic associa-

1978; Redding & Gerjets, 1977; Scheibe, Shaver,

tion between the concept of number and the sym-

& Carrier, 1967). Some studies have extended this

bols to be counted increased. These symbols in-

result to other domains, such as numerosity and

cluded circles, abstract shapes, letters, common

spatial direction (e.g., Fox et al., 1971).

SDE Modulates Stroop Interference 3

words, Arabic numerals not included in the re- Hinrichs et al., 1981). The SDE does not disap-

sponse set, and, within the response set, incon- pear with extensive practice (Poltrock, 1989), is

gruent Roman numerals, Arabic numerals and observed early in childhood (Duncan &

number names. McFarland, 1980; Sekuler & Mierkiewicz, 1977),

Another numerical variation of the Stroop para- and can be found in different linguistic commu-

digm was developed by Francolini and Egeth nities (Dehaene et al., 1990).

(1980, Experiments 2 and 3), who instructed par- The SDE has also been found with paradigms

ticipants to enumerate red items in a circular dis- that used numbers but did not require any com-

play consisting of red and black items. Compared parison, such as naming tasks. Marcel and Forrin

with a neutral condition in which letters had to be (1974, Experiment 4) presented digits between 2

enumerated, Stroop-like interference was found and 9 and asked participants to name them. They

when the red items were digits that were incon- found a priming effect that varied as a function of

sistent with the enumeration response and a fa- the distance between the target digit and the prime

cilitation effect was found when the red items were digit. In a similar experiment, den Heyer and

compatible digits. Briand (1986) asked participants to name single

letters, asterisks, and digits. Naming a number was

The SDE in Number Comparison facilitated if the previous stimulus was another

Moyer and Landauer (1967) first reported that number rather than a letter or an asterisk. Fur-

the RT to judge which of two digits was the larger thermore, the amount of priming was larger for

was an approximately inverse linear function of close digits and decreased with the distance be-

the numerical difference between the two stimu- tween prime and target digits. More recently,

lus digits1 and named this effect the SDE. The Brysbaert (1995) found that when participants

SDE also occurs when participants are required read a sequence of numbers, reading was facili-

to compare objects in memory on a certain di- tated if the previous number had a close value.

mension. For instance, Moyer (1973) found that Using a different experimental paradigm, in which

in judging which of two animal names represented participants had to judge whether a probe digit

the larger animal, RT varied as an inverse linear was included in a previously presented set of tar-

function of the logarithm of the estimated differ- get digits, Morin, Derosa, and Stultz (1967) found

ence in animal size. that latencies for the no responses varied as a

Several researchers have investigated the SDE function of the distance between the probe digit

for numerical comparisons (Aiken & Williams, and the target set: Close probes were rejected

1968; Banks, Fujii, & Kayra-Stuart, 1976; slower than far probes. Duncan and McFarland

Dehaene, Dupoux, & Mehler, 1990; Duncan & (1980) found that same-different judgments were

McFarland, 1980; Folz, Poltrock, & Potts, 1984; also affected by the numerical distance between

Henik & Tzelgov, 1982; Hinrichs, Yurko, & Hu, two numbers. The wide generality of this phe-

1981; Parkman, 1971; Sekuler & Mierkiewicz, nomenon led Dehaene (1992) to contend that the

1977; Sekuler, Rubin, & Armstrong, 1971) and SDE is a universal characteristic of human nu-

found a similar relationship between RT and num- merical cognition.

bers to be compared. The SDE appears to be con-

The SDE and Stroop Tasks

tinuous in two-digit numbers, with a significant

influence of the units and with little or no discon- In numerical variations of the Stroop task, par-

tinuity at decade boundaries (Dehaene et al., 1990; ticipants respond to the number of items in the

display and ignore their identity. In the semantic

1. In particular, the equation proposed by Welford (1960) gradient version of this paradigm, two variables

best describes the experimental results of Moyer and

are usually manipulated: (a) the association be-

Landauer (1976) and Parkman (1971). Reaction times were

tween printed symbols and the concept of num-

defined as RT = a + b log [(minimum/distance) + 1], where

ber and (b) the congruence between the enumera-

distance is the difference in stimulus values and minimum

is the smaller of the two stimulus values.

SDE Modulates Stroop Interference 4

tion response and numerical symbols. The litera- display with four 3s) or symbolically far (e.g., a

ture on the SDE suggests that, in an enumeration display with four 1s) from the enumeration re-

task, the strength of the association between a sponse. The results showed that inconsistent close

relevant dimension (i.e., the number of items in digits always yielded greater interference than

the display) and a nonrelevant dimension (i.e., the inconsistent far digits regardless of the number

identity of the items) can be manipulated by vary- of items to be counted (four or five). Furthermore,

ing the arithmetic distance between the correct digit identities larger and smaller than the enu-

response and the magnitude represented by the meration responses yielded a similar amount of

digits. The semantic gradient effect suggests that interference.

this manipulation should result in a change in the In the current study, this effect was further

interference effect. Displays in which the items explored to verify the hypothesis that the SDE is

to be counted represent a quantity that is sym- related to the activation of the magnitude repre-

bolically close to the enumeration response (e.g., sentation of irrelevant Arabic numerals.

a display with four 5s) should be enumerated

slower than displays in which the items represent This experiment was designed to investigate

a quantity that is symbolically far from the enu- two important characteristics of the effect of sym-

meration response (e.g., a display with four 7s) bolic distance on Stroop interference in enumera-

The presence of the SDE in a numerical Stroop tion tasks. First, we wanted to verify whether the

task would demonstrate that the amount of inter- effect of symbolic distance on interference was

ference is related not only to the strength of the affected by the type of enumeration process

association between the nonrelevant dimension (subitizing or counting) that participants used.

and the relevant domain (e.g., between the Subitizing is the effortless, confident, fast, and

nonrelevant word and the concept of color in a accurate enumeration process for a small number

color-naming task) but also between the particu- of items (Kaufman, Lord, Reese, & Volkmann,

lar value of the nonrelevant and relevant dimen- 1949; Mandler & Shebo, 1982). The subitizing

range is widely defined as 1 4, although the lit-

sions in that trial (e.g., the color denoted by the

word and the color of the ink; Klopfer, 1996). erature reports different estimates, and relevant

Hock and Petrasek (1973, Experiment 3) first individual differences have been found (Atkinson,

reported that the arithmetic distance between item Campbell, & Francis, 1976; Mandler & Shebo,

identity and numerosity can affect enumeration 1982; Trick & Pylyshyn, 1993; 1994). Counting

latencies. In their experiment, participants were is a process that can handle a larger number of

presented with lists of digit strings that had to be items but is slow, effortful, and error prone. Both

enumerated, ignoring their identity. When digit processes can be defined as enumeration (Trick

identity was close to the enumeration response & Pylyshyn, 1994). Subitizing and counting are

(e.g., 33), response latencies were longer than characterized by typical patterns of latencies and

when digit identity was far from the enumeration error rate. In the subitizing range RT increases

response (e.g., 55). Pavese and Umilt (1997) used reliably but slowly (slope = 40-100 ms) as a func-

Francolini and Egeth s (1980) paradigm to verify tion of numerosity, whereas in the counting range

the effect of symbolic distance on a numerical RT increases faster (slope = 250-350 ms; Trick &

version of the Stroop task. Circular arrays of green Pylyshyn, 1994). Errors are typically low for

and red items were presented for 200 ms and then numerosities of 1-3 and increase for larger

masked. The task was to enumerate the red items numerosities (Mandler & Shebo, 1982). In this

and ignore the green ones. Red items could be experiment, we used the first nine digits and sev-

letters (the neutral condition), digits consistent eral combinations of enumeration responses and

with the enumeration response, or digits incon- nonrelevant digits. The effect of symbolic distance

sistent with the enumeration response. Inconsis- on interference was tested for numerosities that

tent digits could be symbolically close (e.g., a belong to the subitizing range (1-5) and to the

SDE Modulates Stroop Interference 5

counting range (5-9). numerosities that were included in the counting

Another purpose of this study was to investi- range. Letters were used as items to be counted

gate the characteristics of the representation un- for the neutral condition. Within each experimen-

derlying the SDE, measuring interference varia- tal group all the possible combinations of num-

tions as a function of numerosity and item iden- ber of items and identities were used, for a total

of 30 cells (5 display numerosities 6 nonrelevant

tity. It has been proposed that the magnitude of

numbers is represented as a compressed number item identities) in each group.

line, in which the symbolic distance between one

Apparatus and Materials

number and the next decreases as a function of

The experiment was carried out on a Macintosh

numerosity (Dehaene, 1992; Restle, 1970). Stroop

IIci. Stimulus displays were generated and con-

interference is known to increase as a function of

trolled by the software Psyscope (Cohen,

the degree of association between relevant and

MacWhinney, Flatt & Provost, 1993), and pre-

nonrelevant dimensions (Klein, 1964; MacLeod,

sented on an Apple color monitor. The display

1991). If one assumes that symbolic distance is a

was a standard phosphorous display with a graphic

measure of the strength of the association between

resolution of 640 480. The computer recorded

two number representations, one should expect

vocal enumeration RTs using a microphone con-

that the amount of interference caused by

nected to the computer through a response box.

nonrelevant digits would not only be a function

The accuracy of the recorded latency was 1 ms.

of the arithmetic distance between the nonrelevant

The identity of the participant s vocal response

digit identity and the enumeration response but

was manually entered by the experimenter at the

also of the absolute value of the enumeration re-

end of each trial. The screen intensity was adjusted

sponse (e.g., its position on the number line). For

to an easy reading level and was maintained at

instance, according to the compressed number line

that level throughout the experiment. Stimuli ap-

hypothesis, because the distance between 1 and 2

peared in red against a black background. Each

is larger than the distance between 8 and 9, the

element was located at one of 18 equally spaced

digit 1 should produce less interference on the

locations on the circumference of an imaginary

enumeration of a two-item display than the digit

circle. At the viewing distance of 65 cm, the cen-

8 on the enumeration of a nine-item display.

ter-to-center distance between the two diametri-

cally opposed stimulus elements subtended a vi-

Method

sual angle of approximately 4.1 . The mean vi-

Participants sual angle between the edges of two adjacent po-

Thirty undergraduate students at the Univer- sitions was approximately 0.5 . Each item sub-

sity of Oregon participated in the experiment. All tended a visual angle of approximately 0.2 in

had normal or corrected-to-normal visual acuity. height and 0.4 in width. The symbols were dis-

They were tested individually in two sessions of played using the Macintosh system font Times

approximately 50 min each. Participants were (type size = 14 points).

randomly assigned to one of two experimental The items were randomly distributed on the

groups: subitizing and counting. circumference. In the subitizing condition, two

items were never presented in adjacent positions.

Design

Stimuli were either randomly selected uppercase

Participants in the subitizing group were pre-

letters (A, C, G, H, K, L, M, P, R, U, V, Y, and Z)2

sented with numerosities between 1 and 5,

or the digits 1, 2, 3, 4 and 5 for the subitizing

whereas participants in the counting group were

group and 5, 6, 7, 8, and 9 for the counting group.

presented with numerosities between 5 and 9.

A white fixation cross was presented in the cen-

Therefore, the subitizing group responded to

ter of the imaginary circle for the duration of the

numerosities that were included in the subitizing

trial.

range, whereas the counting group responded to

SDE Modulates Stroop Interference 6

Procedure RT data. In the subitizing group, the main

The experiment took place in a sound-attenu- effect of numerosity was significant, F(4, 56) =

ated, dimly lit room. Participants viewed the 33.23, MSe = 4,666, p

stimuli binocularly at a distance of about 65 cm sons showed that all the differences were signifi-

from the display. They were tested in two experi- cant (ps .25). Inconsistent close trials were

Numerosity (+1) (+2) (-1) (-2)

significantly slower than inconsistent far trials,

One 2 3 - -

t(14) = 1.915, p = .038, one-tailed .

Two 3 4 - -

Three 4 5 2 1 Error data. A condition by group mixed

Four - - 3 2 ANOVA was carried out on error percentages. The

Five - - 4 3

only significant effect was the main effect of

group, F(1, 28) = 21.25, MSe = 23.46, p .5.

84) = 1.79, MSe = 3.12, p > .15, nor the condition

The condition by group interaction approached

by group interaction, F(3, 84) = 1.46, MSe = 3.12,

significance, F(3, 84) = 2.49, MSe = 891.2, p =

p > .23, reached significance.

.065. This interaction was caused by the particu-

Separate one-way repeated measures ANOVAs

lar behavior of the neutral condition, which was

were carried out for the two groups. In the

faster than the inconsistent close condition in the

subitizing group, the main effect of condition was

subitizing group and slower than the inconsistent

significant, F(3, 42) = 3.847, MSe = 0.936, p .3. The percent-

subitizing group, the effect of condition was sig-

ages of errors were 4.5, 5.1, 4.9, and 6.1 for the

nificant, F(3, 42) = 40.8, MSe = 83.9, p .25), all other differences were signifi- vious experiments (Hock & Petrasek, 1973;

cant (ps

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