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Acta Psychologica 127 (2008) 485–490

Effect of time of day on arithmetic fact retrieval in anumber-matching task

Marco Fabbri a,*, Vincenzo Natale a, Ana Adan b

a Department of Psychology, University of Bologna, Viale Berti Pichat, 5, 40127 Bologna, Italyb Department of Psychiatry and Clinical Psychobiology, School of Psychology, University of Barcelona, Spain

Received 20 December 2006; received in revised form 22 August 2007; accepted 25 August 2007Available online 4 October 2007

Abstract

The goal of this study is aimed to investigate a possible effect of time of day on arithmetic fact retrieval in a number-matching task.We tested 96 students (age range 19–33 years) at 9 a.m. and at 1 p.m., in a counterbalanced order. The subjective alertness levels werealso recorded. As regards retrieval efficiency, the results showed that the sum interference effect was significantly more pronounced in themorning (9 a.m.) than at midday (1 p.m.). As expected, participants showed higher subjective alertness levels at 1 p.m. than at 9 a.m..However, the difference of subjective alertness did not completely explain differences in interference at two testing sessions. The resultscould be explained with respect to the variation of working memory efficiency during the day.� 2007 Elsevier B.V. All rights reserved.

PsycINFO classification: 2340; 2346

Keywords: Time of day; Interference effect; Automatic activation; Subjective alertness; Working memory efficiency

1. Introduction

Numbers and calculation models (Dehaene, Piazza,Pinel, & Cohen, 2003; McCloskey, 1992) have posited theexistence of a long-term memory store for simple arithme-tic facts. The simple arithmetic facts are stored in anassociative network in which the nodes are numbers andthe links between them represent arithmetic relations(Ashcraft, 1987, 1992, 1995; Campbell, 1987). Empiricalevidences (Galfano, Rusconi, & Umilta, 2003; LeFevre,Bisanz, & Mrkonjic, 1988; LeFevre & Kulak, 1994; Thibo-deau, LeFevre, & Bisanz, 1996; Zbrodoff & Logan, 1986)point to the automatic activation of arithmetic facts, inthe sense that activation of related nodes occurs withoutintention upon presentation of the appropriate stimuli. In

0001-6918/$ - see front matter � 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.actpsy.2007.08.011

* Corresponding author. Tel.: +39 051 2091877; fax: +39 051 243086.E-mail address: marco.fabbri21@unibo.it (M. Fabbri).

a number-matching task (LeFevre et al., 1988), the reject-ing latencies were higher if the target number was associ-ated (for example it was the sum of a presented pair as in3, 4 and 7) with a prior digit-pair (called cues), than therejecting latencies when the target was unrelated to thenumber pair (e.g. 3, 4 and 5). This finding highlights howactivation of the sum occurs even when mental arithmeticis completely irrelevant to the task and interfers with theperformance in a number-matching task. This interferenceeffect is present over brief intervals between cues and tar-gets (60 and 120 ms) but not over longer intervals (180,240 and 480 ms), indicating that either the automatic acti-vation of arithmetic facts is short-lived or that its effect canbe inhibited during longer intervals (LeFevre et al., 1988).The interference effect with regards to addition has alsobeen found for multiplication (Galfano et al., 2003; Rus-coni, Galfano, Speriani, & Umilta, 2004; Thibodeauet al., 1996). The obligatory activation of arithmetic factsis independent of the presence or absence of either the addi-

486 M. Fabbri et al. / Acta Psychologica 127 (2008) 485–490

tion (+) or multiplication (·) sign (Galfano et al., 2003;LeFevre et al., 1988). Moreover, automatic activation ofthe nodes adjacent to the product in the multiplicationtable has also been found (Galfano et al., 2003). These find-ings suggest that arithmetic facts are stored in a very clo-sely interconnected network, where activation spreadsautomatically from the nodes to the product or sum nodethrough associative links across nodes. The number-match-ing task is an indirect way of looking at long-term repre-sentation of arithmetic facts. According to the threecriteria of automaticity proposed by Jonedis (1981), a pro-cess can be considered automatic if it does not require pro-cessing resources, is resistant to suppression, and if it istriggered by presentation of the specific information. Allthese criteria are respected in the number-matching task.

In the number-matching task, automatic activation ofsum nodes has to be inhibited because it is a task-irrelevantdimension. For this inhibition, the role of working memoryhas been underlined (for a review see DeStefano & LeFe-vre, 2004). The working memory capacity, thus reflectsthe ability to control attention and resist interference,and this capacity depends on the amount of attentionalresources available to activate knowledge from long-termmemory (Engle, 2001; Zacks & Hasher, 1994).

Chronopsychological studies have underlined that cog-nitive efficiency varies as a function of time of day, detect-ing the time of day of maximum and minimum efficiencyduring the day for several cognitive tasks (Carrier & Monk,2000; Guerrien, Leconte-Lambert, & Le conte, 1993;Natale, Alzani, & Cicogna, 2003). The entrainment of cog-nitive efficiency rhythms is driven by circadian rhythm ofarousal (Adan & Guardia, 1993; Poirel, 1995). Thisentrainment is dependent on the amount of resources usedto solve the task (Owens et al., 1998). Results from studiesusing time of day recordings have documented circadianvariations in choice serial reaction time, subjective vigi-lance, card sorting, letter cancellation, digit span, arithme-tic operations (Blake, 1967) and memory tasks (Adan,1993, 1995). In particular, working memory tasks followa circadian pattern with rapid improvement early in themorning and a peak at midday 12 noon–2 p.m., followedby a steady decline throughout the afternoon into lateevening when the poorest performance is observed (Adan,1993, 1995).

The aim of the present study is to investigate, for thefirst time, the effect of time of day on number interferenceeffect, using a number-matching task involving automaticactivation of stored arithmetic facts. In this study, we choseto test our sample at 9 a.m. and at 1 p.m. We expectedgreater automatic activation in number-matching tasks(i.e. interference effect) at 9 a.m., because working memoryefficiency is lower at 9 a.m. than at 1 p.m. The subjectivealertness also shows increasing values from 9 a.m. to1 p.m. For this reason, we collected subjective alertness rat-ings, in order to distinguish the role of working memoryefficiency from subjective alertness levels on the expectedinterference effect.

Time of day effects are usually studied by means ofrepeated measures designs. However, such designs invitelearning effect (Monk, 1989a), which may mask circadianeffects. In the present study, we applied methodologicaland statistical procedures to control for learning effects asfar as possible.

2. Method

2.1. Subjects

Ninety-six students (mean age = 22.85 ± 2.40; range 19–33 years) from the Universities of Bologna (Italy) and Bar-celona (Spain) participated in the experiment. Overall therewere 68 females (mean age = 22.95 ± 2.42; 70.84% of thetotal sample) and 28 males (mean age = 22.60 ± 2.36;29.16% of the total sample). There were 69 students fromthe University of Bologna (mean age = 23.13 ± 2.57; 54females and 15 males) and 27 participants from the Univer-sity of Barcelona (mean age = 22.14 ± 1.72; 14 women and13 men). The participants were all right-handed and had anormal or corrected-to-normal vision. The subjects were allnon-paid volunteers and were unaware of the hypotheses ofthe experiment.

2.2. Materials

The materials for the number-matching task were thesame as those described by LeFevre et al. (1988). The par-ticipants had to judge in a rapid and accurate mannerwhether a numerical target had been present in a priordigit-pair, pressing two different buttons on a keyboard.Two sets of 48 stimuli were created and presented on acomputer screen. Each trial included an initial cue (twodigits) and a subsequent target. All stimuli were in Arabicformat. Ties were excluded because the response latencieswere faster than the non-ties (tie-effect; Blankenberger,2001). Trials that elicited activation based on multiplica-tion (e.g. 2 4 = 8) were also excluded. For half of the stim-uli, the cues were made up of one single-digit number andone double-digit number (e.g. 15 and 4), according to theprevious rules. In the other half, both number cues weresingle-digit. The order of stimuli presentation was fixedwithin each list, but the list presentation was counterbal-anced between subjects. Four problem types were definedfor validity (i.e. whether the target matched one of the val-ues in the number pair) and for their pair-target relation-ship. The set of stimuli therefore included sum, neutral,pair control and target control problems, and each problemcontained 12 items (see Appendix A). For the sum and neu-tral problems, the target did not match any of the digit-pairnumbers, so the correct response was NO (24 items in eachlist). For the sum problem, the target was equal to the sumof the numbers in the pair, while for neutral problems thetarget was equal to the sum ±5. For pair control and targetcontrol problems, the target matched a number in the ini-tial pair, so the correct response was YES (24 items in each

M. Fabbri et al. / Acta Psychologica 127 (2008) 485–490 487

list). For pair control problems the number pairs wereidentical to those used in the sum and neutral problems,and for target control problems the targets were identicalto those used in the sum and neutral problems (see thematerials used in LeFevre et al., 1988). In each of the prob-lem types, the number range was 1–41. All numbers werepresented horizontally in white fore-color 30 CourierNew bold font (0.95� · 1.14�) on a black background. Allstimuli were presented at the centre of the display. Thenumbers in pairs were not divided by the addition sign(+) (LeFevre et al., 1988). Bearing in mind the presenceof the interference effect for additions with brief intervalsbetween cue and target (LeFevre et al., 1988), the stimuliwere given a fixed SOA (stimulus onset asynchrony) of120 ms.

Subjective alertness levels were measured via a visual-analogue scale: the Global Vigor Scale (GVS) (Monk,1989b). The subjects were asked to score the intensity oftheir feelings (vigor, tiredness, effort put into everydaytasks and sleepiness) along a 10 cm line ranging from‘‘not at all’’ to ‘‘very much’’. The left end of the line indi-cated the minimum and the right end indicated the maxi-mum of feeling. The global scores for all four questionswere used to measure subjective alertness. Higher scoresindicated greater alertness.

9 a.m. 1 p.m.

GDAY 1

GROUP A

+Fixation (200 ms)

Cue (60 ms)

Mask (40 ms)

ISI (2

2 5

+++++++

7

Fig. 1. Experimental design, with particular reference to p

2.3. Procedure

The experimental design required that participants berandomly divided into two groups depending on the timeof day when they started the procedure. Morning Group(MoG) (N = 48) performed the first experimental sessionat 9 a.m., and the second session at 1 p.m. on the sameday. Midday Group (MiG) (N = 48) the first session at1 p.m. and the second session at 9 a.m. on the followingday. Before computer tests started, GVS was administered.

In the number-matching task, the subject was placed30 cm from the computer screen (800 · 600). The partici-pants were instructed to respond accurately, but as fastas possible. At the centre of the black screen a white crossappeared as fixation point. After 200 ms a pair of numbersappeared for 60 ms. Seven white crosses then appeared for40 ms. After this masking, an inter stimulus interval (ISI)of 20 ms was presented on a black screen. Finally, a targetnumber appeared at the centre of the screen. The digit tar-get remained on the screen until the subject responded YESor NO or for 5000 ms (Fig. 1). For the yes response, thebutton key was ‘‘-’’, pushed with the right hand, whilefor the no response, the button key was ‘‘z’’, pushed withthe left hand. The order of the two sets of stimuli was bal-anced between subjects. The response keys have been kept

9 a.m.

ROUP B DAY 2

0 ms)

Target (until response or 5000ms)

Sequence of events on a single trial in number-matching task.

rocedure of number-matching and verification tasks.

488 M. Fabbri et al. / Acta Psychologica 127 (2008) 485–490

constant across subjects because our participants were allright-handed. The subjects were trained by 12 training tri-als, before the test. Each experimental session lasted15 min.

2.4. Data analysis

For subjective alertness, a repeated measures t-test wasperformed. The behavioural data were analyzed by athree-way ANOVA, with Group (2 levels: MoG andMiG), as between-subject factor, and Time of Day (2 lev-els: 9 a.m. and 1 p.m.) and Type of Problems (2 levels:sum and neutral problems), as within-subject factors. Totest our hypotheses of time of day effect on automatic acti-vation of number network, we further computed the inter-ference effect, as the difference between mean RT sumproblems minus mean RT neutral problems (dRT = RTsum problems � RT neutral problems). A positive differ-ence meant the presence of number interference effect onRTs. Then we conducted a repeated measures t-test onRT difference. The same analyses were carried also outon accuracy (as percentage of correct responses), after thearcsine transformation. Values with p < .05 were consid-ered significant.

3. Results

The t-test comparison of subjective alertness was signif-icant (t(95) = 4.25; p < .0005). The subjects reported lowermean alertness levels at 9 a.m. (mean = 56.81; SD = 18.32)than those reported at 1 p.m. (mean = 64.73; SD = 15.01).

Data analysis focused only on non-matching trials, sincematching trials did not address our hypotheses. The three-way ANOVA on RTs showed that all main factors werenot statistically significant. The interaction Groups · Timeof day reached significance (F(1,94) = 13.40; p < .0005).Also, the interaction Time of day · Problems was statisti-

800

900

1000

1100

1200

9 a.m. 1 p.m.

MoG

mea

n R

T

sum problems

Fig. 2. Pattern of mean RTs (and their MSE), in numb

cally significant (F(1,94) = 7.11; p < .05). These interac-tions were discussed later. The interaction Group ·Problems and the triple interaction were not statisticallysignificant (see Fig. 2).

The comparison between interference effect at 9 a.m.and 1 p.m. was significant (t(95) = 2.65; p < .05). At9 a.m. (mean = 29.21; SD = 117.68) the dRT was higherthan those at 1 p.m. (mean = �13.21; SD = 123.94). More-over, we performed an ANCOVA on dRTs, with Time ofday (2 levels, at 9 a.m. and at 1 p.m), as within-subjectsand alertness levels as a covariate. The ANCOVA stillshowed a significant time of day effect (F(1,94) = 9.93;p < .005), excluding an exclusive role of subjective alertnesson interference effect.

According to our experimental design, the interactionGroups · Time of Day (learning effect and circadian effect)was expected, due to the order of conditions done by MoGand MiG. To better understand this interaction, we per-formed an ANCOVA, with alertness levels as a covariate,on interference effect for each group separately. TheMoG did not reach any significant level, comparing inter-ference effect in both testing times (at 9 a.m.: mean = 20.25;SD = 121.67 and at 1 p.m.: mean = 0.34; SD = 101.52).On the contrary, the interference effect was significantlyhigher at 9 a.m. (mean = 38.16; SD = 114.12) than at1 p.m. (mean = �26.77; SD = 142.71) in the MiG(F(1,46) = 16.15; p < .0005).

The comparison between interference effect at 9 a.m.and 1 p.m. statistically did not reach significance, for accu-racy. The same ANCOVA on accuracy confirmed a notime of day effect.

4. Discussion

The goal of the present study aims to test a possible timeof day effect on number interference effect in number-

9 a.m. 1 p.m.

MiG

neutral problems

er-matching tasks for both groups at testing times.

Cue Cue Target Category

List 13 1 4 Sum problem8 1 9 Sum problem3 4 7 Sum problem1 4 5 Sum problem1 2 3 Sum problem6 2 8 Sum problem9 30 39 Sum problem

31 4 35 Sum problem7 11 18 Sum problem

15 4 19 Sum problem21 6 27 Sum problem

6 22 28 Sum problem3 1 9 Neutral problem8 1 4 Neutral problem3 4 2 Neutral problem1 4 10 Neutral problem1 2 8 Neutral problem6 2 3 Neutral problem9 30 34 Neutral problem

31 4 40 Neutral problem7 11 13 Neutral problem

15 4 24 Neutral problem21 6 22 Neutral problem

6 22 33 Neutral problem

List 2

2 7 9 Sum problem6 1 7 Sum problem1 3 4 Sum problem3 2 5 Sum problem4 2 6 Sum problem2 5 7 Sum problem5 31 36 Sum problem

33 4 37 Sum problem9 20 29 Sum problem

23 6 29 Sum problem7 12 19 Sum problem

10 8 18 Sum problem2 7 4 Neutral problem6 1 2 Neutral problem1 3 9 Neutral problem3 2 10 Neutral problem4 2 1 Neutral problem2 5 12 Neutral problem5 31 41 Neutral problem

33 4 32 Neutral problem9 20 24 Neutral problem

23 6 34 Neutral problem7 12 14 Neutral problem

10 8 23 Neutral problem

M. Fabbri et al. / Acta Psychologica 127 (2008) 485–490 489

matching task. We have posited greater interference effectat 9 a.m.

In a number-matching task, a significant time of dayeffect has been found, comparing dRTs between sum andneutral problems. In fact, the RTs to reject digit targetsarithmetically related to cues were significantly longer thanthe RTs to reject digit targets unrelated to cues at 9 a.m.but not at 1 p.m. The influence could be affected by differ-ent working memory capacity at two different momentsduring the day. The study seems to indicate that inhibitoryefficiency is compromised when the working memory effi-ciency is low (in the present work at 9 a.m.). This resultcould also depend on circadian variation in subjectivealertness levels. As expected, significant lower levels of sub-jective alertness in the present work have been found at9 p.m. in comparison to 1 a.m. However, the time of dayeffect did not disappear, including alertness levels, as acovariate. This finding could claim a difference of workingmemory efficiency in inhibition function (May, 1999; May& Hasher, 1998) independently by subjective alertnesslevels.

Our result could agree with the results of experiment 2by Rusconi et al. (2004). The authors demonstrated thepersistence of the interference effect for multiplication alsoin dual-task paradigm (backward subtraction and randomtapping). In other words, the authors found that the inter-ference effect seemed to be independent from the atten-tional resources available. We could also add that theinterference effect depends on working memory efficiencyin inhibition function, and that such efficiency is modulatedby the time of day.

Independently from starting session (MoG and MiG),RTs decreased in the second testing session with respectto first one (learning effect). However, the learning effectslightly masks the interference effect. In fact, MiG didthe task for the first time at 1 p.m., and the latency averagein rejecting neutral problems was slower than that inrejecting sum problems (negative difference). On the con-trary, the same group showed an interference effect (posi-tive difference) at the second time (9 a.m.). The MoG,instead, showed an interference effect at 9 a.m. but theeffect tended to disappear at 1 p.m. Taken together, thesefindings show that time of day and not learning effectinfluences the task performance, with the sum interferenceeffect more pronounced at 9 a.m. than at 1 p.m. in bothgroups.

In conclusion, the present study points to a time ofday effect on number-matching task. Previous incongru-ent studies can be due to the lack of a methodologicalaspect, taking into account the time of day effect. Wesuggest bearing in mind the testing time in performingtasks in numerical cognition. For example, in numericaldomain the SNARC effect (Dehaene, Bossini, & Giraux,1993) claims an automatic association between numbermagnitude and space of response code (i.e. left and righthand). This effect could also be modulated by time of dayeffect.

Appendix A. The digit cues and their targets presented for

sum and neutral problems in both lists

490 M. Fabbri et al. / Acta Psychologica 127 (2008) 485–490

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