Top

Gepubliceerd in:

01-03-2013 | Original Article

Processing numerosity, length and duration in a three-dimensional Stroop-like task: towards a gradient of processing automaticity?

Auteurs: Valérie Dormal, Mauro Pesenti

Gepubliceerd in: Psychological Research | Uitgave 2/2013

Abstract

The existence of a possible continuum of automaticity for numerosity, length and duration processing was tested with a three-dimensional Stroop-like paradigm. Participants had to compare the numerosity, the length or the duration of two successive linear arrays of sequentially flashed dots in which the three dimensions were manipulated independently to create congruent, incongruent or neutral pairs. The results show that numerosity and length both affected duration processing separately and cumulatively, whereas temporal cues did not influence judgements of numerosity or length. Moreover, length and numerosity influenced each other, with numerical cues having a stronger influence on length processing than the reverse. These findings support the idea that, in sequentially presented stimuli, numerosity, length and duration are processed with different levels of automaticity, with numerosity being processed most, and duration least automatically.

vorige artikel Measuring the allocation of attention in the Stroop task: evidence from eye movement patterns

volgende artikel The impact of task rules on distracter processing: automatic categorization of irrelevant stimuli

The size-congruity paradigm also investigates the bilateral influence between numerical and spatial dimensions but with stimuli in symbolic notation. In this paradigm, the numerical magnitude and the physical size of Arabic digits are varied independently and participants have to judge either the physical size of the digits while ignoring their numerical magnitude, or the numerical magnitude while ignoring their physical size. Typically, physical size interferes with numerical processing and vice versa, showing that the participants are unable to ignore the irrelevant dimension and implicitly process this dimension (e.g., Henik & Tzelgov, 1982).

In separate analyses, the relevant distance (small or large) was introduced as an additional within-subject variable. A main effect was found on latencies (mean RLs for small: 450 ± 119 ms, for large: 436 ± 115 ms), F(1, 51) = 8.601, p < 0.01, and on error rate (% of errors for small: 22.7 ± 9.7, for large: 14.9 ± 11.8), F(1, 51) = 184.996, p < 0.001. In the error rate analysis, the relevant distance entered into some interactions but, as it never changed the direction of the main effect of other factors, it was not included in the main analysis. It is also worth noting that irrelevant dimensions 1 and 2 changed depending on the task (e.g., for the numerosity task, the irrelevant dimensions were length and duration; for the length task, the irrelevant dimensions were numerosity and duration, etc.)

To ensure that the presentation duration was not a confounded variable possibly affecting the error rate (for example, it could be globally more difficult to process 700-ms than 1,300-ms stimuli), a post-hoc analysis was carried out on the mean percentage of errors as a function of presentation duration. This analysis revealed no significant difference (mean % of errors for 700 ms: 15.3 ± 11.6, for 1,300 ms: 14.1 ± 10.8), t(17) = 1.969, p > 0.07.

Again, a post-hoc paired t-test showed no difference between stimuli lasting 700 ms and those lasting 1,300 ms (mean % of errors for 700 ms: 17.4 ± 11.5, for 1,300 ms: 18.1 ± 12), t(17) = 1.205, p > 0.2.

Even if there was no reliable statistical difference in the latencies between the three tasks in the neutral conditions, participants were slightly faster for numerosity processing and slower for the length comparison. However, these weak differences in the relative speed of processing cannot account for the observed effects of interference. Indeed, classical “Horse Race” models (Dyer, 1973; Schwarz & Ischebeck, 2003) predict an interference of the fastest processed dimension on the slowest one, but not the reverse. Yet, here, although length was processed more slowly than numerosity and duration, it interfered with these two dimensions. (Note that whatever be the task, participants had to wait till the end of the presentation of the array to be able to answer; anticipated responses were discarded from the analyses.)

A statistically significant main effect of duration was observed on error rates in the numerosity task, but it is worth noting that this effect did not correspond to a regular pattern of facilitation and interference. It was only due to the congruent condition leading to more errors, which in fact stemmed from the incongruency effect of length.

Algom, D., Dekel, A., & Pansky, A. (1996). The perception of number from the separability of the stimulus: the Stroop effect revisited. Memory & Cognition, 24(5), 557–572.CrossRef

Atkinson, C. M., Drysdale, K. A., & Fulham, W. R. (2003). Event-related potentials to Stroop and reverse Stroop stimuli. International Journal of Psychophysiology, 47(1), 1–21.PubMedCrossRef

Besner, D., Stolz, J. A., & Boutilier, C. (1997). The Stroop effect and the myth of automaticity. Psychonomic Bulletin & Review, 4, 221–225.CrossRef

Block, R. A., & Zakay, D. (1997). Prospective and retrospective duration judgments: A meta-analytic review. Psychonomic Bulletin & Review, 4, 184–197.CrossRef

Breukelaar, J. W. C., & Dalrymple-Alford, J. C. (1998). Timing ability and numerical competences in rats. Journal of Experimental Psychology: Animal Behavior Processes, 24(1), 84–97.PubMedCrossRef

Brown, S. (1997). Attentional resources in timing: interference effects in concurrent temporal and nontemporal working memory tasks. Perception & Psychophysics, 59(7), 1118–1140.CrossRef

Bueti, D., & Walsh, V. (2009). The parietal cortex and the representation of time, space, number and other magnitudes. Philosophical Transactions of the Royal Society B: Biological Sciences, 364, 1831–1840.CrossRef

Casasanto, D., & Boroditsky, L. (2008). Time in the mind: Using space to think about time. Cognition, 106, 579–593.PubMedCrossRef

Casasanto, D., Fotakopoulou, O., & Boroditsky, L. (2010). Space and time in the child’s mind: Evidence for a cross-dimensional asymmetry. Cognitive Science, 34, 387–405.PubMedCrossRef

Church, W. M., & Broadbent, H. A. (1990). Alternative representations of time, number, and rate. Cognition, 37, 55–81.PubMedCrossRef

Clark, H. H. (1973). Space, time, semantics and the child. In T. E. Moore (Ed.), Cognitive development and the acquisition of language (pp. 27–63). New York: Academic Press.

Cohen, J. D., Dunbar, K., & McClelland, J. L. (1990). On the control of automatic processes: A parallel distributed processing model of the Stroop effect. Psychological Review, 97, 332–361.PubMedCrossRef

Cohen, J., Hansel, C. E. M., & Sylvester, J. D. (1953). A new phenomenon in time judgment. Nature, 172, 901.PubMedCrossRef

Colby, C. L., & Goldberg, M. E. (1999). Space and attention in parietal cortex. Annual Review of Neuroscience, 22, 319–349.PubMedCrossRef

de Hevia, M. D., Girelli, L., Bricolo, E., & Vallar, G. (2008). The representational space of numerical magnitude: Illusions of length. Quarterly Journal of Experimental Psychology, 61, 1496–1514.CrossRef

de Hevia, M. D., & Spelke, E. S. (2009). Spontaneous mapping of number and space in adults and young children. Cognition, 110(2), 198–207.PubMedCrossRef

de Hevia, M. D., & Spelke, E. S. (2010). Number-space mapping in human infants. Psychological Science, 21(5), 653–660.PubMedCrossRef

Dehaene, S. (1992). Varieties of numerical abilities. Cognition, 44, 1–42.PubMedCrossRef

Dehaene, S., & Changeux, J.-P. (1993). Development of elementary numerical abilities: A neuronal model. Journal of Cognitive Neuroscience, 5(4), 390–407.CrossRef

Dormal, V., Andres, M., & Pesenti, M. (2008). Dissociation of numerosity and duration processing in the left intraparietal sulcus: a transcranial magnetic stimulation study. Cortex, 44, 462–469.PubMedCrossRef

Dormal, V., Andres, M., & Pesenti, M. (2012). Contribution of the right intraparietal sulcus to numerosity and length processing: An fMRI-guided TMS study. Cortex (in press).

Dormal, V., Dormal, G., Joassin, F., & Pesenti, M. (2012). A common right fronto-parietal network for numerosity and duration processing: An fMRI study. Human Brain Mapping. doi:10.1002/hbm.21300 (in press).

Dormal, V., & Pesenti, M. (2007). Numerosity-length interference: A Stroop experiment. Experimental Psychology, 54(3), 1–9.

Dormal, V., & Pesenti, M. (2009). Common and specific contributions of the intraparietal sulci to numerosity and length processing. Human Brain Mapping, 30(8), 2466–3476.PubMedCrossRef

Dormal, V., Seron, X., & Pesenti, M. (2006). Numerosity-duration interference: A Stroop experiment. Acta Psychologica, 121, 109–124.PubMedCrossRef

Droit-Volet, S. (2010). Speeding up a master clock common to time, number and length? Behavioural Processes, 85(2), 126–134.PubMedCrossRef

Droit-Volet, S., Clément, A., & Fayol, J. (2003). Timing and number discrimination in a bisection task with a sequence of stimuli: A developmental approach. Journal of Experimental Child Psychology, 84(1), 63–76.PubMedCrossRef

Droit-Volet, S., Clément, A., & Fayol, J. (2008). Time, number and length: Similarities and differences in discrimination in adults and children. Quarterly Journal of Experimental Psychology, 61(12), 1827–1846.CrossRef

Duncan, J., & Humphreys, G. W. (1992). Beyond the search surface: Visual search and attentional engagement. Journal of Experimental Psychology: Human Perception and Performance, 18, 578–588.PubMedCrossRef

Dyer, F. N. (1973). The Stroop phenomenon and its use in the study of perceptual, cognitive, and response processes. Memory & Cognition, 1, 106–120.CrossRef

Fias, W., Lauwereyns, J., & Lammertyn, J. (2001). Irrelevant digits affect feature-based attention depending on the overlap of neural circuits. Cognitive Brain Research, 12, 415–423.PubMedCrossRef

Fischer, M. H. (2001). Number processing induces spatial performance biases. Neurology, 57(5), 822–826.PubMedCrossRef

Grondin, S., Meilleur-Wells, G., & Lachance, R. (1999). When to start explicit counting in time-intervals discrimination task: a critical point in the timing process of humans. Journal of Experimental Psychology: Human Perception and Performance, 25(4), 993–1004.CrossRef

Helson, H. (1930). The Tau effect: An example of psychological relativity. Science, 71, 536–537.PubMedCrossRef

Henik, A., & Tzelgov, J. (1982). Is three greater than five: the relation between physical and semantic size in comparison tasks. Memory & Cognition, 10, 389–395.CrossRef

Houdé, O. (1997). Numerical development: From the infant to the child. Wynn’s (1992) paradigm in 2- and 3-year olds. Cognitive Development, 12, 373–391.CrossRef

Houdé, O., & Guichart, E. (2001). Negative priming effect after inhibition of number/length interference in a Piaget-like task. Developmental Science, 4(1), 119–123.CrossRef

Kahneman, D., & Chajczyk, D. (1983). Tests of the automaticity of reading: Dilution of Stroop effects by color-irrelevant stimuli. Journal of Experimental Psychology: Human Perception and Performance, 9, 497–509.PubMedCrossRef

Kaufman, E. L., Lord, M. W., Reese, T., & Volkmann, J. (1949). The discrimination of visual number. American Journal of Psychology, 62, 498–525.PubMedCrossRef

Koechlin, E., Naccache, L., Block, E., & Dehaene, S. (1999). Primed numbers: exploring the modularity of numerical representations with masked and unmasked semantic priming. Journal of Experimental Psychology: Human Perception and Performance, 25(6), 1882–1905.CrossRef

Lakoff, G., & Johnson, M. (1980). Metaphors we live by. Chicago: University of Chicago Press.

Levin, I. (1979). Interference of time related and unrelated cues with duration comparisons of young children: analysis of Piaget’s formulation of the relation of time and speed. Child Development, 50, 469–477.PubMedCrossRef

Levin, I. (1982). The nature and development of time concepts in children. The effects of interfering cues. In W.J. Friedman (Ed.), The developmental psychology of time (pp. 47–85). New York: Academic Press.

MacLeod, C. M., & Dunbar, K. (1988). Training and Stroop-like interference: Evidence for a continuum of automaticity. Journal of Experimental Psychology. Learning, Memory, and Cognition, 14(1), 126–135.PubMedCrossRef

Meck, W., & Church, R. (1983). A mode of control model of counting and timing processes. Journal of Experimental Psychology: Animal Behavior Processes, 9, 320–334.PubMedCrossRef

Merritt, D. J., Casasanto, D., & Brannon, E. (2010). Do monkeys think in metaphors? Representations of space and time in monkeys and humans. Cognition, 117, 191–202.PubMedCrossRef

Moyer, R. S., & Landauer, T. K. (1967). Time required for judgments of numerical inequality. Nature, 215, 1519–1520.PubMedCrossRef

Naparstek, S., & Henik, A. (2010). Count me in! On the automaticity of numerosity processing. Journal of Experimental Psychology. Learning, Memory, and Cognition, 36(4), 1053–1059.PubMedCrossRef

Oliveri, M., Vicario, C. M., Salerno, S., Koch, G., Turriziani, P., Mangano, R., et al. (2008). Perceiving numbers alters temporal perception. Neuroscience Letters, 432, 308–311.CrossRef

Piaget, J. (1946). Le développement de la notion de temps chez l’enfant [The development of the notion of time in children]. Paris: PUF.

Piaget, J. (1952). The child’s conception of number. New York: Basic Books.

Piazza, M., Izard, V., Pinel, P., Le Bihan, D., & Dehaene, S. (2004). Tuning curves for approximate numerosity in the human intraparietal sulcus. Neuron, 44, 547–555.PubMedCrossRef

Pufall, P. B., & Shaw, R. (1972). Precocious thought on number: The long and short of it. Developmental Psychology, 7, 62–69.CrossRef

Schneider, W., Eschman, A., & Zuccoloto, A. (2002). E-prime user’s guide. Pittsburgh: Psychology Software Tools, Inc.

Schwarz, W., & Heinze, H. J. (1998). On the interaction of numerical and size information in digit comparison: A behavioural and event-related potential study. Neuropsychologia, 36(11), 1167–1179.PubMedCrossRef

Schwarz, W., & Ischebeck, A. (2003). On the relative speed account of number-size interference in comparative judgments of numerals. Journal of Experimental Psychology: Human Perception and Performance, 29, 507–522.PubMedCrossRef

Stavy, R., & Tirosh, D. (2000). How students (mis-) understand science, mathematics: Intuitive rules. New York: Teachers College Press, Columbia University.

Thomas, E. A. C., & Weaver, W. B. (1975). Cognitive processing and time perception. Perception and Psychophysics, 17, 363–367.CrossRef

Trick, L. M., & Pylyshyn, Z. W. (1993). What enumeration studies can show us about spatial attention: Evidence for limited capacity preattentive processes. Journal of Experimental Psychology: Human Perception and Performance, 19(2), 331–351.PubMedCrossRef

Tzelgov, J., Meyer, J., & Henik, A. (1992). Automatic and intentional processing of numerical information. Journal of Experimental Psychology. Learning, Memory, and Cognition, 18, 166–179.CrossRef

Vicario, C. M., Pecoraro, P., Turriziani, P., Koch, G., Caltagirone, C., & Oliveri, M. (2008). Relativistic compression and extension of experiential time in the left and right space. Plos One, 3(3), e1716, 1–4.

Walsh, V. (2003). A theory of magnitude: common cortical metrics of time, space and quantity. Trends in Cognitive Sciences, 7, 483–488.PubMedCrossRef

Xuan, B., Zhang, D., He, S., Chen, X. (2007). Larger stimuli are judged to last longer. Journal of vision, 7(10):2, 1–5.

Zakay, D. (1998). Attention allocation policy influences prospective timing. Psychonomic Bulletin & Review, 5(1), 114–118.CrossRef

Titel: Processing numerosity, length and duration in a three-dimensional Stroop-like task: towards a gradient of processing automaticity?
Auteurs: Valérie Dormal
Mauro Pesenti
Publicatiedatum: 01-03-2013
Uitgeverij: Springer-Verlag
Gepubliceerd in: Psychological Research / Uitgave 2/2013
Print ISSN: 0340-0727
Elektronisch ISSN: 1430-2772
DOI: https://doi.org/10.1007/s00426-012-0414-3

Bohn Stafleu van Loghum

Deel dit onderdeel of sectie (kopieer de link)

Abstract

Log in om toegang te krijgen

Andere artikelen Uitgave 2/2013

Overtraining and the use of feature and geometric cues for reorientation

Cross-cultural differences in meter perception

Measuring the allocation of attention in the Stroop task: evidence from eye movement patterns

Detecting perturbations in polyrhythms: effects of complexity and attentional strategies

The impact of task rules on distracter processing: automatic categorization of irrelevant stimuli

How reliable is the attentional blink? Examining the relationships within and between attentional blink tasks over time