Effects of Response and Presentation Format on Measures of Approximate Number System Acuity

Effects of Response and Presentation Format on Measures of Approximate Number System Acuity Marcus Lindskog (marcus.lindskog@psyk.uu.se), Anders Winman (anders.winman@psyk.uu.se), Peter Juslin (peter.juslin@psyk.uu.se) Department of Psychology, Uppsala University, P. O Box 1225, Uppsala, 751 42 Sweden Abstract Human adults, infants, and non-human animals are believed to be equipped with an Approximate Number System (ANS) supporting non-symbolic representations of numerical magnitudes. Recent research has questioned both the validity and reliability of tasks intended to measure acuity in the ANS. Issues with validity and reliability might be due to differences in methodology. In the present study, we compare four tasks designed to measure ANS acuity, using a within-subjects design. The tasks are compared with respect to response and presentation format effects previously studied in the psychophysics literature, but largely ignored in the ANS literature. We find a presentation format effect and show that when non-symbolic numerical stimuli are presented sequentially the magnitude of the second stimulus is overestimated. Further, the results indicate that people’s sensitivity to differentiate between non-symbolic numerosities is dependent on response format. The implications of the results to measures of ANS acuity are discussed. Keywords: Approximate number system, response format, presentation format, validity, reliability Introduction Imagine walking in the countryside. As you approach a large field you spot two flocks of sheep, one with only white sheep and one with only black sheep, and amuse yourself by making a snapshot judgment of whether there are more white than black sheep. Later in your walk, you encounter another two flocks of sheep. This time the two flocks emerge from a tunnel, one flock after the other, separated by some short time interval. Once again, you test your judgment skills by deciding which of the two flocks that is the more numerous. Human adults, infants and non-human animals have a common ability to represent numerical magnitudes, such as the number of sheep, without using symbols (Feigenson, Dehaene, & Spelke, 2004). The core cognitive system supporting this ability, the Approximate Number System (ANS), represents magnitudes in an approximate fashion with representations becoming increasingly imprecise as numerosity increases (Dehaene, 2009; but see, Brannon, Wusthoff, Gallistel, & Gibbon, 2001). The accuracy with which the ANS can represent numerical magnitudes, often referred to as the acuity of the ANS, is conceptualized as the smallest change in numerosity that can be reliably detected and is often quantified by a Weber fraction (w). Acuity in the ANS progresses (i.e., w decreases) developmentally from childhood to adolescence (Halberda & Feigenson, 2008; Halberda, Ly, Wilmer, Naiman, & Germine, 2012) but even among adults there is considerable individual variability (e.g., Halberda & Feigenson, 2008; Halberda et al., 2012; Tokita & Ishiguchi, 2010). Studies using brain imaging have identified a neurological basis for the ANS in the intraparietal sulcus (IPS) on the lateral surface of the parietal lobe (Castelli, Glaser, & Butterworth, 2006). Within the IPS, specialized neurons (numerons) sensitive to numerosity have been identified in macaque monkeys (Nieder, Freedman, & Miller, 2002). The IPS, however, is not only activated by non-numerical stimuli. In humans, it is also activated when they observe numbers in different modalities and when they perform simple arithmetic tasks (Piazza, Izard, Pinel, Le Bihan, & Dehaene, 2004). That the IPS is activated for a wide variety of numerical stimuli suggests a relationship between ANS acuity and achievement in formal mathematics. Such a relationship has been documented with children, even when controlling for a large number of cognitive abilities, (Halberda, Mazzocco, & Feigenson, 2008; Inglis, Attridge, Batchelor, & Gilmore, 2011) but results from studies on adults are mixed (Gebuis & van der Smagt, 2011; Inglis et al., 2011; Price, Palmer, Battista, & Ansari, 2012). At least part of the mixed results might be attributed to differences in methodology. Recently the reliability and validity of some of the most commonly used measures of ANS acuity have been challenged (Gebuis & Van der Smagt, 2011; Gilmore, Attridge, & Inglis, 2011; Lindskog, Winman, Juslin, & Poom, 2013; Price et al., 2012) and studies indicate that while some formats show reasonable reliability and validity others are neither reliable nor valid (Lindskog et al., 2013). The differences in reliability and validity between different tasks that measure ANS acuity highlight the question of whether task features influences performance. Put differently, will you be better at deciding which of the two flocks of sheep that is the more numerous when you see them coming out of the tunnel, one flock at a time, or when you see both flocks at the same time on the field? The question of what factors that influence the reliability of ANS acuity measures is important also because reliability sets an upper limit on correlations between ANS acuity and other cognitive abilities. The present study addresses this question by comparing four ANS acuity tasks, in a within-subjects design, that use different presentation and response formats.