RESEARCH ARTICLE Spatial biases in number line bisection tasks are due to a cognitive illusion of length Elisabeth Sto ¨ttinger • Britt Anderson • James Danckert • Barbara Fru ¨ hholz • Guilherme Wood Received: 23 January 2012 / Accepted: 5 May 2012 Ó Springer-Verlag 2012 Abstract Placing arrow heads (Judd Illusion) or numbers of different magnitude at the end of a line biases perception of the centre of the line. For the Judd Illusion, it is known that this bias depends on the method used: a deliberate (more perceptually based) marking of the centre with a pen is more subject to the illusion than are fast (more action-based) ballistic pointing movements made towards the centre. It has been suggested that the number bias also reflects a cognitive illusion of length. To test this assumption, we used two dif- ferent response methods in line bisection tasks while lines were flanked by arrow heads or numbers of different mag- nitudes. For both conditions, we found that the more action- based response method showed less bias. Since the pattern of biases induced by flanking numbers and arrow heads are similar, we confirm that the spatial bias produced by numerical magnitude reflects a cognitive illusion of length. Keywords Judd illusion Á Numerical magnitude Á Line bisection Á Shift of spatial attention Á Cognitive illusion of length Introduction Biases in line bisection performance have long been used as a method to understand spatial cognition. A variety of peripheral cues can influence perception of the midpoint of a line including arrow heads (Judd illusion, henceforth JI), physical (Baldwin illusion) and numerical magnitude and numbers (for an overview, see de Hevia 2011). For example, when required to give a perceptual judgment concerning the exact midpoint of the JI (Fig. 1a), partici- pants place their bisection marks considerably more towards the tail (see Bruno et al. 2008 for an overview). This JI seems to be largely pre-attentive, is insensitive to deficits in attentional orienting (Ro and Rafal 1996) and is intact in patients with visuo-spatial hemineglect (Olk et al. 2001). A similar illusory bias is found in the context of num- bers. When participants have to bisect lines by marking the middle with a pen and the lines are flanked by numbers, bisections are systematically biased towards the larger number (Fischer 2001a, b). Moreover, when participants have to bisect strings of Arabic digits (Fischer 2001b), they demonstrate a bias to the left while bisecting strings of small numbers (e.g. 111111111111111111, with the bolded number indicative of typical bisection judgements), but to the right while bisecting strings of larger numbers (i.e. 999999999999999999). Calabria and Rossetti (2005) also reported a similar pattern to that described by Fischer (2001b), although the overall effect was stronger with written number words (e.g. deux: two) than with Arabic digits (e.g. 2). Finally, Bonato et al. (2008) have shown that patients with left neglect bisect more to the right in bisecting lines flanked by large numbers (e.g. 9), but more to the left in bisecting lines flanked by small numbers (i.e. 1). E. Sto ¨ttinger (&) Á B. Anderson Á J. Danckert Department of Psychology, University of Waterloo, 200 University Avenue West, Waterloo, ON N2L 3G1, Canada e-mail: estoettinger@uwaterloo.ca B. Fru ¨hholz Department of Psychology, Paris-Lodron University of Salzburg, Salzburg, Austria G. Wood Institute of Psychology, Karl-Franzens-University of Graz, Graz, Austria 123 Exp Brain Res DOI 10.1007/s00221-012-3125-5