Size-Mass Illusion Figure 1. Description of the stimuli and set-up. (A) Dimensions of the four objects constructed out of medium density fibre (MDF). The three test objects (small, medium, large) had a mass of 250 g, the reference object had a mass of 200 g. Each object had two hooks attached to the top surface such that they could be suspended from a double wire attached to the ceiling. (B) A schematic representation of the set up. Subjects were seated in front of a table above which the objects could be suspended one at a time. The distance from the object to the ceiling (the effective length of the pendulum) was 2.3 m. The subjects were asked to push the object such that it travelled over an indicated distance of 50 cm (black arrow). Either an obstacle (withe bar; group with visual feedback) or a screen (white outline; group without visual feedback) ensured that the participant could not keep contact with the object for a distance larger than 10 cm. The experimenter caught and replaced the object after each push. (C) In the lifting task an object was placed on the table in front of the participant and he or she was asked to lift the object to a marked height (20 cm) and place it back on the table. The objects were always grasped on the horizontal 6 cm axes, such that grip aperture was the same for all object sizes. doi:10.1371/journal.pone.0042518.g001 gravitational forces acting on the object. Furthermore, visual feedback of the trajectory did not affect the illusion size. In Fig. 3A it can be seen that the peak velocity the object reached correlated with its size: the small object reached a lower peak velocity than the large object. This indicates that participants expected the small object to be lighter than the large one and therefore used less pushing force than for the large one resulting in a smaller peak velocity. Repeated measures ANOVA with object size as a within subjects factor on the peak velocities in the full visual feedback task showed an effect of object size (F (3,27)~11:9,pƒ0:001). Participants that had no visual feed- back of the trajectory of the object gradually reduced their force so that the peak velocity decreased over trials (Fig. 3B). Still, however, the peak velocity was larger for the small object than for the large object without visual feedback (F (1:3,11:8)~8:4,p~0:01, Green- house-Geisser corrected values). Although participants reduced their pushing force, the heaviness percept was stable over all trials. So different amounts of force were used for the different object sizes based on prior expectations, but the amount of force used itself was not a direct factor determining the percept. Lifting After pushing, the small object was rated almost twice as heavy as the large object, which is a very large effect given that the volume was halved. The illusion found in our pushing task is larger than typically reported [2,12]. We investigated whether this large magnitude of the illusion is due to our specific choice of objects or that gravity might reduce the magnitude of the size–mass illusion. To compare the magnitude of the illusion without gravity to the traditional size–weight illusion for our stimuli, we asked eight of the participants that performed the pushing with visual feedback to repeat the experiment but this time the task was to lift the objects (Fig. 1C). The judged heaviness is shown averaged over participants in Fig. 2C. It can be seen that the heaviness ratings are comparable between pushing and lifting. A 263 (task6object size) repeated measures ANOVA on the z-scores of the lifting and PLoS ONE | www.plosone.org 3 August 2012 | Volume 7 | Issue 8 | e42518