perception of inertial forces [15,16]. So, clearly the perceived heaviness of an object depends on whether inertial or gravitational forces are perceived, even though the underlying object property, mass, is the same. In the present study we investigated whether the size-weight illusion depends on perceiving the pull of gravity, i.e. whether it is caused by a prior for weight or a by more general prior for the mass of an object. To this end we investigated whether the size– weight illusion occurs in the absence of weight through perception of inertial forces only. If the size–weight illusion occurs indepen- dent of gravitational forces, the illusion must be related to the mass of an object independent of the forces acting upon it. One reason for not expecting the illusion to occur in the absence of gravitational forces is that in daily life we rarely experience the heaviness of an object without perceiving gravitational forces. This means that the prior for larger objects being heavier may be limited to perception of gravitational forces, i.e. weight. Secondly, for perceiving inertial mass it is necessary to combine information about the acceleration of an object with efferent or afferent information about the applied amount of force. Gravitational forces (weight), in contrast, can be perceived purely tactual through the pressure of an object on the skin of the static hand. Therefore, fundamentally different sources of information are being used for perception of mass through inertial or gravitational forces. To investigate whether the size–weight illusion occurs in the absence of weight, a set of objects differing in size but with the same mass was constructed. To let participants perceive inertial forces only, we suspended the objects from a long pair of wires and asked the participant to give the objects a short push after which they rated the perceived heaviness. This way perception of gravitational forces acting on the object was minimised. We let participants perform this task with and without visual feedback of the trajectory of the object after pushing to test whether participants used visual information about how far the object travelled. Finally, we also asked participants to rate heaviness after lifting the objects and placing them back as a control task. This allowed us to test whether the magnitude of the illusion as obtained through perception of inertial forces differed from the illusion obtained in the traditional way. Materials and Methods Participants Twenty self-reported right-handed participants volunteered in the experiment (age range 22 to 40 years). All participants were naive as to the purpose of the experiment. Half of the participants performed the experiment pushing the objects with full vision. The other half also pushed the objects, but without visual feedback of the object’s trajectory. Eight of the subjects that performed the pushing with full visual feedback task also performed the control task of lifting with full vision. Ethics Statement The experiment was conducted as part of a program that was approved by the ethical committee of the Faculty of Human Movement Sciences of VU University. All participants signed a statement of informed consent prior to participation in the experiments. Stimuli The stimuli consisted of a set of four objects constructed out of MDF (medium density fibre). Three test objects differing in size (small, medium, large) were weighed down such that the mass of Size-Mass Illusion each object was 250 g (Fig. 1A). The fourth object (reference) had the same dimensions as the medium sized test object, but had a mass of 200 g. The ratings for the two medium sized objects were used to convert the heaviness ratings of the other objects into grams. A small infrared Light Emitting Diode was attached in the centre of each object’s surface facing away from the subject. The position of the object was recorded at 500 Hz using an Optotrak position tracking system (Northern Digital). These data were used to calculate the objects’ velocities. Task In the pushing task the objects were suspended just above table height from a pair of long wires in front of the participant. The participants were asked to give the object a short push such that it travelled over a distance of 50 cm (Fig. 1B) and rate how heavy the object felt using arbitrary numbers (i.e. method of absolute magnitude estimation [17]). These ratings were converted into z- scores by taking the difference between the individual ratings of a participant and his or her average rating, before dividing by the standard deviation of the ratings. For the task without visual feedback a screen was placed in front of the subject, such that the object was initially visual, but it disappeared behind the screen shortly after the push. The procedure in the control task was the same as in the pushing task, but now participants were instructed to lift the objects between their thumb and index finger. They lifted the objects grasping them in the centre along the 6 cm axis, such that grip aperture was the same for all objects (Fig. 1C). In all tasks the test objects were presented in 15 sets of three trials; in every set each object was presented once and the order of presentation within each set was randomised. After these 15 sets of three trials, another 10 trials were performed in which the reference object was presented 5 times randomly interleaved with 5 times one of the test objects. All trials were performed in one continuous run such that subjects were not aware of the introduction of the reference object. Analysis Repeated measures ANOVA was performed on the z-scores of the heaviness ratings with object size as a repeated factor and visual feedback as a between subjects factor. The effect of object size was also tested with a repeated measures ANOVA on the peak velocities of the objects. Finally, a repeated measures ANOVA with object size and task as repeated factors was performed to compare the lifting and pushing with visual feedback conditions. Results Pushing The heaviness ratings were converted into z-scores and are shown for the participants in the full vision tasks in Fig. 2A. Using the difference in the ratings for the two medium sized objects, the z-scores were converted into grams. The results show that the small 250 g object was consistently rated as being almost 100 g heavier than the large 250 g object. This was the case with full visual feedback and without vision of the object’s trajectory (Fig. 2B): a repeated measures ANOVA with object size as a within subjects factor and visual feedback as between subjects factor on the z-scores showed an effect of object size (F (2,36)~106,pƒ0:001) but no interaction between visual feedback and object size (p~0:1). Therefore, the size–weight illusion occurs without any haptic or visual information about PLoS ONE | www.plosone.org 2 August 2012 | Volume 7 | Issue 8 | e42518