534 (height: 14.7 visual angle, width: 9.0 visual angle). The hand was always shown with palms pointing downwards. This photograph had been edited with the software Photoshop CS3 Extended (version 10.0.1, 2007) in order to create identical pictures of a right and a left hand. The initial hand picture of the rotation task was pre- sented either from the ﬁrst-person perspective of partici- pant A (rotation level 0 ) (implying that participant B saw the hand from a third-person perspective/rotation level 180 ) or from the ﬁrst-person perspective of participant B (implying that A saw the hand from a third-person per- spective). The second stimulus showed a picture of a hand that was rotated relative to the ﬁrst hand by 0 , 30 , 60 , 90 , 120 , 150 , 180 , 210 , 240 , 270 , 300 , 330 or 360 . Participants were asked to respond as fast and as accu- rately as possible to the appearance of the second-hand picture by pressing one of two keys with their index and middle ﬁngers of the right hand. Responses were collected using two keyboards with two horizontally arranged active keys each (‘W’ and ‘R’ for participant A, and ‘3’ and ‘5’ for participant B). In order to prevent subjects from using the sight of their own hands as cues for the rotation task, carton boxes were placed above participants’ hands. These boxes also prevented participants from observing each other’s responses. Ten experimental blocks followed two practice blocks. Each block consisted of 42 trials and was followed by a short rest. Trials were randomized within blocks. The assignment of stimuli (same versus different hand) to responses (index versus middle ﬁnger) was counterbal- anced across subjects. After the session, participants were debriefed. During debrieﬁng, participants were asked whether they thought the other’s attention inﬂuenced the way they solved the task or their performance. They were then asked to attempt to guess in which way they thought that the other’s attention had affected their behaviour. Design A 2 (attention condition) 9 7 (rotation) factorial within- subject design was employed. Participants performed one- third of the trials alone (single-attention trials), and one-third simultaneously with the other participant (joint-attention trials). On the remaining third of the trials, their eyes were closed (single-attention trials of the respective other participant). Thus, 50% of the responses came from single- attention trials and 50% from joint-attention trials. Rotations to the left and to the right side were considered equivalent. As a consequence, there were 7 different levels of rotation: no rotation (0 and 360 ), level 1 (30 and 330 ), level 2 (60 and 300 ), level 3 (90 and 270 ), level 4 (120 and 240 ), level 5 (150 and 210 ) and level 6 (180 ). 123 Exp Brain Res (2011) 211:531–545 Data analysis In order to assess the effect of joint attention on the mental rotation pattern, we compared intercepts and slopes of the rotation curves of the single and joint-attention condition (for analysis of slopes in mental rotation tasks, see Shepard and Metzler 1971; Cooper 1975; Amorim et al. 2006). To this end, two linear regression equations were calculated for each participant (see Lorch and Myers 1990, method 3; for a review, see Fias et al. 1996); one for the single condition and one for the joint-attention condition. Angle of rotation served as predictor variable, RTs and errors as dependent variables. Intercepts (indicating response times for non-rotated stimuli) and slopes (reﬂecting the time taken for rotation processes; see Just and Carpenter 1985) for the single and the joint-attention condition were com- pared with t tests. By means of this method, the rotation effect can be judged as a main effect and can be quantiﬁed in size (slope). We focused on trials in which the initial hand picture was seen from a ﬁrst-person perspective (1st PP trials). It can be assumed that in these trials, an egocentric reference frame is taken by default (Klatzky 1998; Tversky and Hard 2009). Thus, these trials allow to test whether joint atten- tion leads to a change from an egocentric to an allocentric reference frame. In contrast, it is unlikely that participants would adopt an egocentric reference frame when seeing the ﬁrst-hand picture rotated by 180 (3rd PP trials; see Saxe et al. 2006; Vogeley and Fink 2003). Therefore, these trials are unsuitable for testing whether joint attention leads to changes from an egocentric to an allocentric reference frame. Note that showing the initial hand picture from a third-person perspective in 50% of the trials was necessary to collect data from both participants who sat opposite each other. Therefore, the main analyses only included trials for each participant in which the initial hand picture was seen from a ﬁrst-person perspective. In an additional analysis of 1st PP trials, data points of the 180 rotation condition were excluded in order to assess whether the pattern of results holds without these data points. If participants in the 180 condition of the rotation tasks applied ﬂipping strategies (ﬂipping the picture along its horizontal axis), one should see a ‘dip’ in the performance rotation curve when stimuli are rotated by 180 (Cooper and Shepard 1973). Third-person perspective trials (3rd PP trials) were analysed separately. Assuming that participants adopt an allocentric reference frame in 3rd PP trials, no ﬁrm pre- dictions can be made regarding differences between the individual condition and the joint-attention condition. The reason is that using an allocentric reference frame should allow a participant to ﬂexibly map different stimuli along their own body axis or along the other’s body axis.