Results 61 

3.4.2.1 Side Error

Overall, only few side errors (less than 0.95% for all subjects) were observed. A mixed-design ANOVA on percentage of side errors revealed no significant effect for Preferred Strategy [F(1, 17) = 0.003, p = .957], Number of Turns [F(1,

Chapter 3 – Behavioral Analyses 17) = 1.021, p = .325], or Eccentricity of End Position [F(2.08, 51) = 0.982, p = .387].

3.4.2.2 Other Incorrect Solutions

In contrast to the previous experiment, no arrowback responses were regis- tered in Experiment 2. Further, for the whole study set, 2 reaction slips were detected (approx. 0.06%).

3.4.2.3 Angular Fit

Correlations of observed angular response with strategy-specific expected an- gular response revealed significant interrelationships for both Nonturners, r(144) = .956, p < .0001, and Turners, r(220) = .923, p < .0001. However, stan- dardized correlation coefficients of Turners and Nonturners differed signifi- cantly (p < .01). When angular fit was computed separately for tunnels with one turn and two turns Nonturners revealed significant lower correlations be- tween adjusted and expected angular response for more complex tunnels as compared to tunnels with only one turn (one turn: r(72) = .976; two turns: r(72) =.937; ps < .0001; difference between tunnels with one and two turns: p < .004). Although Turners displayed a comparable declining pattern (one turn: r(80) = .950; two turns: r(140) = .924; ps < .0001), no statistically significant difference was found between tunnels with one and two turns (p = .129) for this strategy group. The significant difference in angular fit between Turners and Nonturners was caused by angular responses for tunnels with one turn (p < .02)9.

3.4.2.4 Response Time

Analysis of response times revealed a significant main effect of Number of Turns [F(1, 17) = 10.125, p < .005, ηG2 = .016] and a significant interaction of the factors Preferred Strategy ¯ Number of Turns [F(1, 17) = 8.432, p < .01, ηG2 = .013]. Multiple comparisons revealed response time of Turners to be sig- nificantly increased when confronted with two turns (p < .008), whereas Non- turners’ response time was unaffected by the number of turns. Despite the sig- nificant interaction of strategy and path complexity, the difference between Turners and Nonturners’ response times at both complexity levels was found to be comparable (see Figure 3.8).

9 _{In case of consecutive turns bending into the same direction, cognitive headings of Turners and}

Nonturners were misaligned, so that for paths of higher complexity allocentric and egocentric ec- centricities did not correspond. The computation of angular fit took this into consideration, result- ing in a higher amount of categorical egocentric end positions for Turners (N = 10 participants × 14 categorical egocentric eccentricities = 140) as compared to Nonturners (N = 9 participants × 8 ca- tegorical allocentric eccentricities = 72).

Figure 3.8: Experiment 2 – Mean RT (± 1 SD, depicted by the error bars) of the adjusted hom- ing vector for tunnels with one turn and two turns, separately for Nonturners (solid line) and Turners (dashed line).

3.4.2.5 Absolute Error

The analysis of absolute error revealed a significant main effect of Eccentricity of End Position [F(1.75, 51) = 34.486, p < .0001, ηG2 = .246], as well as a signif- icant interaction Preferred Strategy ¯ Eccentricity of End Position [F(1.75, 51) = 4.907, p < .02, ηG2 = .046]. These effects were qualified by the interaction Preferred Strategy ¯ Number of Turns ¯ Eccentricity of End Position [F(1.70, 51) = 4.506, p < .023, ηG2 = .060] (see Figure 3.9). For tunnels with one turn, subsequent post-hoc tests revealed only for Nonturners significant differences in absolute error scores between end positions of 15° and 30°, as well as be- tween 15° and 45° eccentricity (ps < .001). This strategy group also displayed differing absolute error scores for paths of higher complexity, between 30° and 45° eccentricity (p < .001). However, Nonturners’ absolute error scores did not differ between complexity levels. By contrast, absolute error scores of Turners were shown to be comparable both within as well as between complexity le- vels. Also, differences between absolute error scores of Turners and Nonturn- ers were too weak to obtain statistical significance.

Chapter 3 – Behavioral Analyses

Figure 3.9: Experiment 2 – Mean absolute error (± 1 SD, depicted by the error bars) of the adjusted homing vector for tunnels with one turn and two turns, dependent on the eccentricity of end position relative to the origin of the path (data from left and right turn values of equal eccentricities were pooled), separately for Nonturners (solid line) and Turners (dashed line).

3.4.2.6 Relative Error

The analysis of relative errors revealed a significant main effect of Strategy [F(1, 17) = 13.086, p < .002, ηG2 = .224], and Eccentricity of End Position [F(1.29, 51) = 27.629, p < .0001, ηG2 = .175]. Further, statistical significance was obtained for the interaction of Preferred Strategy ¯ Number of Turns [F(1, 17) = 5.290, p < .034, ηG2 = .056], as well as Preferred Strategy ¯ Eccentricity of End Position [F(1.29, 51) = 7.532, p < .008, ηG2 = .058]. These effects were qualified by the interaction of Preferred Strategy ¯ Number of Turns ¯ Eccen- tricity of End Position [F(2.14, 51) = 13.767, p < .0001, ηG2 = .064] (see Figure 3.10).

Figure 3.10: Experiment 2 – Mean signed error (± 1 SD, depicted by the error bars) of the ad- justed homing vector for tunnels with one turn and two turns, dependent on the eccentricity of end position relative to the origin of the path (turns of equal eccentricity to the left and right were pooled), separately for Nonturners (solid line) and Turners (dashed line).

Post-hoc tests found no significant differences between strategy groups tra- versing tunnels with one turn. Turners as well as Nonturners tended to unde- restimate the eccentricity of end position with increasing eccentricity. Non- turners’ signed error rates for tunnels with one turn were found to differ signif- icantly between eccentricities of 15° vs. 30°, as well as marginally between 15° vs. 60° eccentricity (ps < .0001). For Turners traversing tunnels with one turn, the difference between end positions of 45° vs. 60° eccentricity obtained statis- tical significance (ps < .001). When confronted with two turns, only Nonturners showed a more pronounced underestimation of end position at more lateral eccentricities, with signed error at the end position of 60° eccentricity differing significantly from the other end positions (ps < .0006). Further, signed error at 45° differed significantly from error rates at 15° and 30° eccentricity (ps < .0002). By contrast, Turners’ relative error scores for tunnels with two turns were found to be comparable at all eccentricities. At the outmost eccentricities of 45° and 60°, Turners and Nonturners differed significantly in signed error scores (ps < .0009).