The three-way ANOVA revealed significant main effects of landmark type (F(1, 28) = 56.94, p < .0001, ηp2 resulted from a shorter P in the later trials (1.48) than in the earlier trials (1.65).
Significant interactions were found between landmark type and trial blocks (F(1, 28) = 4.30, p < .05, ηp
2 = .13), and between landmark type and gender (F(1, 28)
= 5.04, p < .05, ηp
2 = .15). The landmark type by trial blocks interaction was due to the larger difference between trials (1.83 for the first half vs. 1.61 for the second half of trials; p < .01) for the local landmarks than for the global landmarks (1.46 for the first half vs. 1.35 for the second half of trials; p = .034).
The landmark type by gender interaction was due to the larger difference between global and local landmarks for males (1.39 vs. 1.80; p < .0001) than for females (1.42 vs. 1.64; p = .003). In addition, the difference between females
41
A trend of three-way interaction was present but did not reach significance (F(1, 28) = 3.46, p = .07, ηp
2 = .11). As can be seen in Figure 13a, the difference in P between the first and second half of trials was larger for local than for global landmarks for males, but this difference did not occur for females.
Consistent with this observation, we conducted two separate two-way ANOVAs with landmark type and trial blocks as the within-subject factors for each gender group and found a significant landmark type by trial blocks interaction in males (F(1, 14) = 9.07, p < .001, ηp
2 = .39) but not in females (F(1, 14) = 0.02, p = .89,
η
p2= .001). The significant two-way interaction in males was due to the larger difference between the first half (1.93) and the second half of trials (1.67; p
< .001) for the local landmarks than for the global landmarks (1.41 for the first half vs. 1.37 for the second half of trials; p = .11).
Because the starting position in each trial was randomly allocated, the average length of optimal paths may differ between conditions. If this is the case, it is likely that unequal lengths of corrected paths between groups or conditions were caused not only by experimental manipulations per se but also by the significant. None of the other main effects (trial blocks: F(1, 28) = 0.76, p > .39,
η
p2= .02; gender: F(1, 28) = 0.38, p > .54, ηp2
= .01) or interactions (trial blocks by gender: F(1, 28) = 0.44, p > .51, ηp was quite distinct from those observed for corrected paths. First of all, the main effect showed that optimal path length under the global landmark condition (178)
42
was longer than optimal path length under the local landmark condition (162).
Moreover, post hoc comparisons of the two-way interactions showed that although the optimal paths for females and males differed under the global landmark condition (175 for females vs. 181 for males, p < .05), the optimal paths for both genders did not differ significantly under the local landmark condition (164 for females vs. 160 for males, p = .26). This is exactly the opposite of the pattern observed in the results for corrected path length. In other words, although the optimal path length was shorter for the environment with local landmarks than with global landmarks, the participants actually traveled a longer distance in the former than in the latter. Thus, the results for the corrected path cannot be due to the unequal lengths of the optimal path.
4.1.2. Travel Duration (T)
The main effects of trial blocks (F(1, 28) = 94.45, p < .0001, ηp
2 = .77) and gender (F(1, 28) = 19.13, p < .001, ηp2
= .41) were significant. As can be seen in Figure 13b, earlier trials took longer (10.00 seconds) to complete than later trials (8.64 seconds), and females took longer (10.27 seconds) on average than males (8.27 seconds). There was also a significant interaction between landmark type and gender (F(1, 28) = 6.79, p < .05, ηp2
= .20). A post hoc analysis on the landmark type by gender interaction revealed that male participants spent similar amounts of time in both landmark environments (8.27 vs. 8.46 seconds for global and local landmarks, respectively; p > .05), whereas female participants spent less time finishing a trial under the local (9.78 seconds) than under the global condition (10.76 seconds; p < .05). In addition, males spent less time than females under both landmark conditions, and the difference between genders was larger in the global (2.52 seconds; p = .0001) than in the local (1.32 seconds;
p = .047) condition. None of the other main effects (landmark type: F(1, 28) =
3.13, p = .09, ηp2= .10) or interactions (trial blocks by gender: F(1, 28) = 0.87, p
= .36, ηp2 = .03; landmark type by trial blocks: F(1, 28) = 1.06, p = .31, ηp2 = .04;
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three-way interaction: F(1, 28) = 0.01, p = .93, ηp2
= .00) approached significance (see Figure 13b).
Figure 13. The corrected travel distance (a) and total travel duration (b) as a function of trial block, landmark types, and gender. Squares and asterisks indicate local and global landmarks, respectively. Error bars indicate standard error. The trial blocks were averaged separately for the first four trials (#1) and the second four trials (#2).
4.1.3. Ratio of duration for moving away from the target location to the total duration (TRaway)
The main effects of landmark type (F(1, 28) = 43.27, p < .001, ηp
2 = .61), trial blocks (F(1, 28) = 19.25, p < .001, ηp
2 = .41), and gender (F(1, 28) = 6.28, p
< .05, ηp
2 =.18) were significant. Figure 3a shows that in general, the proportion of time moving away from the target location was larger under the local (.057) than under the global (.033) landmark condition, larger in the earlier trials (.050) than in the later trials (.039), and larger for males (.052) than for females (.038).
Significant interactions were also found between landmark type and trial blocks (F(1, 28) = 8.50, p < .01, ηp2
= .23). Post hoc analysis revealed that the difference in TRaway between the first and the second half of the trials was larger for the local landmarks (0.07 vs. 0.05; p < .05) than for the global landmarks
44
(0.04 vs. 0.03; p = .22). The landmark type by gender interaction was marginally significant (F(1, 28) = 3.71, p = .06, ηp
2 = .12). A post hoc comparison revealed that the difference between females and males was not significant in the global landmark condition (0.03 vs. 0.04; p = .7), but this difference was significant in the local landmark condition (0.05 vs. 0.07; p = .014). In addition, the difference between global and local landmarks was larger in males (0.04 vs. 0.07; p < .001) than in females (0.03 vs. 0.05; p = .013). The trial blocks by gender interaction was not significant (F(1, 28) = 0.18, p = .67, ηp
2 = .01).
The three-way interaction was also significant (F(1, 28) = 6.83, p < .05, ηp2
= .20). As can be seen in Figure 14a, the difference in TRaway between the first and second half of the trials was larger for the local than for the global landmarks for males, whereas there was no difference for females. In accordance with this observation, separate follow-up tests for each gender revealed a significant interaction between landmark types and trial blocks (F(1, 14) = 15.19, p < .01, ηp
2 = .52) for males but not for females (F(1, 14) = .05, p = .83, ηp 2
= .00).
4.1.4. Ratio of duration without translation to the total duration (TRno-translation) The main effects of landmark (F(1, 28) = 48.48, p < .0001, ηp2 proportion of time spent at the same location was longer under the global (0.66) than under the local (0.58) landmark condition, longer in the first half of trials (0.63) than in the second half of trials (0.61), and longer for females (0.67) than for males (0.57).
Significant interactions were also found between landmark types and trial blocks (F(1, 28) = 7.03, p < .05, ηp
2 = .20). Post hoc analysis revealed that the difference in TRno-translation between the first and the second half of trials was larger for the global landmarks (0.67 vs. 0.64; p = .12) than for the local
45
landmarks (0.58 vs. 0.58; p = .87). The three-way interaction (F(1, 28) = 3.44, p
= .07, ηp
2 = .11) and trial blocks by gender interaction (F(1, 28) = 3.92, p = .06,
η
p2 = .12) were marginally significant. As can be seen from Figure 14b, the difference in TRno-translation between the first and second half of trials was larger for global than for local landmarks for males, whereas no difference was apparent for females. Consistent with this observation, separate follow-up tests for each gender revealed a significant interaction between landmark types and trial blocks (F(1, 14) = 7.46, p < .05, ηp2 = .35) for males but not for females (F(1, 14) = .50, p = .49, ηp2
= .03). The landmark type by gender interaction did not approach significance (F(1, 28) = 0.21, p = .65, ηp2
= .01).
Figure 14. TRaway(a) and TRno-translation(b) as a function of trial block, landmark types, and gender. Squares and asterisks indicate local and global landmarks, respectively. Error bars indicate standard error. The trial blocks were averaged separately for the first four trials (#1) and the second four trials (#2).
4.1.5. Rotation angle with translation (ROTtranslation)
The main effects of landmark type (F(1, 28) = 12.54, p < .01, ηp
2 = 0.31) and gender (F(1, 28) = 32.03, p < .0001, ηp2
= 0.53) were significant. The angle of rotation during translation was larger under the local (72°) than under the global (56°) landmark condition and larger for males (95°) than for females (33°)
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4.1.6. Rotation angle without translation (ROTno-translation)
The main effects of landmark type (F(1, 28) = 22.32, p < .0001, ηp
2 = .44), trial order (F(1, 28) = 70.68, p < .0001, ηp
2 = .72) and gender (F(1, 28) = 23.57,
p < .0001, η
p2= .46) were significant. The angle at which participants rotated at the same location was larger under the global (259°) than under the local (219°) landmark condition, larger in the first half of trials (261°) than in the second half of trials (217°), and larger for females (271°) than for males (207°) (Figure 15b).
The landmark type by gender interaction was marginally significant (landmark type by gender: F(1, 28) = 3.29, p = .08, ηp2
= .11). Post hoc comparisons revealed that the difference between females and males was larger in the global landmark condition (299° vs. 210°, p < .001) than in the local
None of the other interactions approached significance (trial blocks by gender:
F(1, 28) = 0.25, p = .62, η
p2 = .01; three-way interaction: F(1, 28) = 0.57, p = .46,
η
p2 = .02).
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Figure 15. ROTtranslation(a) and ROTno-translation(b) as a function of trial block, landmark types, and gender. Squares and asterisks indicate local and global landmarks, respectively. Error bars indicate standard error. The trial blocks were averaged separately for the first four trials (#1) and the second four trials (#2).