Finally, we assessed direction-related biases in perception. A 5 × 2 ANOVA on PSE values showed a nonsignificant effect of reference direction,
F(1, 29) = 2.48,
p = 0.13,
Display Formula\(\eta \rm{_p^2}\) = 0.08, and a significant effect of direction difference,
F(4, 116) = 3.74,
p = 0.007,
Display Formula\(\eta \rm{_p^2}\) = 0.11. However, we were most interested in the interaction between reference direction and direction difference, which was significant,
F(2.32, 67.38) = 8.85,
p < 0.001,
Display Formula\(\eta \rm{_p^2}\) = 0.23. Given that we expected biases to vary depending on the reference direction, we conducted separate ANOVAs with each reference direction to investigate these biases further. As in
Experiment 3, we found that the effect of direction difference was not significant for the upwards reference direction,
F(2.79, 81.00) = 2.27,
p = 0.09,
Display Formula\(\eta \rm{_p^2}\) = 0.07, but was significant for the oblique reference direction,
F(2.96, 85.87) = 13.40,
p < 0.001,
Display Formula\(\eta \rm{_p^2}\) = 0.32. Planned contrasts showed that there were significantly lower PSE values in the +0° direction difference condition (
M = 6.08,
SE = 0.05) than the +90°, −90°, and +180° direction difference conditions; +90:
M = 5.59,
SE = 0.09,
F(1, 29) = 25.70,
p < 0.001,
Display Formula\(\eta \rm{_p^2}\) = 0.47; −90:
M = 5.62,
SE = 0.09,
F(1, 29) = 22.73,
p < 0.001,
Display Formula\(\eta \rm{_p^2}\) = 0.44; +180°:
M = 5.69,
SE = 0.09,
F(1, 29) = 12.55,
p = 0.001,
Display Formula\(\eta \rm{_p^2}\) = 0.30, with an oblique reference direction. Meanwhile, the +45° direction difference condition (
M = 6.37,
SE = 0.15) did not differ significantly from the +0° direction difference condition,
F(1, 29) = 3.78,
p = 0.06,
Display Formula\(\eta \rm{_p^2}\) = 0.12. Corroborating this pattern of results, one-sample
t tests showed that the +90°, −90°, and +180° direction difference conditions for the oblique reference direction all led to significantly lower PSE values than 6°/s; +90°:
t(29) = 4.76,
p < 0.001; −90°:
t(29) = 4.46,
p < 0.001; +180°:
t(29) = 3.42,
p = 0.002, indicating that the oblique comparison stimuli were perceived to be moving faster than the oblique reference stimulus. Conversely, and in line with
Experiment 3, the +45° direction difference condition with an oblique reference had a PSE value significantly
above 6°/s,
t(29) = 2.55,
p = 0.02, reflecting that the horizontal comparison stimulus was perceived to be moving more slowly than the oblique reference stimulus. Meanwhile, the PSE value in the +45° direction difference condition with an upwards reference did not differ significantly from 6°/s,
t(29) = 1.23,
p = 0.23, suggesting that the oblique stimuli were not perceived as moving faster than vertical stimuli. This result is in line with
Experiment 2, but not in
Experiment 1, where we reported a bias for perceiving oblique stimuli as moving faster than vertical stimuli.