Results and discussion
We calculated the average response error for the duration reproduction
trials and there was a minor positive general bias (M ±SE : 97 ± 25 ms, t (23) = 3.911, p =
.001, d = 0.798). Then, we computed the average response errors
for two conditions: task-relevant (TT) and task-irrelevant (DT). The
mean errors were 113 ± 24 ms for TT and 78 ± 27 ms for DT conditions. We
observed a significant difference between TT and DT conditions
(t (23) = 3.393, p = .003, d =
0.278), indicating that reproduction errors were larger in the TT
condition compared to the DT condition.
Central tendency effect. Both the TT and DT conditions exhibited
significant central tendency biases, with participants consistently
overestimating short durations and underestimating long durations. The
mean central tendency index (\(-a\)) was 0.318 ± 0.048
(t (23) = 6.654, p <.001,d = 1.358) for the TT condition and was 0.354 ± 0.048
(t (23) = 7.329, p <.001,d = 1.496) for the DT condition. The central tendency biases were
comparable between the two conditions (t (23) =
1.503, p = .147, d = 0.154), as depicted in Figure 2c.
This suggests that the central tendency effect was not influenced by the
task relevance. The lack of a significant difference in the central
tendency effect between task relevance can be attributed to the same
distribution and range of the tested durations across both tasks,
resulting in a stable long-term representation of prior durations across
conditions. This finding aligns with previous research indicating that
random mixing of durations leads to a generalization of prior knowledge
across different conditions \cite{Roach2017}.
Serial dependence effect. Figure 2d demonstrates that
reproduction errors increased as the prior duration increased,
indicating a significant attractive sequential effect. We quantified
this effect using the mean slope \(\left(b\right)\) from linear regressions on
the previous duration (\(T_{n-1}\)), resulting in slopes of 7.7% and
3.1% for the TT and DT conditions, as shown in Figure 2e. Both slopes
were significantly different from zero (TT condition:t (23) = 4.370, p < .001,d = 0.892; DT condition: t (23) = 2.921,p = .008, d = 0.596), confirming the presence of a
sequential effect in both task-relevant (TT) and task-irrelevant (DT)
conditions. To investigate whether the task relevance influenced the
sequential effect on current duration reproductions, we compared the
slopes of the TT condition to the DT condition. It revealed the slope
was significantly larger in the TT condition, where the prior task was
also duration reproduction (t(23) = 2.368,p =.027, d = 0.652). To rule out statistical artifacts
(Cicchini et al., 2014), we
also tested the linear regression of reproduction errors on the
durations presented in future trials (n+1), which showed no significance
(ps > .479).
In Experiment 2, we observed the assimilation effect in time
reproduction, where current duration estimates were biased toward the
preceding interval. Additionally, a larger attractive sequential effect
was observed when the prior task also involved timing reproduction.
These findings provide clear evidence that, at least in the case of the
time reproduction task, post-perceptual processes enhanced the
sequential effect in time perception.