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.