We further conducted an omnibus analysis to compare the sequential effects across the timing discrimination (Experiment 1) and the time reproduction (Experiment 2) tasks. An ANOVA on the sequential effect index, considering factors of Experiment and Task Relevance, revealed a significant main effect of Task Relevance (F (1,46) = 4.206, p = .046,\(\eta_{p}^{2}\) = 0.084), indicating a more pronounced sequential dependence in trials with consecutive timing tasks. However, neither the main effect of Experiment (F (1,46) = 0.010, p = .922,\(\eta_{p}^{2}\) = 0.000) nor the interaction effect (F (1,46) = 2.505, p = .120,\(\eta_{p}^{2}\) = 0.052) was significant (Figure 4E). Further paired t-tests for the difference of sequential effect between task relevance (Time vs. Direction) failed to reveal any significant difference in Experiment 1 (t(23) = 0.371, p =.714,d = 0.110), but a significant difference in Experiment 2 (t(23) = 2.341, p =.028,d = 0.723). For the decisional carry-over effect, a separate t-test on the sequential effect index did not show a significant difference between Experiments 1 and 2 (t(23) = 0.911, p =.367,d = 0.263).
Overall, both time discrimination and reproduction tasks demonstrated consistent assimilation toward prior durations, indicating a robust sequential effect in time perception. The comparative analysis revealed that task relevance enhanced sequential biases in the time reproduction task, but not in the time discrimination task. This suggests that the measurement type modulates the mechanism of sequential effect. The difference might stem from the interaction of the timing task with memory retrieval of the encoded duration, with the time reproduction task requiring continuous attention and memory comparison during reproduction.

General Discussion

The present study explored the impact of task relevance on sequential effects in time perception, using discrimination and reproduction tasks, extending upon previous research that predominantly explored sequential dependence in non-temporal domains \citep[see][]{Fischer2014}. Across both timing tasks, we observed a consistent assimilation effect: participants perceived current durations as longer following long previous stimuli and shorter following short ones. Interestingly, while the assimilation effect in the discrimination task was unaffected by task relevance, it was more pronounced in the time reproduction task following the same time task, highlighting the importance of task relevance in sequential dependence during time reproduction. Furthermore, we observed significant decisional carry-over effects in both tasks, where participants were more likely to repeat their responses, with no significant difference between the two types of tasks, consistent with previous studies on duration judgments \cite{Brown2005,Wehrman2018,Wehrman2020,Wiener2014}. This tendency for participants to repeat their prior choice, especially under response uncertainty, aligns with the notion of motoric repetition, where participants tend to repeat their previous motor response when uncertain about the test stimulus \cite{Akaishi2014}.
Recent past time intervals, being more accessible in memory, can influence the perception of current intervals. The brain forms time perception by integrating noisy sensory inputs with recent past stimuli (sequential effect) and the general knowledge of the stimuli (central tendency effect) to enhance processing efficiency, leading to an assimilation effect of prior stimuli in time perception. \citet{Fischer2014} suggested that the assimilation effect could be due to a "continuity field", where the brain smooths out noises by averaging the past information and the current input to promote sensory stability and continuity. 
In the current study, the notable sequential effect was evident in both duration discrimination and reproduction tasks, indicating its general applicability across various tasks. However, comparing sequential effects between discrimination and reproduction tasks, we found distinct patterns in how task relevance affects sequential effects. This difference between the two tasks is unlikely attributable to task-specific estimations. As we converted reproductions from Experiment 2 to binary "Short" vs. "Long" categories, similar to the task used in Experiment 1, the difference remained evident (see Figure 4E). 
One explanation could be the difference in memory processes between the reproduction and discrimination tasks. In the reproduction task, participants actively maintain the encoded duration in working memory through the reproduction phase, as it is used as a reference for stopping the reproduction. This active maintenance in timing trials differs from direction trials (recognizing direction may not be needed for the entire presentation), leading to unequal carryover effects between reproduction-reproduction and direction-reproduction trials. The active memory trace of the target duration during reproduction may thus bias the encoding of the subsequent trial, similar to findings in spatial memory tasks where the increased memory retention interval between the stimulus and response enhances sequential dependence \cite{Bliss2017}. In contrast, the binary discrimination task only requires participants to monitor the target duration until it matches a reference duration (1 second).  If the target duration finishes before the reference, a response is made; if it surpasses the reference, a response is made without waiting for the entire duration. This means fully encoding the target duration is unnecessary for the discrimination task, leading to a smaller sequential effect and making the preceding task-irrelevant. This observation aligns with previous research suggesting that in discrimination tasks, the information retained is related to a pre-established criterion value \cite{Lages_1998}. In this context, participants create internal or external criteria and compare incoming sensory input with this response criterion, likely showing less dependence on the working memory and post-perceptual processes \cite{Bausenhart2014,Dyjas2012,Lages_1998}.  
Our findings highlight that the nature of the task plays a crucial role in shaping sequential dependence in time perception. Time perception is distinct from visual perception, not being tied to a specific sensory process and more susceptible to contextual distortions from mental states, emotions, or selective attention \cite{Shi2013,Wittmann2009}. However, the varied impact of different tasks on working memory usage, as observed in our study, could be a universal phenomenon. Therefore, the distinct sequential effects by task relevance we noted in time perception might also be relevant to other perceptual domains, presenting an intriguing avenue for future research. 
In conclusion, our research revealed assimilation effects in time perception and highlighted the distinctive role of task relevance on sequential effects in both time discrimination and reproduction tasks. While the assimilation effect in the time discrimination task was unaffected by task relevance, it was notably stronger in the time reproduction task following the same duration task. These results indicate that the sequential bias in time perception are likely modulated by working memory processes that link sensory representation and decisional templates, resulting in a more pronounced sequential bias when the prior tasks involve relevant time reproduction tasks. Our findings thus imply that a reassessment of the existing evidence for sequential dependence,  considering its potential association with the specific nature of the task, may be beneficial.