To compare the sequential effects between the timing discrimination (Experiment 1) and the time reproduction (Experiment 2) tasks, we conducted an omnibus analysis across both experiments. For the sequential effect of the prior stimulus, we performed an ANOVA on the sequential index, considering factors of Experiment and Task Relevance. We found a significant main effect of Task Relevance (F (1,46) = 4.098, p = .049,\(\eta_{p}^{2}\) = 0.082), indicating a larger serial dependence effect in the TT condition. However, neither the main effect of Experiment (F (1,46) = 0.000, p = .984,\(\eta_{p}^{2}\) = 0.000) nor the interaction effect (F (1,46) = 2.660, p = .110,\(\eta_{p}^{2}\) = 0.055) was significant (see Figure 3d). For the decisional carry-over effect, we conducted a separate two-tailed paired sample t-test on the sequential index to compare the effects between Experiment 1 and Experiment 2. The results indicated no significant difference between the two experiments in terms of the decisional carry-over effect (t(23) = 1.080, p =.286,d = 0.312).
In summary, we consistently observed assimilation towards prior stimuli for both time discrimination and reproduction tasks, indicating a robust sequential effect in time perception. Furthermore, our comparison across experiments revealed the prior relevant task enhanced sequential biases, suggesting that the attractive sequential bias in time perception is influenced by post-perceptual processing. Although the interaction effect did not reach significance, the results in Experiment 1 and Experiment 2 exhibited distinct patterns. In contrast to the comparable sequential effects observed in TT and DT conditions in Experiment 1, the sequential effects in Experiment 2 were primarily evident in the TT condition. The discrepancy may arise from the fact that the timing task may interact with the encoding phase, while more attention and cognitive resources are being engaged in the encoding phase when a time reproduction task is required later.

General Discussion

In this study, we investigated the impact of task relevance on sequential effects in time perception, using discrimination and reproduction measurements. Our main question was whether both measurements would yield similar sequential effects in terms of magnitude and patterns. The results from both time discrimination and reproduction tasks consistently showed an attractive sequential effect—when the previous stimuli had a long duration, participants tended to perceive the current duration as longer, and vice versa. Interestingly, the assimilation effect in the time discrimination task remained consistent regardless of task relevance, while in the time reproduction task, the sequential effect was notably stronger following duration reproduction trials, emphasizing the role of task-relevant response in sequential dependence. Furthermore, we observed significant decisional carry-over effects in both tasks, with participants more likely to repeat their reports as “Longer” after previously reporting “Long” and vice versa. There was no significant difference between the two tasks regarding the decisional carry-over effect.
Our study seeks to extend upon previous research, which has predominantly explored sequential dependence in non-temporal domains \citep[see][]{Fischer2014}. First, we observed the assimilation effect of prior stimuli in both duration discrimination and reproduction tasks, an aspect that was scarcely investigated in time perception \cite{Fornaciai2023,Glasauer2022,Togoli2021,Wehrman2020}. The assimilation effect in time estimates could be explained in terms of the “continuity field” \cite{Fischer2014}, where brief changes in the stable external environment are integrated with past information to promote sensory stability and continuity. For time perception, there are no dedicated sensors and it may be easily influenced by attention, memory, and temporal context \cite{Wittmann2009}. Recent time intervals are more accessible in memory and could bias our perception of the current interval. The brain infers stimulus value from noisy sensory input and generates an internal representation of time based on the recent past (sequential effect) or average stimulus distribution (central tendency effect) to optimize processing efficiency. Moreover, the assimilation effect in time reproduction may also be linked to memory processes. Our study found a small assimilation effect in the time reproduction task following direction-report trials, possibly due to working memory demands during the encoding phase, where participants had to maintain both duration and direction features. Previous research showed that increasing the retention interval of stimulus \cite{Bliss2017} or involving memory tasks  (Markov et al., 2023) in the current trials enhances sequential dependence, suggesting the working memory load may modulate the strength of the sequential effect. 
We observed significant decisional carry-over effects in line with previous studies on duration judgment \cite{Brown2005,Wehrman2018,Wehrman2020,Wiener2014}. For example, \citet{Wiener2014} found that participants tended to repeat their prior choice, with a ‘short’ choice in the prior trial increasing the likelihood of a subsequent ‘short’ decision for the test duration. Studies indicated that decisional carry-over effects were more pronounced when judging the duration of a test stimulus is challenging compared to when it is easy \cite{Wehrman2020,Wiener2014}. This decisional bias has been attributed to response uncertainty, where participants are more likely to stick to their recent response when uncertain about the test stimulus. It’s worth noting that some studies propose a motoric repetition explanation for decisional carry-over bias, suggesting participants tend to repeat their previous motor response \cite{Akaishi2014}. However, other research highlights a response alternation bias in motor responses, where choosing ‘left’ in the prior trial may lead to a higher likelihood of choosing ‘right’ in the following trial \cite{Pape2016}. While motoric response bias is essential for future research, the effect of decisional carry-over may not solely be attributed to pure motoric repetition. In fact, it is stronger than estimated, considering the counterbalance of motoric alternation to response repetition.
Importantly, we explored sequential effects using discrimination and reproduction tasks, shedding light on the ongoing debate surrounding the role of task relevance underlying these effects. We found distinct patterns of task relevance underlying sequential effects in time discrimination and reproduction tasks. Our results revealed that, in time discrimination, prior durations influenced current judgments regardless of task relevance, while in time reproduction, a stronger assimilation effect was observed following duration reproduction tasks. The present findings suggest that it may be appropriate to re-examine the evidence for sequential dependence in the literature, considering its potential attribution to the task’s specific nature. In \citet*{Fornaciai2018}  study on numerosity perception, participants engaged in a numerosity discrimination task, ignoring an inducer and determining whether the reference or probe had more dots. Their results showed an attractive serial dependence, suggesting a serial bias induced by the presence of an object, even when responses were not required in the previous trial. In Experiment 1 of our study (using the time discrimination task), assimilation effects were observed, aligning with this research, irrespective of task-relevant responses in previous trials. However, Experiment 2 revealed that the strength of sequential effects tends to be more prominent following task-related responses in a reproduction task. It is conceivable that the specific task can influence sequential dependence \cite{Fritsche2017,Pascucci2019}, thus, it is crucial to clarify the tasks’ contributions when interpreting and comparing results to achieve a clearer understanding of observed sequential effects.
The observed discrepancy in findings across different tasks cannot be ascribed to potential biases in response motor or prior choice. This is evident from the distinct result patterns between the 2AFC and reproduction tasks when categorizing reproduction responses into “shorter” or “longer” judgments (Figure 3b). Even with this categorization, a significant sequential effect was observed for prior task-related responses, while no effect was evident for prior task-unrelated responses, indicating that the difference may be linked to the internal representation of the stimulus rather than the response bias itself. One possibility is that the adjustment task and forced-choice task may differ in what information is retained in memory. In the adjustment task, stimuli had to be retained in the working memory during the entire encoding phase, and the continuing trace of the stimulus can be easily influenced by the working memory and post-perceptual processing. Sequential dependence may be partly attributed to interference between previous and current memory traces of the stimuli \cite{Bliss2017,Mei2019,Bae_2019}. For example, in a spatial adjustment task, increasing the delay between stimulus and response enhances sequential dependence \cite{Bliss2017}. Sequential biases in time perception manifested only when the preceding task involved active duration reproduction, but diminished when participants passively viewed a prior duration without reproduction (citations). These findings suggest that working memory and response-related post-perceptual processes play a crucial role in explaining the occurrence of sequential dependence effects in the adjustment task. Instead, the forced-choice task appears to differ from the adjustment task in terms of how it utilizes memory traces of the stimulus. Previous research indicated that the information retained in the discrimination task pertains to the value of a criterion that is established beforehand \cite{Lages_1998}. In this context, participants create either internal or external criteria in the discrimination task and compare incoming sensory input with a response criterion. Discrimination tasks may involve two types of decision criteria: a long-term reference decision criterion and trial-to-trial adjustments of the decision criterion. The goal of these adjustments is to ensure that the criterion for each trial is optimized for that specific decision, and these decision criteria form the basis of sequential dependencies, which may show less dependence on the working memory and post-perceptual processes \cite{Bausenhart2014,Dyjas2012,Lages_1998}.
Our findings indicate that sequential dependence in time perception can be influenced by the measurement methods. Whether these observations in time perception can be generalized to other perceptual domains requires further investigation. Unlike visual features, time perception is susceptible to contextual distortions arising from mental states, emotions, or selective attention \cite{Shi2013,Wittmann2009}. The sequential bias in time perception appears to be modulated by working memory processes that link sensory representation and decisional templates. Thus, in tasks involving time reproduction, the brain rapidly assimilates current duration estimates with past representations, resulting in a more pronounced sequential bias. Moreover, sequential effects are known to be influenced by variable factors, including the nature of the stimulus, the passage of time, the number of intervening stimuli, and individual characteristics \cite{Ceylan2023,Fritsche2017,Fritsche2020,Glasauer2022,Samaha2019}. For example, a larger serial dependence effect was observed in previous highly confident trials compared to less confident trials for orientation estimation \cite{Samaha2019}, and observers strongly believing in the correlation of successive stimuli exhibit strong serial dependence, whereas those with an opposite belief in randomness show less bias in interval reproduction \cite{Glasauer2022}
In conclusion, our research revealed attractive sequential effects in time perception and highlighted a distinctive role of task relevance in shaping sequential effects between time discrimination and reproduction tasks. Specifically, the assimilation effect in the time discrimination task was unaffected by task relevance, while in the time reproduction task, it was notably stronger following duration reproduction trials. These findings underscore the need for careful interpretation and comparison of results across different tasks, as measurement methods can significantly impact sequential effects, as demonstrated in our study. A general implication is that findings which show a sequential effect of a prior stimulus on the judgement of a later one should not automatically be considered evidence for a perceptual mechanism of the preceding stimulus. Instead, the possibility that the effect is mediated by decision strategies (i.e., response criterion) should be considered.