Data analysis

As our study focused on how previous trials influence duration judgments in timing tasks, we categorized trials based on the duration (less than or more than 1 second) and type (Time or Direction) of the previous trial, creating four categories: "Short/Direction", "Long/Direction", "Short/Time", and "Long/Time". We further classified consecutive Time-Time trials according to the preceding timing trials' responses as "Short Response" or "Long Response." Excluding the first trial of each block, we analyzed responses using a psychometric function, a cumulative Gaussian function, including an initial 5% lapse rate for attention errors  \cite{Wichmann2001}. We then determined each participant's Points of Subjective Equality (PSE) to identify biases in duration perception and computed the just-noticeable difference (JND) and Weber fraction (WF = JND/PSE) for precision. Participants with a WF greater than one were excluded. Lastly, we used repeated measures ANOVAs and t-tests to determine the significance of our findings. 

Results and discussion

Trials were categorized into four groups based on prior task (Time or Direction) and duration (Short or Long), as shown in Figure 2A's psychometric curves. A distinct difference was visible between curves for the preceding 'Short' vs. 'Long' conditions while preceding 'Time' and 'Direction' tasks had similar curves.  PSEs (with standard errors) were 770 ± 48, 833 ± 51, 775 ± 49, and 820 ± 54 ms for Time/Long, Time/Short, Direction/Long, and Direction/Short, respectively (Figure 2B). A two-way repeated measures ANOVA revealed a significant effect of Prior Duration, F(1,23) = 6.083, p = .022, \(\eta_{p}^{2}\) = 0.013. However, there was no significant main effect of task relevance (  = 0.012, but not of Prior Task (F(1,23) = 0.045, p = .833, \(\eta_{p}^{2}\) = 0.000) nor an interaction between the two factors ( < 0.001) or their interaction (F(1,23) = 0.138, p = .714, \(\eta_{p}^{2}\) = 0.000) < 0.001). These findings indicate that prior duration impacts current duration judgment, with shorter prior durations leading to shorter perceived current durations and vice versa, indicating an assimilation bias. The type of prior task (time or direction), however, had little effect. 
Further analysis on the impact of preceding responses revealed a decisional carry-over effect. Figures 2C and 2D show psychometric curves according to prior responses, with a leftward shift for "Long" prior responses, indicating a tendency to judge current durations as longer following "Long" report. The PSE was significantly lower after "Long" responses (741 ± 44 ms) than "Short" (901 ± 51 ms), t(23)= 3.795, p =.001, d = 0.684.
These findings indicate that duration judgments are influenced by both previous durations and decisions, manifesting as both an assimilation effect and a decisional carry-over effect. Interestingly, the type of preceding task (Time or Duration) did not significantly impact these biases, suggesting that the task relevance may not be involved in the sequential effect underlying duration discrimination tasks.  It is important to note, however, that in the discrimination task, decisions are binary, involving simple judgments as either "shorter" or "longer" than one second. This raises the question of whether these findings from Experiment 1 are applicable to tasks with continuous variables, such as reproduction tasks. Therefore, Experiment 2 employed a time reproduction task, asking participants to replicate the duration of a given stimulus.