Experiment 2
Method
Participant
Twenty-four participants were recruited in Experiment 2 (13 females; age 18 - 27,
mean ± SD: 20.75 ± 2.45 years), all right-handed, with
normal or corrected-to-normal vision and color vision. Before the
experiment, participants provided written informed consent and received 9 Euros/hour compensation.
Stimuli and
procedure
Experiment 2 closely followed the design of Experiment 1, with some changes for the timing task. This time, participants had to reproduce
the duration of the target stimuli, randomly selected from 0.6, 0.8, 1.0,
1.2, 1.4, 1.6, and 1.8 s (see Figure 1). After the post-cue display, participants initiated the task at their own pace by pressing and holding the down arrow key, releasing it when they felt the elapsed duration matched the target duration. Immediately after pressing the down arrow key, a display showing static green random dots(15 dots, each dot diameter of 0.4°; the luminance of 45.8 cd/m2) turned into a random motion display (velocity of
6°/s) to minimize inter-trial bias. The key holding duration was
recorded as the reproduced duration. If their reproduction error exceeded 30%, they received feedback: "Too short" for
relative errors below -30% and "Too long" for errors above 30%. The procedure for the direction adjustment task remained the same as in Experiment 1.
Data analysis
Response errors in duration reproduction trials were calculated
as the difference between the reproduced and actual
durations. We excluded the first trial of each block and filtered
out trials where errors exceeded three standard deviations from
the participant’s mean error, accounting for accidental presses or attention lapses. These outliers constituted only 0.39% of
trials. The remaining trials were
categorized into two conditions based on the prior task (Time or Direction).
Previous research has demonstrated that subjective timing
is susceptible to contextual factors, such as the "central tendency effect", leading to underestimating long durations and overestimating short durations \cite{Burr2009,Jazayeri2010,Nakajima1992}, and the sequential effect, where reproductions are influenced by preceding durations \cite{Glasauer2022,Dyjas2012}. We modeled these effects using multiple linear regressions, with current (\(T_{n}\)) and previous (\(T_{n-1}\)) durations as predictors:
\[\text{Error}_n=a*T_n+b*T_{n-1}+c.\]
The model’s slope (a) for the current duration indicates the central tendency effect. Following the convention adopted in the literature \cite{Cicchini2012,Jazayeri2010,Shi2013}, we used the positive value (|a|) as the central tendency index, with 0 indicating no central tendency. The slope (b) for the previous duration reflects the sequential bias \cite{Glasauer2022,Cicchini2014}, and a positive slope indicates that the current estimation is attracted towards the previous duration, denoted as the “assimilation”, while a negative slope indicates that the current time estimation is repelled from the previous duration.
Furthermore, we categorized reproduced durations as "Longer" or "Shorter" than 1.2 s (omitting 1.2 s) and analyzed sequential effects based on prior stimuli and responses, such that we can compare sequential effects between Experiments 1 and 2.
Additionally, to visualize the variability of the sequential effect
between experiments, we computed a sequential effect index as the
difference in PSEs between groups with prior short and prior long durations for each prior task condition. To
assess the decisional carry-over effect between experiments, we
calculated a decisional carry-over effect index as the difference in PSEs between prior short and prior long reports separately for each
experiment.
Results and discussion
The overall mean response error (with SE) for the duration reproduction
trials was significantly positive (97 ± 25 ms, t(23) = 3.911, p =
.001, d = 0.798), indicating a general overestimation. The
mean reproduction error for the prior Time task was 113 ± 24 ms, significantly larger than the mean error for the prior Direction task (78 ± 27 ms),
t(23) = 3.393, p = .003, d =
0.278.
Central tendency effect. Both the preceding Time and Direction conditions exhibited
significant central tendency biases, with participants tending to overestimate short durations and underestimate long durations. The
mean central tendency index was 0.318 ± 0.048
(t(23) = 6.654, p <.001,d = 1.358) for the Time condition and 0.354 ± 0.048
(t(23) = 7.329, p <.001,d = 1.496) for the Direction condition. They were
comparable (t(23) =
1.503, p = .147, d = 0.154), as depicted in Figure 3A.
This suggests that the task relevance did not influence the central tendency effect. The lack of difference can be attributed to the same
distribution and range of durations tested in both tasks,
resulting in a stable prior representation of durations across
conditions. This finding aligns with previous research that mixing durations leads to generalized prior representation across different conditions \cite{Roach2017}.