Results and discussion
The mean accuracy for the duration judgment task was 80.35% (SEM
=1.76), indicating that participants successfully encoded duration
information in a large proportion of trials. Figure 1c displays
psychometric curves separately for the TT and DT conditions based on
whether the prior duration was short or long. Notably, there is a small
but clear difference in the curves for both TT and DT conditions
concerning prior duration. When the prior duration was long, the curve
appears shifted leftward compared to when it was short, indicating an
attractive sequential effect toward the prior duration. Specifically,
participants tend to judge the current comparison durations as “Longer
than one second” more often when the prior duration was long compared
to when it was short.
We then calculated the corresponding PSE for each psychometric curve (as
illustrated in Figure 1d). In the TT condition, the PSE for prior long
and short durations were 0.766 ± 0.047 and 0.828 ± 0.051 s,
respectively. In the DT condition, the PSE for prior long and short
durations were 0.770 ± 0.049 and 0.818 ± 0.054 s, respectively. In
general, the PSE is smaller than the standard one-second stimulus,
indicating an overall underestimation of current duration. A two-way
repeated measures ANOVA with “prior stimuli” (short vs. long) and
“task relevance” (TT vs. DT) revealed a main effect of the prior
stimuli on current duration judgment, F(1,23) =
6.324, p = .019, \(\eta_{p}^{2}\) = 0.013. However, there were no
significant main effect of task relevance
(F(1,23) = 0.033, p = .857,\(\eta_{p}^{2}\) = 0.000) nor an interaction between the two factors
(F(1,23) = 0.098, p = .757,\(\eta_{p}^{2}\) = 0.000), with comparable sequential effects for the
task-relevant (TT) and task-irrelevant (DT) conditions in the current
duration discrimination task. These findings indicate that prior
duration had a noticeable impact on current duration judgment, leading
to shifted psychometric curves in both TT and DT conditions. This shift
reflects an attractive bias towards the previous duration, resulting in
a higher proportion of judgments of the current duration as longer than
the standard one-second stimulus when the prior duration was long
compared when it was short. However, sequential effects in the
task-relevant (TT) and task-irrelevant (DT) conditions did not differ
significantly.
To examine whether current duration judgments were influenced by
preceding reports (decisional carry-over effect), we grouped all TT
trials based on participants’ reports (“Short” or “Long”) in the
previous trial. In Figure 1e (left panel), we present psychometric
curves based on these prior reports. Notably, a distinct difference is
evident in the curves concerning prior reports. When participants
reported “Long” in the previous trial, the curve shifted leftward
compared to when they reported “Short”, indicating an attractive
sequential effect toward the prior report. Specifically, participants
tended to judge the current comparison durations as “Longer than one
second” more frequently after reporting “Long” compared to “Short”
reports. The PSE for “Long” and “Short” reports in the previous
trial were 0.741 ± 0.045 and 0.898 ± 0.051 s, respectively (Figure 1e,
right panel). A two-tailed paired sample t-test on the PSE revealed a
significant decisional carry-over effect. The PSE was significantly
shifted leftward when participants reported “Long” compared to
“Short” decisions in the previous trial (t(23)= 3.740, p =.001, d = 0.671).
These findings demonstrate that current duration judgments were
influenced by both preceding durations and the decisions made in the
previous trials. Specifically, durations presented immediately after
long intervals tend to be perceived as longer, while durations following
short intervals are perceived as shorter, showing an attractive
sequential effect. However, there was no significant difference between
trials following the timing discrimination task and the direction
adjustment task, suggesting that post-perceptual processes may not be
involved in the sequential effect underlying duration discrimination
tasks. Furthermore, participants exhibited a significant decisional
carry-over effect, meaning they were inclined to continue making
“Long” judgments in subsequent duration discrimination tasks when they
had reported a stimulus as “Long” in the previous trial, and vice
versa for “Short” judgments. However, it is important to note that in
the time discrimination task, decisions are categorical, involving
dichotomous judgments as either “shorter” or “longer” than one
second. It remains uncertain whether these findings from Experiment 1
can be generalized to tasks involving continuous critical dimensions.
Therefore, in Experiment 2, we employed the time reproduction task,
where participants were required to reproduce the duration of the
presented stimulus.
Experiment 2
Method
Participant
24 participants were recruited in Experiment 2 (13 females; age 18 - 27,
mean ± SD: 20.75 ± 2.45 years), all of them were right-handed, with
normal or corrected-to-normal vision and color vision. Before the
experiment, participants provided written informed consent and received
compensation of 9 Euros/hour for their participation. The study was
approved by the ethics committees of the Psychology Department at LMU
Munich.
Stimuli and
procedure
Experiment 2 closely followed the design of Experiment 1, with two
notable modifications. In this experiment, participants had to reproduce
the duration of the target stimuli for the timing task (see Figure 2a).
Besides, the target duration was randomly sampled from 0.6, 0.8, 1.0,
1.2, 1.4, 1.6, and 1.8 s.
After the post-cue display, when the task involved duration
reproduction, a display of static green RDK (15 dots, each dot diameter
of 0.4°; the luminance of 45.8 cd/m2) was presented on
the center of the screen. Participants initiated the reproduction
process at their own pace by pressing and holding the down arrow key on
the keyboard, then released the key when they believed the elapsed
duration matched that of the coherent motion of the green dots during
the encoding phase. Immediately after pressing the down arrow key, the
static green dots transitioned into a random motion pattern (velocity of
6°/s) to minimize inter-trial bias. The key holding duration was
recorded as the reproduced duration. Participants would receive visual
feedback if the relative error exceeded 30%, with “Too short” for
relative errors below -30% and “Too long” for relative errors
exceeding 30%. The procedure for the direction adjustment task remained
identical to that used in Experiment 1.
Data analysis
The response error for each duration reproduction trial was calculated
as the difference between the reproduced duration and the actual
duration. We eliminated the first trial of each block and then filtered
out trials with response errors exceeding three standard deviations from
the participant’s mean error to account for accidental button presses or
lapses in attention. These outliers were rare, comprising only 0.39% of
the duration reproduction trials (ranging individually from 0 to 4
outlier trials). The remaining duration reproduction trials were
categorized into two conditions based on the task relevance: “Time to
Time” (TT) as the task-relevant condition and “Direction to Time”
(DT) as the task-irrelevant condition.
Previous research has demonstrated that subjective timing reproduction
is susceptible to contextual factors, with the primary bias known as the
“central tendency effect”. This effect results in the underestimation
of long durations and the overestimation of short durations, reflecting
a tendency toward the mean value of the stimulus distribution
(Burr et al., 2009; Jazayeri & Shadlen, 2010; Nakajima et al., 1992). Another bias
arises from the sequential effect, where subjective reproduction is
influenced by preceding durations
(Dyjas et al., 2012; Glasauer & Shi, 2022). We assumed that the response error at trial
n depended on both the current duration (
\(T_{n}\)) and the
previous duration (
\(T_{n-1}\))
(Glasauer & Shi, 2022). The variation
in the current duration primarily contributes to the central tendency
effect, while the variation in the previous duration causes the
sequential bias. These two effects were combined into a single model
expressed as:
\[\text{Error}_n=a*T_n+b*T_{n-1}+c.\]
To quantify the central tendency and sequential effects in the time
reproduction task, we performed multiple linear regressions using
response errors (
\(\text{Error}_{n}\)) as the dependent variable, with
the current duration (
\(T_{n}\)) and the previous duration
(
\(T_{n-1}\)) as predictors. In this equation, the slope (
\(a\)) was
computed for the current duration (
\(T_{n}\)), and
\(-a\) represented
the central tendency index, where 0 indicated no central tendency and 1 indicated a strong central tendency
(Cicchini et al., 2012; Jazayeri & Shadlen, 2010; Shi et al., 2013). The slope
(
b ) of the linear fit on the previous duration (
\(T_{n-1}\))
served as the sequential bias index
(Cicchini et al., 2014, 2018; e.g., Glasauer & Shi, 2022). A positive slope
indicates that the current estimation is attracted towards the previous
duration, denoted as the “assimilation” or “attractive sequential
effect”, while a negative slope indicates that the current time
estimation is repelled from the previous duration. The statistical
significance of both the central tendency effect and the sequential
effect was assessed individually using two-tailed one-sample t-tests
against the null hypothesis of zero effect for each condition
(task-relevant: TT and task-irrelevant: DT) to determine the presence
and strength of these effects. Subsequently, a two-tailed paired sample
t-test was conducted to compare the difference between conditions (TT
vs. DT).
Furthermore, to compare sequential effects between the two experiments,
we categorized the reproduced durations into two groups: “Longer” for
reproductions exceeding 1.2 s, and “Shorter” for reproductions shorter
than 1.2 s, considering that the target durations were centered around
1.2 seconds. Sequential effects of prior stimuli and prior reports were
then calculated separately, following the same methodology as in
Experiment 1. First, we grouped previous durations into “Short” (0.6,
0.8, and 1.0 s) and “Long” (1.4, 1.6, and 1.8 s), omitting 1.2
seconds. Consequently, there were two factors: task relevance (TT vs.
DT) and previous durations (short vs. long), resulting in four
conditions mirroring Experiment 1. For each condition, we fitted
psychometric functions and calculated the PSE individually for each
participant. A two-way repeated measures ANOVA was applied to the PSE to
assess main effects and the interaction effect. To investigate the
decisional carry-over effect, we grouped all TT trials based on
preceding “Short” or “Long” reports, fitted psychometric functions
for each group, and calculated the PSE individually for each
participant. We then performed a two-tailed paired sample t-test on the
PSE to assess the decisional carry-over effect between prior reports
(“Short” vs. “Long”).
Additionally, to visualize the variability of the sequential effect
between experiments, we computed a sequential effect index as the
difference in PSE between the prior short and prior long categories
separately for each condition (i.e., for the TT condition, PSE in the
prior short category minus the PSE in the prior long category). A 2
(task relevance: TT vs. DT) × 2 (experiments: Experiment 1 vs.
Experiment 2) repeated measures ANOVA was applied on the sequential
effect index to assess the main effects and the interaction effect. To
assess the decisional carry-over effect between experiments, we
calculated a decisional carry-over effect index as the difference in PSE
between prior short and prior long reports separately for each
experiment. A two-tailed independent sample t-test was performed on the
decisional carry-over effect index to assess the effect between
experiments (Experiment 1 vs. Experiment 2).