ENTREVISTAS CUALITATIVAS NO ESTANDARIZADAS INDEPENDIENTES

switching

Fourteen Psychology Students and members of the laboratory volunteered to each experiment, 2C and 2D (2C: all female, mean age 20.2 y/o; 2D: 9 female, mean age 21.2); one participant participated twice in both experiments. The dataset for each experiment had 9000 trials in total, of which half (4500) were of either type (RAN/DIR).

Figure 8. Experiments 2C-2D: Results. Comparison of serial dependence in a pre-cued versus post-cued task- switching paradigm: similar results in both experiments indicate that the differences between tasks are not attention- related. 8a - 8b. Normalized relative error in current response (zREn) as a function of the StD presented in the previous

trial (StDn-1), plotted separately by trial n-1 type: RAN (variance report required) and DIR (mean report required). In

8a, the trial type (i.e. the required decision) is pre-cued, while in 8b it is post-cued. The error bars represent the between-participant standard error. In both cases we observe positive serial dependence only for RAN n-1 trials, as suggested by the ascending slope of the RAN plot. No trace of positive serial dependence is observed in relation to post-cued n-1 DIR trials, indicating that the process that gives rise to serial dependence in variance is necessarily post- perceptual. 8c-8d. Fixed-effects coefficient estimates in 20 Bayesian LMMs withStDn-t (t=1…10) as predictor of

8d. Since the dependent variable is the current variance (‘randomness’) judgment, trial n is always a RAN trial. The error bars represent the 95% credible intervals for the true value of the coefficient. Analyses further confirm that positive serial dependence only arises in relation to dimension-specific decision-making, even if such decision was post-cued. 8e-8f. Normalized relative error in current response (zREn) as a function of the StD presented in trial n-2

(StDn-2), plotted separately by trial n-1 type: RAN (variance report required) and DIR (mean report required). Both trial

n-2 and trial n are RAN trials. The required decision is pre-cued in 8e and post-cued in 8f. In both cases, we observe a neat ascending slope for n-1 DIR trials. By contrast, when the intermediate trial (n-1) was a RAN trial, the effect of StDn-2 is less clear. In other words, positive serial dependence driven by a decision about variance made 2 trials before

is eroded if another decision about the same feature-dimension (variance) is interposed (RAN n-1 trial), compared to cases where the intermediate decision was about a different dimension (DIR n-1 trial). This suggests an iterative modification of decisional representations as a new decision about the same feature-dimension is made, consistent with the hypothesis that sees serial dependence as result of the interaction of past and present decisional representations in visual working memory.

TABLE 3. Serial dependence and cued decision - Model comparison

3a. Pre-cued dimension-specific judgment (Experiment 2C)

Models P(M) P(M|data) BF M BF 10 error %

Null model (incl. subject) 0.200 1.070e -4 4.281e -4 1.000

StDn-1 0.200 0.029 0.121 273.553 0.364

Trial n-1 type (variance vs. mean estimation) 0.200 1.428e -4 5.711e -4 1.334 1.234

StDn-1 + Trial n-1 type 0.200 0.052 0.221 488.333 1.719

StDn-1 + Trial n-1 type + StDn-1  ✻   Trial n-1 type 0.200 0.918 44.913 8580.923 10.424

3b. Post-cued dimension-specific judgment (Experiment 2D)

Models P(M) P(M|data) BF M BF 10 error %

Null model (incl. subject) 0.200 0.286 1.601 1.000

StDn-1 0.200 0.014 0.058 0.050 0.490

Trial n-1 type (variance vs. mean estimation) 0.200 0.088 0.387 0.308 1.677

StDn-1 + Trial n-1 type 0.200 0.004 0.018 0.016 3.618

Note. All models include subject.

Table 3. Experiment 2: 2C-2D. Serial dependence (associated with trial n-1) and cued decision in trial n-1.Each table section presents the model performance on Experiment 2C and 2D datasets, respectively, according to the results of a Bayesian repeated-measures ANOVA on zREn, with two within-subject factors: StDn-1 and trial n-1 type (pre-cued

RAN/DIR trial in Experiment 2C, post-cued RAN/DIR trial in Experiment 2D). P(M): prior probability of each model, assumed to be equal for all. P(M/data): posterior probability of the model (given the data). BFM: Bayes factor for the

model. BF10: Bayes factor for the alternative hypothesis relative to a null model (expressed by each model).

Figures 8a and 8b present the distribution of normalized variance reports (zREn) as a

function of StDn-1 and trial n-1 type, for experiment 2C (pre-cue) and 2D (post-cue),

respectively. On visual inspection we observe a similar pattern in both experiments, and similar as well to Experiment 2B (pre-cued task-switching with minor methodological differences compared to 2C). A roughly ascending plot is observed for current reports in relation to StDn-1 presentation, only when trial n-1 required a judgment about variance

(RAN n-1 trial). On the contrary, we do not observe any trace of positive serial dependence in relation to StDn-1, if the required decision in trial n-1 was about the mean

of the RDK motion. Rather, there seems to be a negative effect associated to StDn-1 for

post-cued n-1 DIR trials. Results in the post-cued design appear to confirm the post- perceptual origin of serial dependence, in relation to dimension-specific decision- making.

Table 3 presents the results of a Bayesian RM ANOVA on current variance report (zREn)

with two within-participant factors: StDn-1 and trial n-1 type (RAN/DIR), computed on

the data of Experiments 2C (pre-cued task-switching) and 2D (post-cued task-switching, respectively). In both cases, the model with more explanatory power is the one with all terms: both main factors and the interaction term StDn-1*trial n-1 type, although for

Experiment 2D the advantage over the null model is anecdotal (BF10=2.125).

Nevertheless, in Experiment 2D there is moderate evidence for inclusion of the interaction term StDn-1*trial n-1 type, the one that determines whether the influence of

if the comparison is made between two identical models except for the inclusion of the term of interest (interaction term), namely between the model with both main factors and the one that also contains the interaction term, evidence in favour of the latter is extreme: BFfull/main effects=139.563.

Figures 8c and 8d depict serial dependence in relation to trials up to n-10: each data point represents the fixed-effects B coefficient for the relationship between StDn-t

(t=1…10) and current normalized variance judgment (zREn) according to a Bayesian

LMM. Data are split by trial n-t type (RAN/DIR), while the current trial (n) is necessarily a RAN trial. Figure 8c corresponds to the pre-cued (2C) and 8d to the post-cued (2D) experiment. Once more we observe that the positive bias exerted by recent trial history is only driven by trials wherein a decision about variance was required, even if the cue for the required decision was presented after stimulus offset. Interestingly, this positive bias seems to last longer than in previous experiments: it appears still present in relation to trials n-3 or n-4, while in previous cases it had entirely disappeared by n-3. We propose two non-exclusive explanations for this: the interposing DIR trials (which are half of the total trials in the current experiments) might reduce the number of interposing decisions about variance, thus enhancing the carry-over effect of more remote decisions that are not disrupted by subsequent operations about the same feature-dimension (see below, section 2.2.2). In addition, the shorter duration of the RDK presentations (250 ms instead of the previous 500 ms) might render the competing negative effect weaker (particularly if it is related to adaptation processes).

In summary, our results show that positive serial dependence depends on dimension- specific decisions made in recent trials, ruling out alternative explanations such as the influence of response (2A) or differences in perceptual attention (2D). For equal stimuli, task requirements and attentional deployment during perception, as guaranteed by the post-cued design, we fail to encounter any trace of attractive serial dependence in relation to the variance of past trials that did not require a (post-perceptual) decision about variance.

2.2.2. Serial dependence by distant trials is disrupted by subsequent dimension-