Descripción del desarrollo de la metodología Delphi en el marco de la presente

In Experiment 1, the similarity of the mean trajectories of consecutive RDKs did not affect the size or sign of the serial dependence in variance reports (see section 2.2.2 of the current chapter). This result is in line with other findings in our study that suggest a high-level source of such serial bias (such as independence of eccentricity and spatial location). However, it may seem counter-intuitive given the close relationship between both statistics in ensemble vision, as well as the purported function of serial dependence, namely promoting perceptual continuity: it seems reasonable to expect that the bias on a certain dimension should be stronger if consecutive stimuli share similar attributes.

As in Experiment 1 mean trajectories could take any integer value from 0o _{to 359}o_{, we}

decided to run an additional experiment (1B) with a limited number of possible means, to rule out that our failure to find any effect of mean similarity on serial dependence in variance was related to the employment of such wide range of trajectories. It could be the case that the attractive bias was much stronger when mean directions were almost identical but became mean-invariant over a certain amount of divergence. Alternatively, the great number of possible mean trajectories could render it futile to rely on trial-by- trial mean estimation to compute variances.

In addition to serial dependence, we wanted to assess the interaction between mean similarity and other aspects of the task, such as accuracy and precision in variance

estimations.

3.3.1. Methods

The methodology was similar to Experiment 1, although in Experiment 1B stimulus presentation was always foveal. Regarding the mean direction of the RDKs, instead of being randomized among all integers from 0o _{to 359}o_{, only three values were allowed,}

presented with equal frequency: 10o_{, 45}o _{and 100}o ₍₀o _{corresponds to the rightward}

horizontal axis and the increase proceeds clockwise). Thus, the difference between the mean trajectories of two trials could take four values: 0o_{, 35}o_{, 55}o _{and 90}o_{. Each}

experimental session was formed of 240 trials.

3.3.2. Results

Twenty-one participants (11 female, mean age 20.5 y/o, standard deviation 2.13) took part in the study, three being members of the laboratory and the rest paid volunteers recruited through the SONA system and by online advertisement in the University website. The overall number of trials was 5040.

Mean similarity does not affect performance on variance judgments

The central variable in this experiment was the absolute inter-trial mean difference, specifically the difference between RDK mean in the current and previous (n-1) trials: Δμn,n-1 =|μn-1 - μn|, as we considered that, if the similarity of RDK means had any effect

on sequential variance judgments, this effect would be particularly meaningful regarding consecutive RDK presentations.

To ascertain whether Δμn,n-1 affected performance on iterative variance estimation (in

other words, whether mean similarity exerted priming effects on variance judgments), we analysed its influence in response time (RT), accuracy and precision. For both accuracy and precision we employed inverse measures: inaccuracy or error size and imprecision or response dispersion. Response (in)accuracy, or ‘error size’, was defined as the absolute value of the difference between response and veridical StD: En = | StDn

- Rn |.Response (im)precision or dispersion was computed as the standard deviation of the responses provided by each participant for a certain combination of StDn and inter-

trial mean difference (σR). For all three measures (RT, error size and response

dispersion), smaller values indicate better performance. A Bayesian repeated-measures ANOVA was conducted on the effect of current StD (StDn) and inter-trial mean difference

(Δμn,n-1) –as within-subject factors- on each of these three measures of performance (RT,

error size and dispersion). Thus, we conducted three RM ANOVAs with the same two within-subject factors, but with a different dependent variable for each. In each case, a model comparison was performed based on the results of the Bayesian RM ANOVA, assessing the evidence in favour of each possible combination of independent variables in terms of explaining the variability of the performance measure. The five competing models, in each case, were the null model, a model with StDn as the sole independent

variable, a model with only Δμn,n-1, a model with both main effects (StDn and Δμn,n-1) and

the full model with both main effects and the interaction term StDn * Δμn,n-1. If intertrial

mean difference had any role in performance in the current trial (measured by RT, error size or response dispersion), a model containing Δμn,n-1 would be more explanatory than

a model without this variable.

In all three ANOVAs, the best model was the one containing StDn only, with a Bayes

factor of BF10=2.352*106 (RT); 4.658*1067 (error size); 2.276*1020 (dispersion). This

model outperformed the second best (the model with both main effects, StDn and Δμn,n- 1, in all three cases) by a factor of BFStDn/main effects=55.79 (RT); 3.402 (error size); 34.344

(dispersion). The Bayes factor for inclusion of the variable of interest, Δμn,n-1, was

against any explanatory role of mean difference with regards of error size, and strong evidence against it with regards of RT and response dispersion. In summary, evidence indicated that inter-trial difference in RDK mean does not have any effect on performance in variance judgments, measured in terms of response time, accuracy or precision.

Mean similarity does not affect serial dependence by previous StD on variance judgments

In order to analyse the influence of mean similarity between consecutive trials on serial dependence in variance, first we conducted a Bayesian RM ANOVA on the effect of previous trial StD (StDn-1) and inter-trial mean difference (Δμn,n-1) –as within-subject

factors- on current normalized response (zREn: normalized response error in variance

judgments, as dependent variable). A model comparison was performed between all combinations of tested factors, based on the evidence given by the RM ANOVA: the five competing models were the null model, two models with a single main effect each (StDn- 1 only, Δμn,n-1 only), a model with both main effects (StDn-1 and Δμn,n-1) and the full model

with both main effects and the interaction term (StDn-1, Δμn,n-1 and StDn-1 * Δμn,n-1). If

mean similarity had any influence of serial dependence, it must be able to modulate the effect of StDn-1 on zREn: consequently, the model including the interaction term StDn-1 *

Δμn,n-1 should be more explanatory than any other model.

According to the results of the Bayesian RM ANOVA, the best model contained both main effects, StDn-1 and Δμn,n-1, but not the interaction; this model outperformed the full

model (including the interaction term, key to our hypothesis) by a factor of BFmain effects/full=69.325, indicating strong evidence in favour of the main effects compared to

the full model. Overall, the evidence for inclusion of the interaction term was BFinclusion=0.050, indicating strong evidence against this term. In conclusion, while inter-

judgments (as shown by the fact that the best model includes the main effect of Δμn,n-1

), there is strong evidence in support of the absence of effect of inter-trial mean difference on StDn-1-related serial dependence in variance.

CHAPTER 2: EXPERIMENT 2: PROCESSING STAGES