Abstract would go here
Introduction would go here
General introduction to E1 here.
The experiment employed a traditional exogenous cuing paradigm whereby targets appeared in peripheral locations following a peripheral cue and participants were asked to indicate detection of these targets as rapidly as possible. Additionally, on each trial a color wheel appeared immediately after detection response on which participants were asked to indicate the color of the preceding target. Variables were manipulated within-participants and included Cue Validity (valid vs neutral vs invalid) and SOA (100ms, 800ms). Targets could appear on the left or right side of the screen and on 20% of trials no target was presented, serving as catch trials to discourage anticipatory responding. Thus, 3\(\times\)2\(\times\)2\(\times\)5 = 60 trials are necessary to complete the design. A total of 480 trials were presented to participants across 8 blocks, where order of trials was randomized within each block of 60 trials and participants were provided opportunity to take a break every 30 trials. Participants also completed 30 practice trials sampled randomly from the 60 trials of the complete design.
Participants were recruited from a local undergraduate participant pool and included a total of 40 individuals (8 male, 5 left-handed, aged between 18 and 25). Participants received course credit compensation.
The experiment was coded in the python and run on a Mac mini computer with a 2GHz processor running Mac OS X 10.5.7. Responses were collected via USB keyboard and mouse. Stimuli were displayed using a 19-inch CRT screen at a resolution of 1024\(\times\)768 pixels and a refresh rate of 120Hz. Participants were seated 60cm from the screen and instructed to maintain this distance by checking their position using a measured length of string during each break in the experiment. The central fixation stimulus was a cross subtending 0.5\(^\circ\)with a line thickness of 0.05\(^\circ\). The target stimulus was an “x” with the same dimensions as the fixation stimulus. A box, subtending 1.5\(^\circ\)and with a line thickness of 0.3\(^\circ\), surrounded the fixation stimulus and the two peripheral target locations, which were offset from center on the left and right by 7\(^\circ\). The colour of the central fixation stimulus was set to 50% white (medium grey) and the colour of the boxes was set to 20% white (dark grey). The cue consisted of a 50ms change in the brightness of one of the boxes to white. The target colour was selected randomly trial to trial from an RGB color wheel. During target colour selection, a randomly rotated color wheel was presented as a central ring with a radius subtending between 5.3\(^\circ\)and 7.5\(^\circ\).
Following consent procedures, participants received verbal instructions describing the task (for complete script, see Appendix A). Each block started with the presentation of the fixation stimulus for 1s. A trial began with the onset of the three boxes, followed by the cue 1000ms later. Upon completion of the trial’s SOA, the target appeared and remained on screen for 200ms. After response or response timeout after 1500ms, the screen was cleared and a color wheel and mouse cursor were presented on screen. Upon clicking an area of the color wheel, the screen was cleared, leaving only the fixation stimulus for 1000ms before the beginning of the next trial.
All analyses were performed using R (R Core Team, 2015). All trials during which a response was made when there was no target on screen (1.7% of trials overall) were removed. Trials were further filtered on the basis of response time using a mild yet robust trimming procedure whereby, for each participant and cell of the experimental design, RTs were first log-transformed then any log-RT deviating from the median by more than 5 times the median absolute deviation from the median (“MADM”) was flagged for rejection. Application of trimming on the logarithmic scale assures that the slow responses and fast responses have equal weight despite the positive skew typical of RT data. Use of the median and MADM ensure robust application of trimming to a given observed RT that is less sensitive to the presence of even more extreme RTs. Application of this procedure yields a rejection of \(2\%\) of trials.
Detection and memory response data were analyzed separately, but using the same general framework for Bayesian inference. For both data types, a hierarchical model was specified such that, for each parameter of the model, a given individual participant’s value for that parameter was drawn from a Gaussian distribution. For readers familiar with the terminology of mixed effects modeling, this scheme implements a random effect of subject on all parameters, but enforces zero correlation amongst the parameters. The assumption of zero correlation was imposed for computational practicality in light of the current work’s interest in the overall effects of the manipulated variables and not individual differences nor correlations therebetween. Detection RT was modeled on the log-RT scale where trial-by-trial log-RT was taken to be Gaussian distributed with a noise term common to all trials and participants. The location parameter for the Gaussian distribution was modeled with an intercept and contrasts corresponding to the manipulated variables. Trial-by-trial memory responses were modeled as a finite mixture of a uniform “guess” response on the circular domain and a Von Mises distributed “memory” response centered on zero degrees of error. The proportion of each memory response type is captured by the parameter \(\rho\), while the concentration (i.e. fidelity) of the memory response is captured by the parameter \(\kappa\). As \(\rho\) is bounded to the domain of \(0\) to \(1\), and \(\kappa\) is a scale parameter that must be \(>=0\), the Gaussian sampling of per-participant parameter values noted above took place on the logit and log scales, respectively.
All models were specified and evaluated within the computational framework provided by \(Stan\), a probabilistic programming language for Bayesian statistical inference. For all models, a first pass at inference was conducted that imposed flat (“uninformed”) priors to provide a general range of reasonable values for the intercept and scale parameters (ex. mean log-RT, between-participants variance of mean log-RT, etc). From this first p