Decomposing delta plots: exploring the time course of the congruency effect using inhibition and facilitation curves

Abstract

When assessing the time-course of evidence accrual in conflict tasks, delta plots are often employed to show the time course of congruency effects. However, delta plots on reaction time and response errors only capture the differences between the congruent and incongruent conditions, detailing that a pattern or shift is occurring, but not what contributes to creating these changes. To gain a clearer idea of what is causing these trends and shifts, the neutral condition can be added to conflict tasks in order to decompose the congruency effect into two components: facilitation and inhibition. Similarly, the traditional delta plot of the congruency effect can also be decomposed to capture the time-course of facilitation and inhibition in separate curves. Thus, this article endeavored to both assess the utility of inhibition and facilitation curves as a tool for parsing apart the congruency effect, and also to see how the observed patterns changed on a larger time frame. To do this, an exploratory study was conducted on three conflict task experiments (a linguistic flanker task, numeric Stroop task, and symbolic Simon task) that were run with a speed-accuracy tradeoff measure implemented as well. By observing the conflict tasks at various speed stresses, we hoped to evaluate how, or if, inhibition and facilitation change at different response thresholds. The addition of delta functions for facilitation and inhibition provided further insight into base mean RT data. The results also provided evidence for numerous assumptions regarding cognitive control, such as a dominant effect of inhibition driving most of the congruency effect.

Fig. 1

This figure describes a visual interpretation and predictions of the Shrinking Spotlight Model (left) and the Diffusion Model of Conflict (right). For the Shrinking Spotlight Model, the shrinking focus (top left) is displayed such that, over time, the amount of attention given to the flankers is lessened, and instead allotted to the central target. The resulting model is shown below, with blue indicating the congruent condition and red indicating the incongruent condition. For the Diffusion Model of Conflict, the top-right shows the rate of accrual for the automatic processes (red and blue lines) as well as the controlled process (dashed black line). Upon being superimposed, the graph (bottom right) is the result, with congruent and incongruent conditions color-coded the same as with SSP

Fig. 2

Above is a figure displaying the difference in expected evidence accumulation for DMC between the Simon and flanker tasks. The expected drift rates for the congruent condition (blue) and incongruent condition (red) are shown for each task. Parameter settings for these were taken from Ulrich et al. (2015). While the difference between the rates shrinks in the Simon task, the difference increases for the flanker task, reflecting an expected increase in congruency effect. By adding a neutral condition (black), it is also easy to see how the difference between the three lines changes over time

Fig. 3

The graphs above display facilitation and inhibition plots for DMC and SSP with different response speed conditions: accuracy-focused responses and speed-focused responses. The simulated inhibition, facilitation, and congruency effects for the accuracy-focused responses are shown on the left, with those for the speed-focused responses shown on the right. Parameter settings were held constant from Fig. 1. These were generated from 100,000 trial simulations for the congruent, neutral, and incongruent conditions. The SAT conditions were manipulated by setting the boundary condition for DMC to 31.30 for speed-focused responses and 71.30 for accuracy-focused responses. Boundary values of 2000 and 4000 were used for SSP. Consult the code resources for further details and scaling

Fig. 4

The stimuli for each task are presented across the three experiments, with the linguistic flanker task in the top row, the numeric Stroop task in the second row, and the symbolic Simon task in the third row. The corresponding response key is placed in the bottom row, with the three conditions changing between the columns

Fig. 5

SAT Flanker task: percent correct and mean RT as a function of congruency and stimulus type. Mean RT is shown on the bottom, percent correct is on upper half. The error bar shows $M\pm SE$

Fig. 6

Top Row: Inhibition and facilitation delta plots for the flanker task. It is notable that an increasing dominance of inhibition was seen across the response focus conditions, while facilitation displayed either a stable, low effect, or a decreasing effect within a given response focus condition. Bottom Row: Percent error delta functions for the flanker task were added for completeness, and show an increasing effect of congruency on response focus. This is expected as faster responses often show lower accuracy.

Fig. 7

SAT Stroop task: percent correct and mean RT as a function of congruency and stimulus type. Mean RT is shown on the bottom, percent correct is on upper half. The error bar shows $M\pm SE$

Fig. 8

Top Row: Inhibition and facilitation delta plots for the Stroop Task are displayed. While the tail behavior appears to shift significantly for facilitation, the overall pattern of inhibition and facilitation remains similar across the response speed conditions. Bottom Row: The delta function for percent error is added for completeness once again, revealing similar effects as in Experiment 1. The means for binned RT are along the x-axis, with change in percent error along the y-axis.

Fig. 9

SAT Simon task: percent correct and mean RT as a function of congruency and stimulus type. Mean RT is shown on the bottom, percent correct is on upper half. The error bar shows $M\pm SE$

Fig. 10

Top Row: Inhibition and facilitation delta plots for the Simon Task are displayed with time in seconds as the x-axis and change in RT is on the y-axis. While the Stroop task showed similar overlap between the two functions, the Simon task exhibits both this overlap as well as significant differences in tail behavior, particularly in the accuracy condition. Bottom Row: The percent error delta functions for facilitation and inhibition is displayed, with change in percent error presented against binned RT.

Fig. 11

Figure displaying facilitation and inhibition plots for DMC’s prediction for the Simon task with speed condition (left) and accuracy condition results (right). Parameter settings were held constant from the original DMC article (Ulrich et al., 2015). These were generated from 100,000 trial simulations for congruent, neutral, and incongruent conditions. The SAT conditions were obtained via setting the boundary condition for DMC to 34.56 for speed and 74.56 for accuracy. Consult the code resources for further details and scaling.