Modeling the interaction of numerosity and perceptual variables with the diffusion model

Area of Science:

• Cognitive Psychology
• Mathematical Psychology
• Decision Science

Background:

• Integrated diffusion models explain decision-making by integrating evidence over time.
• Previous models focused on numerosity judgments but did not fully explore interactions with non-numeric perceptual variables.

Purpose of the Study:

• To extend integrated diffusion models to investigate how non-numeric perceptual variables interact with numerosity judgments.
• To examine the influence of variables like dot area and convex hull on numerosity and area perception tasks.

Main Methods:

• Four experiments were conducted using stimuli with varying numerosity, dot area, and convex hull.
• Participants performed tasks including judging relative numerosity (blue vs. yellow dots, side-by-side arrays) and total area.
• Computational models were developed, extending principled diffusion models to incorporate perceptual variables.

Main Results:

• Non-numeric variables moderated numerosity judgments, especially under high conflict, leading to perceptual dominance.
• An unexpected shift in reaction time distributions was observed in numerosity tasks, which models partially captured.
• When judging area, numerosity influenced decisions, but no leading edge effect in reaction times was found.

Conclusions:

• Integrated diffusion models provide a robust framework for studying numerical and perceptual influences in numerosity tasks.
• The context-dependency of numerical and perceptual variables is crucial for understanding decision-making.
• Further model refinement is needed to fully account for all observed reaction time patterns.