Set Size Matters: Capacity-Limited Perception of Grouped Spatial-Frequency Glyphs

Recent work suggests that shape can encode quantitative data via a mapping between value and spatial frequency (SF). However, the set-size effect when perceiving multiple SF based items remains unclear. While automatic feature extraction has been found to be less affected by set size (number of items in a group), higher-level processes for making perceptual decisions tend to require increased cognitive demand. To investigate the set-size effect on comparing integrated SF based items, we used a risk-based scenario to assess discrimination performance. Participants were asked to discriminate between pairs of maps containing multiple SF glyphs, in which each glyph represents one of four discrete levels (none, low, medium, high), forming an aggregate "risk strength" per map. The set size was also adjusted across conditions, ranging from small (3 items) to large (7 items). Discrimination sensitivity is modeled with a logistic function and response time with a mixed-effect linear model. Results show that smaller set sizes and lower overall strength enable more precise discrimination, with faster response times for larger differences between maps. Incorporating set size and overall strength into the logistic model, we found that these variables both independently and jointly influence discrimination sensitivity. We suggest these results point towards capacity-limited processes rather than purely automatic ensemble coding. Our findings highlight the importance of set size and overall signal strength when presenting multiple SF glyphs in data visualization.