How do humans process numbers

• In Event: Poster Session 06
  In Poster Session: PS 06 Topic - Cognitive Processes

Abstract

The subject’s task was to estimate the relative numerosity of two arrays of dots within a brief time so that counting was impossible. Previous studies showed that longer stimulus duration improves judgement accuracy (Inglis & Gilmore, 2013; Wood & Spelke, 2005) and the current study aims at testing three hypotheses on why the duration might improve performance.

The first hypothesis is that humans enumerate visual items in sequence (instead of in parallel). If this hypothesis is correct, at a given stimulus duration, larger set size of the dot array should lead to lower judgement accuracy. To test this hypothesis, the number of dots in two arrays and the stimulus duration (100ms vs. 500ms) was varied in Experiment 1. To exclude the confounding effects of continuous dimensions, we also manipulated item size to produce three different conditions: number-total area congruent, (2) number-total area incongongruent (3) total area equated.

Similar to results in previous studies, data from Experiment 1 indicated that longer stimulus durations did lead to higher judgement accuracy (M100ms = 0.575, M500ms = 0.649, F (1, 13) = 30.632, p < .001). However, set size did not have a general effect on judgement accuracy, suggesting that items were not enumerated in a serial fashion.

The second hypothesis is that we may estimate numbers not by pulling a single sample from the distribution for a given magnitude, but by pulling multiple samples (Inglis et al., 2013). The greater the stimulus duration, the more samples can be drawn, and the more accurate the estimate. The third competing hypothesis is that although we can extract numerosity relevant information very quickly, processing such information requires more time. A backward visual mask could erase iconic memory and therefore inhibit further processing.

Experiment 2 tested these two hypotheses by manipulating the mask delay (0ms vs. 400ms) while keeping stimulus duration constant (100ms). Results of Experiment 2 suggested that adding a time delay between stimulus and mask indeed improved accuracy (M0ms = 0.606, M400ms = 0.638, F(1, 14) = 19.842, p < .001), therefore supporting the third hypothesis. Analyses on the pooled data from both experiments revealed no significant difference in accuracy between the 500ms stimulus duration condition and the 100ms stimulus duration + 400ms delay condition (F (1, 28) = 0.155, p = .697).

Other than the results directly related to the three hypotheses, joint analysis of the two experiments also showed a significant interaction (Greenhouse Geisser adjusted F (1.448, 39.092) = 19.792, p < .001) between total-area/number congruency conditions and time (here defined as the ISI between stimulus and visual mask). Longer access to stimui, no matter from image or memory, improved performance only in the congruent (Mdif = 0.094, F (1, 28) = 53.562, p <.001) and equated conditions (Mdif = 0.053, F (1, 28) = 39.106, p <.001), not the incongruent condition (Mdif = 0.016, F (1, 28) = 1.628, p =.212). This raises more questions: at what stage and how do continuous dimensions influence number judgement, which needs further research.

Authors

• Yanfei Yu, University of Missouri - Columbia
  Presenting Author

• Kristy Vanmarle, University of Missouri - Columbia
  Non-Presenting Author