Small numerosity advantage for sequential enumeration on RSVP stimuli: an object individuation-based account

Abstract

Although there is a large literature demonstrating rapid and accurate enumeration of small sets of simultaneously presented items (i.e., subitizing), it is unclear whether this small numerosity advantage (SNA) can also manifest in sequential enumeration. The present study thus has two aims: to establish a robust processing advantage for small numerosities during sequential enumeration using a rapid serial visual presentation (RSVP) paradigm, and to examine the underlying mechanism for a SNA in sequential enumeration. The results indicate that a small set of items presented in fast sequences can be enumerated accurately with a high precision and a SOA (stimulus onset asynchrony)-sensitive capacity limit, essentially generalizing the large literature on small numerosity advantage from spatial domain to temporal domain. A resource competition hypothesis was proposed and confirmed in further experiments. Specifically, sequential enumeration and other cognitive process, such as visual working memory (VWM), compete for a shared resource of object individuation by which items are segregated as individual entities. These results implied that the limited resource of object individuation can be allocated within time windows of flexible temporal scales during simultaneous and sequential enumerations. Taken together, the present study calls for attention to the dynamic aspect of the enumeration process and highlights the pivotal role of object individuation in underlying a wide range of mental operations, such as enumeration and VWM.

Appendix

Results of experiment 1d, 1e and 1f

Experiment 1d: 200–100 ms, Experiment 1e: 150–150 ms and Experiment 1f: 50–250 ms (all had 300 ms SOAs)

An ANOVA on percent error rate was conducted in Experiment 1d. A significant main effect of numerosity (Greenhouse–Geisser corrected) was found, F(3.08, 49.33) = 32.976, p < 0.001, $\eta_{\text{p}}^{2}$ = 0.673. The classification criteria were the same as in Experiment 1c, i.e., all the numerosity levels were classified into a small numerosity range from 1 to 3 (ps > 0.99) and a large numerosity range from 4 to 10 (ps < 0.032). One sample t test demonstrated no significant difference between the mean error rate and the response-induced random error of 5% in the small numerosity range, t(16) = 0.058, p = 0.954, Cohen’s d = 0.014, mean = 0.051, SE = 0.017, but a significant difference in the large numerosity range, t(16) = 6.256, p < 0.001, Cohen’s d = 1.517, mean = 0.430, SE = 0.061. Meanwhile, the mean error rates in the small numerosities were significantly lower than those in the large numerosities, t(16) = − 7.135, p < 0.001, Cohen’s d = − 1.998, mean difference = − 0.379, SE = 0.053. Analyses on AC demonstrated bias-free numerical reporting in the small numerosity range, t(16) = 1.247, p = 0.230, Cohen’s d = 0.302, mean = 0.009, SE = 0.007. However, the mean AC was significantly lower than 0 in the large numerosity range, t(16) = − 3.868, p < 0.002, Cohen’s d = − 0.938, mean = − 0.073, SE = 0.019, indicating a significant underestimation during serial subvocal verbal counting. A paired samples t test demonstrated a significantly lower mean VC, i.e., a higher precision, in the small numerosity than in the large numerosity, t(16) = − 2.115, p = 0.05, Cohen’s d = 0.652, mean difference = − 0.032, SE = 0.015. The logistic fittings on error rates demonstrated a mean SNA capacity of 6.02 (SE = 0.56; average R² = 0.92, SE = 0.02).

Experiment 1e showed similar results as Experiment 1c and 1d. A significant main effect of numerosity was found based on error rate data (Greenhouse–Geisser corrected), F(3.28, 52.41) = 66.327, p < 0.001, $\eta_{\text{p}}^{2}$ = 0.806. With the same criteria as in Experiment 1c, all the numerosity levels were classified into a small numerosity range composed of level 1 to level 4 (ps > 0.10) and a large numerosity range composed of level 5 to level 10 (ps < 0.003). Analyses demonstrated no significant difference between the error rate in the small numerosity range and the response-induced random error (5%), t(16) = 1.482, p = 0.158, Cohen’s d = 0.359, mean = 0.088, SE = 0.026, but a significant difference between mean error rate in the large numerosity range and 5%, t(16) = 9.542, p < 0.001, Cohen’s d = 2.314, mean = 0.623, SE = 0.060. Meanwhile, the mean error rates in the small numerosities were significantly lower than those in the large numerosities, t(16) = − 11.581, p < 0.001, Cohen’s d = − 2.717, mean difference = − 0.535, SE = 0.046. Analyses on AC and VC demonstrated a bias-free (t(16) = − 1.518, p = 0.149, Cohen’s d = − 0.368, mean = − 0.013, SE = 0.009), higher-precision (t(16) = − 3.254, p < 0.006, Cohen’s d = − 0.965, mean difference = − 0.038, SE = 0.012) enumeration processing in the small numerosity range and a significant underestimation (t(16) = − 5.821, p < 0.001, Cohen’s d = − 1.412, mean = − 0.118, SE = 0.020) in the large numerosity range, which were all qualitatively in agreement with Experiment 1c and 1d. The logistic fittings on error rates demonstrated a mean SNA capacity of 5.33 (SE = 0.34; average R² = 0.93, SE = 0.02).

Similar results were also found in Experiment 1f. A significant main effect of numerosity (Greenhouse–Geisser corrected), F(2.43, 41.23) = 38, p < 0.001, $\eta_{\text{p}}^{2}$ = 0.691, was found for error rate data. Similar to Experiment 1c, Experiment 1f classified all the numerosity levels into two numerosity ranges with the same criteria, i.e., a small numerosity range from level 1 to level 3 (ps > 0.99) and a large numerosity range from level 4 to level 10 (ps < 0.05). Analyses on error rate demonstrated no significant difference between the mean error rate in the small numerosity and the response-induced random error (5%), t(17) = 0.37, p = 0.716, Cohen’s d = 0.087, mean = 0.056, SE = 0.018. However, the error rate in the large numerosity was significantly higher than the response-induced random error (5%), t(17) = 6.41, p < 0.001, Cohen’s d = 1.510, mean = 0.521, SE = 0.073. Meanwhile, the mean error rates in the small numerosities were significantly lower than those in the large numerosities, t(17) = − 7.260, p < 0.001, Cohen’s d = − 1.987, mean difference = − 0.464, SE = 0.064. Analyses on AC and VC demonstrated bias-free (t(17) = − 0.869, p = 0.397, Cohen’s d = − 0.205, mean = − 0.007, SE = 0.008), higher-precision (t(17) = − 2.143, p < 0.05, Cohen’s d = − 0.488, mean difference = − 0.025, SE = 0.012) enumeration processing in the small numerosity range and a significant underestimation (t(17) = − 3.823, p < 0.002, Cohen’s d = − 0.901, mean = − 0.127, SE = 0.033) in the large numerosity range. The logistic fittings on error rates demonstrated a mean SNA capacity of 5.82 (SE = 0.54; average R² = 0.91, SE = 0.03).