Article Figures & Data
Figures
- Figure 1.
The behavioral task used in experiment 1. Subjects were required to enumerate the number of blue or green squares (target color was counterbalanced across observers) appearing in one hemifield of a visual display. Before the onset of the target display, subjects were shown a spatial cue that indicated the hemifield where targets would subsequently appear with 100% validity. The target display was followed by a 300 ms blank interval and a response cue.
- Figure 2.
Behavioral performance in experiment 1. A, Mean response error (±1 SEM) across subjects is plotted as a function of set size. B, Data from a representative participant. To distinguish between fixed-capacity and continuous estimation models of subitizing, each subject's error rate by set size function was fit with exponential and bilinear functions (see Materials and Methods). C, Subjects' mean responses (ordinate) are plotted as a function of set size (abscissa). Error bars (±1 SEM) are subsumed by the data symbols at all set sizes. Values above the unity line reflect a proclivity to overestimate the number of targets present, whereas values below it reflect a proclivity to underestimate the number of targets present. Because subjects tended to systematically underestimate the number of targets present in large arrays (e.g., set sizes 8 and 10), most modeling was performed using data from set sizes 1–5.
- Figure 3.
Electrophysiological responses observed in experiment 1. A, Grand-averaged ERP difference waves (defined as the difference in amplitude between contralateral and ipsilateral electrode sites O1/2, OL/R, and PO3/4) time locked to the onset of the target array are plotted as a function of set size (colors). By convention, negative is plotted upward. We defined the N2pc as the mean amplitude observed during a period 200–300 ms after the onset of the target array. B, Mean N2pc amplitudes (diamond symbols, error bars are ±1 SEM) are plotted as a function of set size. Note that N2pc amplitudes increase monotonically with set size from set sizes 1–3 before reaching a stable asymptote at set sizes 4–10. The best-fitting fixed-capacity (red line) and continuous estimation (blue line) models are overlaid. C, Individual differences in subitizing span (defined via the inflection point of a bilinear function fit to each subject's error rate by set size function) were strongly correlated with N2pc slopes (defined as the difference in mean amplitude between set sizes 2 and 5). D, Individual differences in subitizing span derived from subjects' behavioral performance (abscissa) were strongly correlated with estimates of subitizing span derived by fitting each subject's N2pc by set size profile with a bilinear function (ordinate). E, Mean electrophysiological responses observed during a period from 200–300 ms after the onset of the target array are plotted as a function of set size (abscissa) and electrode site (contralateral vs ipsilateral to the cued hemifield; square and diamond symbols, respectively). Set-size-dependent changes in electrophysiological responses were observed over contralateral, but not ipsilateral, electrode sites (see Results). Error bars are ±1 SEM.
- Figure 4.
RT data from experiment 1. A, Mean RTs across subjects are plotted as a function of set size. Error bars are ±1 SEM. B, Data from a representative participant. Note that the profiles depicted in both panels are similar to the group- and single-subject error rates depicted in Figure 2, A and B.
- Figure 5.
Behavioral performance in experiment 2. A, Mean response errors across subjects are plotted as a function of set size and trial type (i.e., non-catch vs catch trials; blue and red lines, respectively). Error bars are ±1 SEM. B, As in experiment 1, subjects typically underestimated the number of targets present in large arrays. Thus, we modeled each subject's error rate by set size function using data from set sizes 1–5.
- Figure 6.
Electrophysiological responses observed in experiment 2. A, Grand-averaged ERP difference waves time locked to the onset of the target array are plotted as a function of set size. B, Mean N2pc amplitudes (diamond symbols; units are microvolts; error bars are ±1 SEM) are plotted as a function of set size. As in experiment 1, N2pc amplitudes increased monotonically across set sizes 1–3. C, Like experiment 1, individual differences in subitizing span were strongly correlated with N2pc slopes (defined here as the mean difference in amplitude between set sizes 1 and 3, 1 and 4, and 1 and 5; this correlation was significant when each of these set size pairs were considered independently; see Results). The relationship between subitizing span and N2pc slopes remained significant when the obvious outlier (red diamond) was removed (r = 0.59, p < 0.01). D, In contrast to the results of experiment 1, individual differences in estimates of subitizing span derived from subjects' behavioral performance did not predict span estimates obtained by modeling each subject's N2pc by set size response profile. E, Mean electrophysiological responses observed during a period from 200–300 ms after the onset of the target array are plotted as a function of set size (abscissa) and electrode site (contralateral vs ipsilateral to the cued hemifield; squares and diamonds, respectively). As in experiment 1, set-size-dependent changes in electrophysiological responses were observed over contralateral, but not ipsilateral, electrode sites (see Results). Error bars are ±1 SEM.
Tables
Mean adjusted r2 Minimum adjusted r2 Maximum adjusted r2 Fixed-capacity set sizes 1–5 0.94 0.72 0.99 Continuous estimation set sizes 1–5 0.87 0.58 0.99 Fixed-capacity set sizes 1–10 0.56 0.13 0.99 Continuous estimation set sizes 1–10 0.62 0.14 0.98 Mean adjusted r2 Minimum adjusted r2 Maximum adjusted r2 Fixed-capacity set sizes 1–5 0.89 0.32 0.99 Continuous estimation set sizes 1–5 0.87 0.43 0.99 Fixed-capacity set sizes 1–12 0.81 0.17 0.96 Continuous estimation set sizes 1–12 0.82 0.15 0.97
