From Subitizing to Numerosity:Enumeration of Small Number with Visual Distractors
The number of 1～4 items can be appraised quickly and errorlessly,a phenomenon labeled subitizing.Effects of simultaneous distractor on subitizing are studied in the current study.In Experiment 1,participants were asked to report the number of target dots presented briefly in the visual filed,and to ignore distractor lines which were presented simultaneously and spatially overlapped with the target dots in each trial.Point of subjective equality(PSE)and standard deviation(SD)of estimation for all participants were analyzed in each distracting condition,and linear regression model was tested with PSE as independent variable and SD as dependent variable in each condition.SD is an efficient index of estimation precision for a certain number.Weber fraction,which measures the ability or the precision of numerosity processing irrelevant of the number to be appraised,can be calculated when we divide SD by PSE.We found that distracting items,no matter in the same or distinct colors compared with target dots,have significant effects on number estimation of target dots.Errorless enumeration for small numbers,although was revealed in the baseline condition without distracting items,disappeared in various distracting conditions.According to these results,subitizing can be disrupted by distracting lines presented with target dots.It is suggested that distracting items affect subitizing by automatically diverting attention resource.The more competitive the distractor is,the greater the disrupting effect is.Control experiment showed that subitizing only survived in number tasks which do not require separation of target and distractor,probably because the attention resource stays unaffected and sufficient for subitizing in those cases.Moreover,according to the results of regression models,it is clear that SDs increased linearly with PSE or target number,hence W fractions were constant within a range of 0.1 to 0.3 in each distracting condition.In other words,Weber's law was revealed in distracting conditions.These results further suggest that when subitizing is interrupted,number processing for 1～4 targets is taken over by numerosity mechanism,which is proposed to analyze numerosity features and is typically revealed in the processing of moderate numbers.Experiment 2 investigated occupancy effects in small number processing when target items to be appraised were presented with simultaneous distracting items.Occupancy effect,which suggests that relative spatial approaching can make two items recognized as one object and hence induce underestimating errors,is generally proposed to explain why we have limited precision in number tasks when we are asked to compare or judge moderate numbers(more than 4 items).In Experiment 2a,a programme was designed according to the simplified occupancy model,and was adopted to simulate the results in Experiment la.According to the results,occupancy model succeeded in predicting the observed results in Experiment la,as human and computer subjects showed similar error patterns.Experiment 2b showed that decrease in absolute distance between items would not increase enumeration errors,hence the observed errors are due to occupancy effect,rather than visual approaching.In summary,Experiment 2 further supports the hypotheses that simultaneous distracting items can disrupt subitizing,and that numerosity mechanism takes the job to process small number when subitizing fails.It is proposed that the robust numerosity mechanism,rather than the fragile subitizing mechanism,is more proper to be the candidate for composing the basement of our math ability.
subitizingnumerosity mechanismWeber fractionoccupancy model
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