1. Subitizing, pre-attentive processes and expertise
Roy Allen & Peter McGeorge
School of Psychology, University of Aberdeen

2. Introduction 1 Navigation through the environment
Visual Indexing theory (e.g., Pylyshyn & Storm, 1988)
Evidence from multiple-object tracking (MOT) task:
Target Acquisition (TA) and Target Tracking (TT) phases
TA – preattentive indexing (circa 4), then modality-specific attentional/strategic processes
TT – iterative central executive processes (Allen et al., in press)

3. Introduction 2
Also affected by the extent to which target elements can be grouped (Yantis, 1992):
Yantis suggests tracking may involve a higher-order virtual object (virtual polygon) spontaneously formed from active indexes
For example, novice participants given a grouping clue have an immediate advantage but this disappears with practice – suggesting an expertise effect, something reported by Allen et al., 2004 and associated with the TA phase’s modality-specific attentional/strategic (grouping?) processes.

4. Introduction 3
Trick and Pylyshyn (1993,1994) suggest that subitizing – our apparent ability, with small numbers of elements, to instantly quantify them without the need to count them individually – is also underpinned by visual indexing
i.e., the indexing of elements is preattentive and occurs in a parallel way that makes them all available simultaneously for subsequent attentional processing

5. Introduction 4
Given that the MOT task and subitizing are thought to share a common, indexing process, we might expect performance on an enumeration task to benefit from stimuli that facilitate the formation of a virtual polygon and be hindered by those that resist it (i.e., stimuli composed of elements arranged linearly). Experiment 1 will investigate this
Further, given Allen et al.’s (2004) findings, it might be expected that, in an enumeration task, experts will show better performance than novices when stimuli can be readily grouped, but equivalent levels of performance when grouping is effectively removed. Experiment 2 will investigate this

6. Experiment 1
Participants: 27 psychology students (6 males) aged between 18 and 44 years (M = 25.3, SD = 7.93), all with normal or corrected-to-normal vision
Materials: bitmaps of from 1 – 6 identical items (+’s), whose extents were always defined by a notional 50mm dia circle at the screen’s centre. Items were arranged in regular polygons (triangles, squares, pentagons, hexagons), straight lines and intermediate “collapsed” polygons – see over
Stimuli were displayed using E-Prime running on a 350mhz Pentium II PC with 17-inch monitor set to a resolution of 800 x 600 (SVGA) at a viewing distance of approx 57cm.

7. Stimuli +

8. Paradigm Fixation – 500ms Blank – 500ms+
+ +
Stimulus presentation – 17/34/51ms
Response – unlimited time
respond

9. Design Within-subjects
Number of items (1 – 6) x arrangement (canonical, collapsed, linear) x presentation time (17, 34, 51ms – multiples of the refresh rate)
Arrangements’ orientations were varied to reduce long-term memory pattern learning
Presentation order completely randomised
Total of 864 trials
Duration circa 45 minutes
Note: participants were told there were from 1 – 7 items in the stimuli to minimise any end effect (Simon, Peterson, Patel, & Sathian, 1998)

10. Data

11. Results 1
Hierarchical regression analysis (% accuracy data) - significant quadratic component supportive of a two-process account of enumeration (i.e., subitizing/counting)
Repeated-measures ANOVA (collapsed over arrangement): main effects of presentation time (longer durations lead to greater accuracy) and number of items (the greater the number of items the poorer the accuracy).
Post-hoc t-tests for latter showed performance only varied significantly for trials containing 4 versus 5 and 5 versus 6 items (i.e., subitizing – 1-4 items; counting – 5-6 items)
No significant interaction between presentation time and number of items

12. Data

13. Results 2
Repeated-measures ANOVA, including arrangement but collapsed over presentation time, for trials containing 3 – 6 items:
Main effects of number of items and arrangement, but these were moderated by a significant interaction between the two
Post-hoc t-tests showed that arrangement only had a significant impact when there were more than 4 items per stimulus, such that accuracy for linear arrangements differed significantly from both canonical and collapsed arrangements
Canonical and collapsed arrangements did not differ significantly from each other

14. Conclusions:
We have reaffirmed the fact that the number of items in the display has little influence on enumeration performance for stimuli containing up to four items
Further, that once stimuli contain more than four items performance deteriorates with each additional item
This reiterates the notion that two different processes seem to be involved, one dominating when the stimuli contain up to four elements (the subitizing range) and the other when the stimuli contain a greater number of elements (the counting range)
Compared to the linear arrangements both the canonically-arranged stimuli and the collapsed versions of the canonical stimuli result in better performance
However, grouping information only appears to benefit performance when the display contains more than four items. That is, the grouping advantage only occurs outside of the range in which subitizing is thought to occur

15. Experiment 2
Participants: Eighteen students (8 females) at the University of Aberdeen, aged between 18 and 27 (M = 20.50, SD = 2.77), and 18 civilian air traffic controllers (ATCs) (2 females) employed at Aberdeen airport, aged between 26 and 56 (M = 39, SD = 8.56), all with normal or corrected-to-normal vision
The latter’s experience as ATCs ranged between 1 and 37 years (M = 14.83, SD = 11.11)
ATCs were chosen because the nature of their work, in monitoring display screens for long periods of time, tracking multiple targets and responding appropriately, would qualify them as experts as regards an MOT task, something together with subitizing thought to be underpinned by visual indexing
Materials: same as Experiment 1
Stimuli were displayed using Superlab Pro with 17-inch monitor at a viewing distance of approx 57cm.
The design and procedure were the same as in Expt. 1 except that hardware changes resulted in different stimulus presentation times (13 & 26ms – multiples of refresh rate) and “expertise” was an additional, between-subjects variable

16. Results 1
Hierarchical regression analysis (% accuracy data) – only produced a significant quadratic component, supportive of a two-process account of enumeration (i.e., subitizing/counting), for the 26ms presentation times. 13ms performance appeared to show a linear decline without the subitizing “plateau”. All subsequent analyses were therefore only carried out using the 26ms data
Repeated-measures ANOVA (collapsed over arrangement and with Expertise as the between-subjects variable): main effects of number of items and expertise moderated by a significant interaction between the two
Post-hoc t-tests showed, for trials containing 1 – 4 items, novices performed as well as experts. For trials containing 5 and 6 items, experts were significantly more accurate than novices

17. Data

18. Results 2
Repeated-measures ANOVA, including arrangement and expertise, for trials containing 3 – 6 items:
Again, main effect of expertise (experts’ accuracy was significantly greater than that of novices)
Again, main effects of number of items and arrangement, but these were moderated by a significant interaction between the two (the effect of arrangement only manifested itself with greater than 4 items per stimulus)
a marginal three-way interaction of number of items by arrangement by expert gave some support to the initial predictions, and this was confirmed by post-hoc t-tests that showed experts significantly out-performed novices on canonical and collapsed shapes, but not linear arrangements

19. Expertise by Arrangement

20. Conclusions:
Once again, the number of items in the display has little influence on performance for stimuli containing up to four items. once stimuli contain more than four items performance deteriorates with each additional item. Supports a two-process system
Compared to linear arrangements both the canonically-arranged stimuli and the collapsed stimuli result in better performance. But, grouping information only appears to benefit performance significantly with displays of more than four items (i.e., during counting)
Experts out-perform novices, but mainly this is with arrangements that are readily grouped (canonical, collapsed). When grouping is effectively removed performances do not differ significantly (linear)

21. General Discussion 1
These experiments have reinforced and added to our understanding about enumeration’s two processes
To quantify from 1 to 4 items seems effortless and seldom inaccurate (subitizing)
For greater than 4 items, quantification is more difficult, increasingly inaccurate and benefits from grouping information (counting, i.e., attentionally-based)
Experts outperform novices overall, but significant differences in performance are evident for stimuli containing more than 4 items whose arrangement can be readily grouped

22. General Discussion 2
Previously, researchers have shown both a beneficial grouping effect (Yantis, 1992) and an expertise effect (Allen et al., 2004) in a dynamic multiple-object tracking (MOT) task
This research has demonstrated similar grouping and expertise effects in a static enumeration task
The enumeration task is very much like the target acquisition phase of the MOT task
Therefore, whilst this research does not conclusively show that experts are better at the MOT task because of their superior grouping ability, it does provide strong evidence that, if this is the case, then experts already have such advantage before objects begin to move in the MOT task

23. References
Allen, R., McGeorge, P., Pearson, D. & Milne, A.B. (2004). Attention and expertise in multiple target tracking. Applied Cognitive Psychology, 18,
Allen, R., McGeorge, P., Pearson, D. & Milne, A.B. (in press). Multiple-Target Tracking: A role for Working Memory? Quarterly Journal of Experimental Psychology.
Pylyshyn, Z.W. & Storm, R.W. (1988). Tracking multiple independent targets: Evidence for a parallel tracking mechanism. Spatial Vision, 3(3),
Simon, T.J., Peterson, S., Patel, G., & Sathian, K. (1998). Do the magnocellular and parvocellular visual pathways contribute differentially to subitizing and counting? Perception and Psychophysics, 60,
Trick, L.M. & Pylyshyn, Z.W. (1993). What enumeration studies can show us about spatial attention: Evidence for limited capacity preattentive processing. Journal of Experimental Psychology: Human Perception and Performance, 19(2),
Trick, L.M. & Pylyshyn, Z.W. (1994). Why are small and large numbers enumerated differently? A limited capacity preattentive stage in vision. Psychological Review, 101(1), 1-23.
Yantis, S. (1992). Multi-element visual tracking: Attention and perceptual organization. Cognitive Psychology, 24(3),