The hazard (functions) of detecting the pounce on the prey

How many things can we attend to simultaneously? Imagine being an air traffic controller and you are monitoring O’Hare arrivals on the day before Thanksgiving. How many aircraft can you attend to simultaneously?

Or imagine watching a flock of grazing impalas in Krueger National Park or the Serengeti while a pride of lions is casually strolling in surprising proximity. (They do seem to come closer to each other than I would have ever thought possible.) How many lions can you keep track of when you are trying to determine when one of them starts to pounce?

A recent article in the Psychonomic Society’s journal Attention, Perception, & Psychophysics explored people’s performance in a task resembling the Serengeti situation. Researchers Joseph Lappin, Douglas Morse, and Adriane Seiffert created displays in which a varying number of black dots were moving randomly. At some unpredictable point in time, one of those dots would start moving towards a “prey” (a red dot), which had also been moving randomly and unpredictably among the “predators”. The figure below shows the stimulus display at two points in time:

In the frame on the left the impala and the lions are moving at random. A short while later, in the frame on the right, one of the lions has started pouncing. The “pounce” consisted of a straight linear motion towards the prey.

The observers were trained extensively before the experiment proper commenced. During the experimental session, observers pressed the space bar as quickly as possible the moment they detected the onset of the target motion.

This task differs in at least one important way from some of the conventional visual attention tasks we have discussed in other posts on this page: Unlike other visual-attention tasks, there is no defined onset of a “trial” in this paradigm because the critical events can happen at any moment (after a refractory period of 1/5th of a second following the preceding response).

Lappin and colleagues conducted three experiments using this basic paradigm with only minor variations between them. The main experimental variable of interest was the set size—that is, the number of “predators” that were waiting to pounce. The principal dependent variable was the time taken to detect that a pounce had commenced. (Accuracy was very high and was of lesser interest). The figure below shows the data from the first experiment:

It is obvious that the response time increases with set size, suggesting that the difficulty of distributing attention across multiple targets increases with the number of such targets. Specifically, each additional target slowed responding by an additional 60 milliseconds.

This result supports a large body of literature which shows that as additional targets are added, responding is slowed by a constant amount. In many situations, this finding has been interpreted as being indicative of a serial search, such that people scan each of the “predators” in turn, thereby taking more time on average to detect a “pounce” when there are more targets to monitor. Until recently, the interpretation of results would have ended there. However, we now have more sophisticated means of data analysis available, and Lappin and colleagues pushed their interpretation considerably further.

This is where things get to be a bit tricky and a bit more mathematical, but the end result makes this complication worthwhile.

Note that in the figure above, a further notable aspect of the data is the increasing standard deviation (represented by the error bars) with set size. To explore this increase in variability, Lappin and colleagues computed hazard functions. In a nutshell, hazard functions describe the probability of an event occurring in the next time interval, given that it has not yet occurred. For example, one’s mortality rate at any given age is described by the hazard function for human life expectancy, which from middle age onward, increases with age. Upon some mathematical transformations, the details of which need not concern us here, hazard functions can be converted to a scale that is expressed in bits, where each bit corresponds to a 50% reduction in the probability of an event not having occurred yet.

In the context of the experiment by Lappin and colleagues, the bits correspond to a 50% reduction in the probability of the “pounce” on the target not having been detected yet at a given point in time after the target motion commenced. This result is shown in the figure below:

So for set size 8, the probability of not having responded yet was cut in half—to 50%—after around 1 second, and it was reduced by a further 50%—i.e., to 25%—after another 250 milliseconds (so 1.25 seconds total), and so on.

The most provocative aspect of the results of Lappin and colleagues is shown in the final graph below, which plots the slope of the hazard functions in the above figure (adjusted by differences in set size):

And voila!

Two new properties emerge from the data: First, the set size effect disappears, and second, irrespective of set size, the functions flatten out with a distinct kink and reach a common asymptote. Both features are captured by the solid black line, which successfully models the data from the entire experiment.

Lappin and colleagues interpret these results as revealing two parallel (i.e., independent and concurrent) visual processes that are selectively affected by two different variables: There is one process that is affected by set size but is invariant across time, and there is another process that is affected by time but is invariant across set sizes.

Lappin and colleagues suggest that the first process represents the rate of visual awareness and detection—that is the rate at which a target would be detected—and that this hazard rate was proportional to set size (specifically, the reciprocal of set size; 1/n). Across a wide range of set sizes and response times, those detection rates were described by a single parameter, representing a constant capacity limit of visual attention.

The second process was identified as integration of the visual motion paths of the various “predators”. Remarkably, the motion integration times were invariant with set size and mean response times.

Although the interpretation of those two processes may be up for continued discussion, it is clear that the interpretation of response-time data via hazard functions represents a powerful tool. As Lappin and colleagues put it, “The effects of divided attention on the temporal process of target detection were very large, but surprisingly simple and consistent.” In an email, Joe Lappin pushed this point further, noting that “this study served to clarify three inter-dependent concepts and measurement problems concerning (a) capacity, (b) quantifying behavioral performance, and (c) the complexity of input information.”

This conclusion would not have been possible by inspecting mean response times and accuracy alone. As we have noted previously on several occasions, statistical and computational modeling provides insights into cognition that conventional data analysis cannot achieve.

Article focused on in this post:

Lappin, J. S., Morse, D. L., & Seiffert, A. E. (2016). The channel capacity of visual awareness divided among multiple moving objects. Attention, Perception, & Psychophysics. DOI: 10.3758/s13414-016-1162-z.

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