A New Method for Quantifying Attention: Results Support Optimizing Theory

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    • 00:00


    • 00:10

      SPEAKER: The coauthors were quite ableBoston College undergraduates, who recently graduated.And relating what I'm going to talkabout to the theme of this section,is perhaps the idea that, when it comes to cognitive control,it operates according to principles,

    • 00:32

      SPEAKER [continued]: and I would argue quantitative principles,and to the value of the stimuli that our cognition isfocusing on.So let me begin with the question thatprompted this research project, and then I'll

    • 00:52

      SPEAKER [continued]: follow with the description of the procedure.Following that I'll give the mathematical model thatwe use to calculate attention, and thenfinally, in the last minute, or so, I'll describe all the data.So the question I asked was, do the principles

    • 01:16

      SPEAKER [continued]: that govern the allocation of overt behavior,as in economic activity, or experiments on choice,do those principles also apply to the allocationof cognitive resources as in attention studies?And the choice literature provides uswith many, many, many principles.

    • 01:38

      SPEAKER [continued]: The two that were most relevant to the procedurethat we developed, was the kind of maximizingthat you read about in economic textbooks,and that is that, individual consumers spread outtheir income so as to maximize utilityover all possible options.Applying it to an attention study,

    • 02:00

      SPEAKER [continued]: we could say that individuals allocate attention,so as to obtain the value-- the mostvalue from all of the stimuli.Implicit in this account is the ideathat attending to a stimulus, an activity, a thought,provides value.Another competing idea comes from psychological experiments,

    • 02:26

      SPEAKER [continued]: or competing principle, rather, is something called,probability matching, and in these kindsof experiments, sometimes referred to as two armed banditstudies.The individuals allocate their behaviorso that the probability of a responseis equal to the probability that that response is rewarded.

    • 02:50

      SPEAKER [continued]: In the procedure that we use, these two approaches,these two principles, predict very different relationshipsbetween the allocation of attention and the stimuli.The maximizing view predicts a step function,or a sigmoid relationship, between the allocation

    • 03:11

      SPEAKER [continued]: of attention, and the value of the stimulithat the subject is exposed to.Probability matching predicts a linear relationshipbetween the allocation of attentionand the value of the stimuli, so we canidentify concrete predictions.However, we didn't have a way of measuring

    • 03:36

      SPEAKER [continued]: the allocation of attention in a fashion thatwould allow us to discriminate between a linear relationshipand a sigmoid over relationship.So our first task was to develop a procedure thatwould allow us to make those kinds of measurements.And I'm going to describe the procedure,and then it leads to an equation.

    • 03:57

      SPEAKER [continued]: And the solution to the equation is the allocation of attention,our desired quantity.So the procedure consists of two kindsof sessions, a calibration session,

    • 04:18

      SPEAKER [continued]: and an experimental session.Each session is composed of a series of trials,and each trial has three parts, a preparatory part, and thenpresentation-- the screen presents a stimulus.The stimulus in this study were six digits arranged

    • 04:41

      SPEAKER [continued]: in two rows of three each.And then there was a probe screen, following the stimulusscreen, and the probe screen listed in a columnseven numbers, which we can call sums.One of those numbers was equal to the sumof either the top row of stimulus, the top row, which

    • 05:04

      SPEAKER [continued]: was the three digits in the top row,or the three digits in the bottom row.These were very actually small stimulitaking well within a view of the fixed gaze,and we've measured that with eye tracking,and also just calculating it we know that it'swithin the [INAUDIBLE].So the subject's task then is to add the three digits

    • 05:29

      SPEAKER [continued]: one of these rows, and find the matching sum in the probescreen.What makes this an attention task, a selective task,is that, in the calibration session,we adjust the exposure time, how long the stimulus isavailable to the subject, so that the subject can accurately

    • 05:51

      SPEAKER [continued]: extract the information for one set of digits,one row of digits, but not for both row of digits.And we do this by having cued and non-cued trials.On cued trials the subject is toldwhich row is going to have the correct answer,and we look for performance, we adjust itso that the subject can just about do it 100% of the time.

    • 06:15

      SPEAKER [continued]: And then on uncued trials, where the subjectdoesn't know which row is going to have the correct sum,the subject is responding at chance.And so we set up a situation, at least in principle,based on the calibration, where the subject isable to extract information from one of the two stimuli,but not from both.

    • 06:35

      SPEAKER [continued]: So now I'm going to show you, I'vemade a simulation of how the procedure works.I'm going to show you two cued trials, and onenon-cued trials, and they go rather quickly.So let's see what happens.

    • 06:58

      SPEAKER [continued]: OK, so did you get that?So, OK.And now a non-cued trial.And this is based on his experiment.

    • 07:21

      SPEAKER [continued]: OK, so these, here they're about--and actually I turned out, when we calibratedsubjects, the average exposure time for the stimulus, was--it turns out to be 133 millisecond, soa rather short period of time.Some subjects were under 100 milliseconds, some above.OK, now how do the condition that

    • 07:43

      SPEAKER [continued]: allows us to create the model, I needto describe what goes on in the experimental session.And the key factor here is the likelihoodon uncued trials of the top row, and the bottom row,of having the correct set of digits.By correct I mean, finding and matching

    • 08:05

      SPEAKER [continued]: some on the following probe screen.And this was done with a complimentary fixedprobabilities, so that the top row, for example, Ihave the correct sum on 25% of the trials,and then the bottom row would have the correct sumon 75% of the trials.And we use five different probability combinations.

    • 08:27

      SPEAKER [continued]: In addition, half of the subjectsgot some feedback, that was of two forms in this study.One was every five trials they were told how they were doing.And they were-- got financial rewardthat was in proportion to the number of correct responses

    • 08:48

      SPEAKER [continued]: at the end of the study.And half the subjects had no feedback, just the pleasure,perhaps, of getting a correct response.So now I can, given this set up, wecan describe a-- write an equation that describes

    • 09:09

      SPEAKER [continued]: performance in this procedure.And this is given in the top two rows here.We have two equations and this givesthe expected number of correct responses for the top row,and the expected number of correct responsesfor the bottom row.

    • 09:29

      SPEAKER [continued]: And these are data that we get at the end of the experiment.And then on the right are the different waysof getting a correct response.And there are two ways for each--of getting a correct response for the top,and two ways for the bottom, and they're perfectly analogous.PT stands for the probability that the computer

    • 09:49

      SPEAKER [continued]: chose the top row as being correct,PB, the computer chose the bottom row.p, lowercase p, is the likelihood of attendingto either to the top row, and 1 minus p, is the bottom row,and that's the quantity we wish to calculate.And g is the correct guess rate, which

    • 10:12

      SPEAKER [continued]: given that there were seven possibilities,we know it should, if everything worked, be equal to 1 out of 7,or 0.143.So just as quickly go through howto get a correct top response.Well, the computer sets it up, the top row is correct,and the subject allocates his or her attention to that row,

    • 10:33

      SPEAKER [continued]: and presumably adds correctly, and gets a correct response.Or the computer sets up at the top of row as correct,but the subject attends to the bottom row.So it doesn't have knowledge of the top row,but guesses, 1 out of 7, in principle.

    • 10:55

      SPEAKER [continued]: And so we have two equations, we havetwo unknowns, allocation of attention, correct guess rate,and we can solve it.In addition, there is a version of thisthat takes into account the possibility that the subjectwas just zoning out, wasn't attending to anything blinking,and that adds a kind of error term.

    • 11:15

      SPEAKER [continued]: That is derived empirically from the cued trials.That's a slightly more complicated equation,but it doesn't alter the logic of what we're doing here.So we have-- if we end up with-- at end of the experimentwith this quantity, what the subject actually did,we should be able to solve this equation.

    • 11:36

      SPEAKER [continued]: We know what these are, and find p and g.So now finally we can look at the data and see what happens.And recall that we are expecting two--there are two possible outcomes that we have in mind.OK, so we analyzed the data in terms of half session units.

    • 11:58

      SPEAKER [continued]: There were two sessions.And on the x-axis is the probabilitythat the computer selected the top row as being correct,on the y-axis is the probability that the subject attendedto the top row, as determined by the equation.Each of these data points reflectsthe average of 6 to 9 subjects.

    • 12:21

      SPEAKER [continued]: And we can see that as the experiment proceeds,the correlation between the allocation of attention,and the likelihood of a stimulus leading to the correct answerincreases, and in fact, it approachesby the end of the experiment about-- correlationis about 1.0.

    • 12:42

      SPEAKER [continued]: And these data, the probability matching prediction,recall from the beginning, is supposed to be linear,and actually have a slope of 45 degrees,so these data very nicely fit the probability matchingprediction.However, we are combining here, both the feedbackand the non-feedback subjects, so let's see

    • 13:02

      SPEAKER [continued]: what happens when we pull out the feedback subjects, whathappens.This is the bottom row here, the first halfof the first session, the second half of the second session,and we see that the predicted sigmoid function, whichwill eventually, perhaps over time,

    • 13:23

      SPEAKER [continued]: go to a clear step function, we seethat there are deviations from the diagonal predictingprobability matching.They're deviations, and the deviationsare predicted by the maximizing predictions.So that feedback makes a difference.I think it actually speeds up the learning process here.

    • 13:44

      SPEAKER [continued]: We've repeated the study with a larger sample, a largernumber of subjects, feedback and non-feedback,looking at just one condition, 4 to 1, and 1 to 4,and we see the same result with those subjects with feedbackshown by the green triangles, upside down triangles,

    • 14:04

      SPEAKER [continued]: are moving towards the prediction,the maximizing prediction, which--I guess I should have pointed out more explicitly,it's not just a sigmoid, or a step function--but the maximizing prediction in this procedure,the maximizing strategy, rather, isto respond to whatever row-- attend to whatever row

    • 14:30

      SPEAKER [continued]: is more likely on every trial.That's how you get the step function.Whereas the probability matching saysyou should-- the probability of attending to a stimulusshould equal its probability of paying off.Maximizing says if it's 51%, you go there 100% of the time.There's one more piece of data that

    • 14:51

      SPEAKER [continued]: is relevant to whether or not the procedure workedas intended.And that is the amount of time ittakes the subjects to respond in the probe screen.The probe screen we call-- there are seven numbers, one of them

    • 15:13

      SPEAKER [continued]: matches, either the top of the row of stimulus,or the bottom row of stimulus.There are three kinds of trials that you can have--and this is the time it took to make a correct response.And there are three kinds of trials, cued trials,and then there are the trials thatare correct at the stimulus that was most likely to contain

    • 15:36

      SPEAKER [continued]: the correct three digits, and thenthere are uncued trials that were correctwhen it was the stimulus that was less likely to providethe correct responses.And we can see that these responses, correct responses,

    • 16:00

      SPEAKER [continued]: are the cued, and the most likely stimulus decreaseover time, the subjects get betterat finding the correct response.But there is no change here, and they're much longerfor correct responses at the less likely stimuluson uncued trials.Why is that?Well, what appears to be going onis that the subjects at the less likely stimulus are guessing.

    • 16:25

      SPEAKER [continued]: And guessing takes longer.You have to look down the entire list of seven numbers,you don't find the three digits that you added,you don't have in-- or put another way,you don't have information about the stimulus you did notattend to, and you guess.And so that takes a longer amount of timebecause you have to review each seven

    • 16:45

      SPEAKER [continued]: and then take a wild stab.And so the response times fit with our assumptionthat the subjects were selectively attendingto one stimulus, but not both.So we can now-- these are all the data that I'mgoing to show now, and we can go to the conclusions,

    • 17:06

      SPEAKER [continued]: or discussion.So did the procedure work?There are several ways of measuring it.First, we needed to give them enough timeto make a correct response, at least one of the two stimuli.And on cued trials, when they know which one to attend to,

    • 17:26

      SPEAKER [continued]: their accuracy rates were approximately 90%in this study, and 95% in another.The estimated guess rate should be 1 out of 7,if they only have knowledge-- affective knowledge of oneof the two stimuli.They should be guessing at about a rate of 1 to 7, 0.134.Are calculated from the equation,

    • 17:48

      SPEAKER [continued]: guess rate was 0.164 in this study, whichis not significantly different.And in their second study it was closer to 0.143.The response times reflect the subjectwho is learning to attend to the most likely stimulus,and has little, or no knowledge, of the informationin this unattended stimulus.

    • 18:09

      SPEAKER [continued]: Again, the equation assumes that the subject can attendto one stimuli, but not two, and all these data supportthat assumption, so that the calculations seem valid.The subjects with feedback deviatedfrom probability matching, in the waypredicted by maximizing.

    • 18:30

      SPEAKER [continued]: And the correlates of deviating from probability matching,were the same correlates that yousee in behavioral-choice studies,and that is feedback, drive subjects towards maximizingwhen there are these overt responses, like respondingon two slot machines.

    • 18:51

      SPEAKER [continued]: And the number of trials.Subjects gradually learn to maximize in these procedureswhen they're behavioral studies.The only difference here is that the maximizing takes placein much fewer trials, in this attention procedure,than in overt behavioral procedures.So to go to the take-home messages, the results,

    • 19:15

      SPEAKER [continued]: such as the response times, the probability of a correct guess,those results are consistent with the assumptionsof the mathematical model of this procedure.And the results are compatible with the question thatgenerated this study, and that is,to do the same kinds of principles

    • 19:37

      SPEAKER [continued]: that govern the allocation of overt behavioras an economic activity, play a rolein the allocation of attention.And we see the same patterns of behaviorsuggesting that there are these general principles thatapply to both, cognitive performance,and behavioral performance.[APPLAUSE]

    • 19:58

      SPEAKER [continued]: [MUSIC PLAYING]

A New Method for Quantifying Attention: Results Support Optimizing Theory

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Professor Gene Heyman discusses his research on attention, which explores whether the principles that govern the allocation of overt behavior also apply to the allocation of cognitive resources. Heyman's results showed that the principles that govern overt behavior play a role in the allocation of attention, and that patterns of behavior suggest general principles apply to both.

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A New Method for Quantifying Attention: Results Support Optimizing Theory

Professor Gene Heyman discusses his research on attention, which explores whether the principles that govern the allocation of overt behavior also apply to the allocation of cognitive resources. Heyman's results showed that the principles that govern overt behavior play a role in the allocation of attention, and that patterns of behavior suggest general principles apply to both.

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