In cognitive psychology, any result of interest involves a subtraction between two measures, most often involving the same respondent (the person who is responding). We test a group of participants (usually around 30), and compute the average difference between two (sometimes more) experimental conditions What kind of subtraction? In early work, subtractions were between two different tasks. Mental Chronometry Subtractive Methodology Simple reaction time (RT) task STIMULUS DETECTION RESPONSE EXECUTION CHOICE REACTION TIME (RT) TASK GO/NO GO REACTION TIME (RT) TASK Simple RT Choice RT Go/Nogo RT Choice RT - Go/nogo RT = Choice RT - Go/Nogo RT = Donders’ method is based on three assumptions. First, it is assumed that the mental processes of stimulus detection, stimulus identification, response selection and response execution are arranged sequentially, in the sense that the output of one serves as the input to the next. Second, it is assumed that only one process can be active at each moment in time between stimulus input and response output. Third, it is assumed that a mental process can be added or omitted without affecting the duration of the other processes, the so-called assumption of pure insertion. Donders: Som e people giv e the response (in Task C) when the y shou ld hav e re m ain e d sile n t. An d if this ha ppe n s on ce, the w hole se rie s m u st be re j e cte d: fo r, ho w c an w e be su re t hat w he n t he y had t o m ak e the re spon se an d did m ak e it, the y had properly waited until they should have discrim in ate d? ???????? Go/NoGo Choice RT The subtraction: Choice RT-Go/NoGo RT may not provide a valid measure of Data: Error rate 2AFC GNG 400 RT (ms) Error Rate 0.15 0.1 0.05 0 Data: RT no/nogo 200 0 yes/go Model: Error rate Model: RT RT (steps) Error Rate Figure 1: Systematic error0.2biases in the GNG task. (A) The figure shows error rates associated 15 Task: Lexical 2AFCDecision If this happens once, the whole series must be rejected: for,and how can(forced with a perceptual decision-making task performed by subjects in both Go/NoGo Yes/No GNG 0.15 choice) the error rates in the settings wereand similar both classes we settings. be sureAlthough that when they had to forced makechoice the response didformake it, 10 there wasthey a significant bias the Gountil response theaGNG task, with more false alarms than for a word No nonsense word 0.1towards had Yes properly waited theyinfor should have discriminated omission errors. (B) Mean response time on the GNG task was lower than for the same stimulus on 5 0.05 the 2AFC task. (Data adapted from Bacon-Mace et al., 2007). 0 left/nogo right/go 0 Task: Go/NoGo Stimulus predictions of the optimal decision-making model, including those that specifically differ from the fixed-threshold DDM approximation [2, 12]. Yes for a word Do not respond to a nonsense word 2 Bayesian inference and risk minimization in choice tasks Human choice behavior in the GNG and 2AFC tasks exhibits a consistent Go bias in the GNG task that is not apparent for the same stimulus in the 2AFC task. For example, Figure 1 shows data from a task in which subjects must identify whether a briefly-presented noisy image contains an animal or not [16], under two different response conditions: GNG (only respond to animal-presen images), and 2AFC (respond yes/no to each image). Subjects showed a significant bias towards the Go response in the GNG task, in the form of higher false alarms than omission errors (Figure 1A) as well as faster RT than for the same stimulus in the 2AFC task (Figure 1B). For the 2AFC task, a large body of literature supports the “accumulate-to-bound” model of perceptual decision-making, [23, 20, 26], where moment-to-moment sensory input (“evidence” in favor of either choice) is accumulated over time until it reaches a bound, at which point, a response is gen- Lexical Decision Task (Choice) BOOK YES Letter Identification LYNX MOOK Word Identification Data: Error rate YES 0.1 Letter Identification 400 200 Word Identification 0.05 0 LYNX 2AFC GNG RT (ms) BOOK Error Rate 0.15 Data: RT GO/NoGo Task no/nogo 0 yes/go Model: Error rate Figure 1: MOOK Model: RT RT (steps) Error Rate Systematic error0.2biases in the GNG task. (A) The 15 figure shows error ra 2AFC with a perceptual decision-making task performed by subjects in both Go/NoGo and Y GNG 0.15 choice) settings. Although the error rates in the forced choice settings were similar for 10 there was a significant bias0.1towards the Go response in the GNG task, with more fals omission errors. (B) Mean response time on the GNG task was lower than for the sam 5 0.05 the 2AFC task. (Data adapted from Bacon-Mace et al., 2007). 0 left/nogo right/go 0 Stimulus predictions of the optimal decision-making model, including those that specifically d fixed-threshold DDM approximation [2, 12]. 2 Bayesian inference and risk minimization in choice tasks Human choice behavior in the GNG and 2AFC tasks exhibits a consistent Go bias in Donders’s assumption of pure insertion: an evaluation on the basis of response dynamics. Ralph Ulrich, Stefan Mattes & Jeff Miller Acta Psychologica 1999 Response force was measured by means of a force key ..... One end of a leaf spring was held fixed by an adjustable clamp, and the other end remained free. The participant's forearm rested comfortably on a table while his or her index finger bent down the free end of the leaf spring in response to the stimulus. A force of 10 N bent the free end by about 1 mm. The resolution of this device was about 2 cN (approximately 2 g). Strain gauges were attached to the leaf spring, so force applied to its free end caused changes in an electrical signal that was digitized with a sampling rate of 500 Hz Why use response force as an additional measure? Thus, response force may specifically probe the motor system and thus assess potential differences (if any) between the various RT tasks devised by Donders. In sum, if the type of task affects response execution, then response force should vary as a function of task, providing evidence at odds with Donders’s assumption of an invariant response execution stage. Task: Go/NoGo If circle is on the right, respond. If circle is on the left, do not respond. Go trial Task: Go/NoGo If circle is on the right, respond. If circle is on the left, do not respond. NoGo trial Task: Go/NoGo If circle is on the left, respond. If circle is on the right, do not respond. Go trial Task: Go/NoGo If circle is on the left, respond. If circle is on the right, do not respond. NoGo trial Task: Choice If circle is on the right,respond with the right key. If circle is on the left, respond with the left key. Right keypress Task: Choice If circle is on the right,respond with the right key. If circle is on the left, respond with the left key. Left keypress Subject 1 Subject 2 Subject 3 . . . . Subject N Average RTgo/nogo Average RTgo/nogo Average RTgo/nogo Average RTchoice Average RTchoice Average RTchoice Average RTgo/nogo Average RTchoice . Group Average RTgo/nogo Total=36 Average RTchoice QR Choice versus Go/Nogo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problem..... + It is possible that this extra focusing of attention in the go/nogo task would increase the apparent brightness of the stimulus in this task as compared to the other two tasks. It has been shown in previous publications that brighter stimuli produce more forceful responses. So this attentional hypothesis might explain why participants produced especially forceful responses in the go/nogo tasks of the preceding experiments, even if response execution processes operated identically in all tasks. + + Instructions: Respond with a right key press if the stimulus is an S and with a left key press if stimulus is an X. +SX Go/Nogo RT Instructions: Respond if the stimulus is an X. Do not respond if the stimulus is an S. +S X The assumption of pure insertion is again challenged by these results. Go/Nogo RT’s do not have the same motor output as Choice and Simple RT’s Main result: The go/nogo task produces especially vigorous, or forceful, responses. Why? Consider: How does the subject prevent himself from responding on Nogo trials? Recall Donders’ remark: Som e people giv e the response (in Task C) when the y shou ld hav e re m ain e d sile n t. Threshold Motor preparation Go/Nogo Choice To produce a “Go” response, the motor system needs a lot of activation from its initial ‘ready’ or prepared state (more than for a simple or choice RT). This bigger activation produces a more forceful action! Interactive-Activation A B C WHICH MODEL IS CONSISTENT WITH THE FOLLOWING! CLAIM BY CATTELL?! ‘we do not therefore perceive separately the letters of which a word is composed but the word as a whole’. Cattell HAND ###D ###D HAND A modern idea JAMES L. MCCLELLAND AND DAVID E. RUMELHART 380 pie weighted average to yield a net input to the unit, which may be either excitatory (greater than zero) or inhibitory. In mathematical notation, if we let «,(<) represent the net input to the unit, we can write the equation for its value as The net input to a node drives the activation of the node up or down, depending on whether it is positive or negative. The degree of the effect of the input on the node is modulated by the node's current activity level to keep the input to the node from driving it beyond some maximum and minimum - 2 yikik(t), (1) values (Grossberg, 1978). When the net in= 2 put is excitatory, n,(0 > 0, the effect on the where ej(t) is the activation of an active ex- node, fj(t), is given by citatory neighbor of the node, each ik(t) is (2) the activation of an active inhibitory neighbor of the node, and a,j and yik are associated where M is the maximum activation level of weight constants. Inactive nodes have no in- the unit. The modulation has the desired fluence on their neighbors. Only nodes in an effect, because as the activation of the unit active state have any effects, either excit- approaches the maximum, the effect of the input is reduced to zero. M can be thought atory or inhibitory. Bottom-u Words Feedforward Letters Features Figure 3. A few of the neighbors of the node for the letter T in the first position in a word, and their interconnections. Excitatory Inhibitory featural analysis employed by Rumelhart (1970) and by Rumelhart and Siple (1974), have been excluded. This sample appears to illustrated in Figure 4. Although the exper- be sufficient to reflect the essential characiments we have simulated employed differ- teristics of the language and to show how ent type fonts, we assume that the basic re- the statistical properties of the language can sults do not depend on the particular font affect the process of perceiving letters in used. The simplicity of the present analysis words. recommends it for the simulations, though it obviously skirts several fundamental issues An Example about the lower levels of processing. Let us now consider a sample run of our Finally, our simulations have been revaluesMODEL, em- PART 1 stricted to four-letter words. We have simulation model. The parameter INTERACTIVE ACTIVATION 383 INTERACTIVE ACTIVATION MODEL, PART 1 ployed in the example are those used to simequipped our program with knowledge of all of the nodes in the system once each cycle ulate allon the experiments discussed in the 1,179 four-letter words occurring at DAVID least the basis of the values on the previous all of the inE.the system once each cycle JAMES L. MCCLELLAND ANDnodes RUMELHART 384 Obviously, this isThese simply a matter of are detwo times per million in the Kucera remainder of Part 1. values on the basisand of the values on thecycle. previous INTERACTIVE MODEL, PART 1 convenience and notACTIVATION a funcycle. is a computational matter down below its resting level, as a result of Obviously, weak, and this theyscribed aresimply easily driven downofwell damental assumption. have endeavored in detail in the We following section. For Francis (1967) word inflected competition withcount. work. The Plurals, words wear and below zero, as a result and of competition from computational convenience not a funto keep the time slices "thin" enough so that are consistent with the only letter ac- theassumption. other word units. activations of these damental We have endeavored forms, first weak names, proper names, acronyms, the purposes this example, imagine that all The of the nodes inof thebehavior system each cycle theof model's isonce continuous for all tive in the first letter position, and onetoofkeep the the units do not drop quite as low, as time slices "thin" enough socourse, that intents and purposes. on the basis of the values on the previous abbreviations, and occasional unfamiliar enthe word WORK has been presented to the the activation level of words such as gill, two active in the fourth letter position.the They model's behavior iscycle. continuous for all Any simulation of the amodel involves this matter of in Obviously, common with the is simply are also inconsistent with the letters active which contain nothing intents and purposes. making explicit assumptions about the apsubject andnot convenience that has extracted tries arisingin Positions from 2apparent sampling flukesinformation. Although shown the subject and 3. Thus, the activation presented Figure 5. A hypothetical set of features tha computational andof not a funpropriate featural analysis the input Any simulation thewords model involves in Figure 6, of these attain near-miniextracted on a trial in an experiment on word they receive from the letter level is quite those features shown Figure 5.font. In the first damental assumption. We in have endeavored We have, simplicity, chosen the font and making explicit assumptions about the ap-for Figureemployed 5. A hypothetical set of features that might be featural analysis by Rumelhart to keep the time slices "thin" enough so that propriate featural analysis of the input font. three letter positions, the features ofon have theperception. leton a trial an experiment word been excluded. This sample ap and byextracted Rumelhart andinSiple (1974), We have, for simplicity,the chosen the(1970) fontbehavior and model's ishave continuous for all word activations be sufficient ters W, O, and R been completely ex- to reflect the essential illustrated in Figure 4. Although the experfeatural analysis employed by and Rumelhart intents purposes. teristics of the iments we have simulated employedThis differhave been excluded. sample appears to language and to sh (1970) and by Rumelhart and Siple (1974), tracted. In the final position a set of features the statistical properties of the lang Any simulation of the model involves ent type fonts, assume that the basic bewesufficient to reflect there-essential characillustrated in Figure 4. Although the experaffect the process of perceiving l sultswith do assumptions notthe depend onofthe particular making about the apconsistent letters and Rfont have been teristics theK language and to show workexplicit iments we have simulated employed differFigure 5. Ahow hypothetical set of featu words. used. The simplicity of the present analysis propriate featural analysis of the input font. the statistical properties ofwould theextracted language ent type fonts, we assume that therecommends basic re- the oncan a trial in an experiment on extracted, with features that disit for the simulations, C simplicity, chosen the fontofthough and affect the fundamental process perceiving letters in sults do not depend onWe the have, particular font skirts itfor obviously several issues o An Example ambiguate the letter • 1-1 words. featural employed Rumelhart We wish used. The simplicity of the presentanalysis analysis about the lower levels unavailable. ofbyprocessing. -p have excluded. sam Letbeen usrenow consider aThis sample ru Finally, our activity simulations have been rerecommends it for thenow simulations, though (1970) by Rumelhart and Siple o toand chart the of(1974), the system simulation model. parameter va stricted to four-letter words. We have be it obviously skirts severalillustrated fundamental issues sufficient to The reflect the ess in Figure 4. Although the experAn Example from thisprogram presentation. 6 the ployed in of the example are thoseand use equipped our with knowledge ofFigure about the lower levelssulting of processing. teristics language iments we1,179 havefour-letter simulated employed differulate allofthe discussed occurring at aleast Letwords us now consider sample run ourexperiments Finally, our simulations have been re- course O shows the time of the activations for the statistical properties of the type fonts, we assume thatinmodel. the retwo times persimulation million the basic Kucera and remainder of Part 1. These values The parameter values emstricted to four-letter ent words. We have affect the process of perceiv scribed in detail in the following sec Francis (1967) word count. Plurals, inflected sults do not depend on the particular font selected nodes at the word and letter levels, equipped our program with knowledge of ployed in the example are those used to simfirst names, proper names,analysis acronyms, words. the purposes of this example, imag used. Theforms, simplicity of the present ulate all the experiments discussed in the 1,179 four-letter words occurring at least respectively. abbreviations, and occasional unfamiliar en- the word WORK has been presente two times per million recommends in the Kucera and remainder of sampling Part though 1. These itarising for the simulations, subjectare anddethat the subject has e from apparent flukes values -0.40 thetries word level, charted the scribed inwe detailhave in the following section. For shown in Figure 5. In Francis (1967) word count. Plurals, inflected itAt obviously skirts several fundamental issues those features An Example forms, first names, proper names, acronyms, the purposes of this example, imagine that three letter positions, the features o about the levels lower levels processing. activity oftheof the nodes for the words abbreviations, and occasional unfamiliar enword have WORKbeen has been presented to the ters W,us O, now and Rconsider have beena compl Let samp Finally, our simulations reletter activations work, word, wear, and weak. that tracted. In the final position a set of subject and that theNote subjectfirst has extracted tries arising from apparent sampling simulation model. TheKparame stricted to flukes four-letter words. We in have consistent with the letters and R h those features shown Figure 5. In the first work is the word inpositions, the lexicon consisployed in with the arethat thos equipped our only program extracted, the features w threewith letter knowledge theoffeatures of the let- example ambiguate the letter unavailable. ulate all the experiments disW 1,179 four-letter words occurring at least tent with all the presented information. As ters W, O, and R have been completely exFigure 4. The features used to construct the letters in nowoftofeatures chartofthePart activity of the syv tracted. In the final position a remainder set timesits peractivation million in the Kucera and 1. These the font assumed by the a two result, level is letters the highest and sulting from this presentation. F c simulation program, and the consistent with the K and R havein been scribed detail in the followin Francis (1967) word count. Plurals, inflected o shows the time course of the activa letters themselves. (From "Process of Recognizing Ta- reaches a value extracted, of .8 through the that first 40 with acronyms, the features would dis- ofthe forms, first names, proper names, the purposes this example, selected nodes at word and lette chistoscopically Presented Words" by David E. Ruambiguate the letter unavailable. We wish respectively. time cycles. The word word is consistent with abbreviations, and occasional unfamiliar enthe word WORK has been pre now to chart the activity of the At system re- level, we have cha melhart and Patricia Siple, Psychological Review, 1974, theand word subject that the subject triesbulk arisingoffrom apparent sampling flukes sulting from this presentation. Figure 6 the the information presented and activity levels of the nodes for th 81, 99-118. Copyright O1974 by the American Psychoshown in Figure shows the time course of the those activations work, features word,for wear, and weak. Note o therefore first rises and later is pushed back logical Association. Reprinted by permission.) three letter positions, featu work the only word in the the lexico selected nodes at the word and letteris levels, 3CIEFGHI JKLMNDPQR BTU^WXYZ w O 3CIEFGHI JKLMNDPQR 3CIEFGHI BTU^WXYZ JKLMNDPQR w -P -0.40 BTU^WXYZ w 3CIEFGHI tent W, withO, all and the presented respectively. Figure 4. The features used to construct the letters in ters R have informa been c the font assumed byAt the the simulation result, its activation is the hig wordprogram, level, and we the havea charted Inthe the finallevel position a letters themselves. (From "Process of Recognizing Ta- tracted. reaches a value of .8 through the activity Words" levels by of David the E. nodes the words chistoscopically Presented Ru- for consistent with the letters K an time cycles. The word word is consist work, wear,Review, and weak. first that melhart and Patricia Siple,word, Psychological 1974, Note extracted, the features th the bulk of with the information presen 81, 99-118. Copyright by the American work 1974 is the only word Psychoin the lexicon consistherefore first risesletter and later is push logical Association. Reprinted by permission.) ambiguate the unavaila JKLMNDPQR BTU^WXYZ w Figure 4. The features used to construct the letters in font assumed by word the simulation program, and the Figure 6. The time course of activations the of selected nodes at the and letter levels after extraction of the features shown in Figure 5. letters themselves. (From "Process of Recognizing Tachistoscopically Presented Words" by David E. Rumelhart and Patricia Siple, Psychological Review, 1974, 81, 99-118. Copyright 1974 by the American Psychological Association. Reprinted by permission.) tent with all the presented information. As now to chart a result, its activation level is the highest and the activity of t sulting from reaches a value of .8 through the first 40 this presentatio time cycles. The word word is consistent shows thewith time course of the a the bulk of the information selected presented nodes and at the word and therefore first rises and later is pushed back respectively. Figure 4. The features used to construct the letters in the font assumed by the simulation program, and the letters themselves. (From "Process of Recognizing Tachistoscopically Presented Words" by David E. Rumelhart and Patricia Siple, Psychological Review, 1974, 81, 99-118. Copyright 1974 by the American Psychological Association. Reprinted by permission.) At the word level, we hav activity levels of the nodes f work, word, wear, and weak. N work is the only word in the l tent with all the presented in a result, its activation level is th reaches a value of .8 through time cycles. The word word is c the bulk of the information p therefore first rises and later i two active in the fourth letter position. They are also inconsistent with the letters active in Positions 2 and 3. Thus, the activation they receive from the letter level is quite units do not drop quite as low, of course, as the activation level of words such as gill, which contain nothing in common with the presented information. Although not shown in Figure 6, these words attain near-mini- word activations work C o • 1-1 -p o JAMES L. MCCLELLAND AND DAVID E. RUMELHART 384 down below its resting level, as a result of competition with work. The words wear and weak are consistent with the only letter active in the first letter position, and one of the two active in the fourth letter position. They are also inconsistent with the letters active in Positions 2 and 3. Thus, the activation they receive from the letter level is quite weak, and they are easily driven down well below zero, as a result of competition from the other word units. The activations of these units do not drop quite as low, of course, as the activation level of words such as gill, which contain nothing in common with the presented information. Although not shown in Figure 6, these words attain near-mini- O O -0.40 word activations letter activations work C o c o • 1-1 -p o O O -P O o -0.40 -0.40 letter activations Figure 6. The time course of activations of selected nodes at the word and letter levels after extraction of the features shown in Figure 5. c o K on its own is quite confusable with R. -P O o -0.40 Figure 6. The time course of activations of selected nodes at the word and letter levels after extraction of the features shown in Figure 5. K in WORK is more confusable with D than R The logic of additive factors What is a factor? Any type of stimulus or response can be varied in some systematic way. We can make letters small or big BIG SMALL We can make words familiar or less familiar BOOK ROOK We can make shapes easy to see or harder to see The logic of additive factors Each of these properties of the stimulus (we can do the same for responses) is termed a factor if we wish to make use of it in an experiment. We can make letters small or big BIG Size SMALL We can make words familiar or less familiar BOOK ROOK Familiarity We can make shapes easy to see or harder to see Stimulus Quality Why might we want to vary a stimulus or response factor? Stimulus Identification Response Mapping Movement Programming Response mapping. Respond with the hand on the same side as the target object Compatible Mapping Response mapping. Respond with the hand on the opposite side to the target object Incompatible Mapping Examples of Compatible versus Incompatible Response Mappings. ject is instructed to: Respond with your left hand to Incompatible response mapping Respond with your right hand to Respond with your left hand to Compatible response mapping Respond with your right hand to Say white to Incompatible response mapping Say black to Why might we want to vary a stimulus or response factor? Stimulus Quality 620 600 580 Reaction Time 540 500 500 Easy Hard Choice of response Hard to see Easy to see
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