donders’ subtractive methodology -...

Donders’subtractive methodology

IAAF policies consider that there is a limit to how fast a human can react to a start signal. As of 2002, if an athlete left the blocks sooner than 100 ms. after the start signal, he was deemed to have false-started. Some fans think this is wrong and that any reaction after the gun should be allowed.

The best athletes reaction times are usually in the range of 120 mSec (0.12 sec) to 160 mSec.

Tim Montgomery improved that to a near perfect 104 mSec - and came very very close to being false-started. The only sprinter to get closer to perfection was Surin Bruny - who managed a 101 mSec in a the 1999 WC 2nd semi-final.

Burrell's 1991 world record began with a reaction time of just 117 mSec.

In the same race, Carl Lewis reacted in a snail's-pace 166 mSec, probably because he'd deliberately slowed his start due to having an earlier false-start posted against him (this put him at risk of disqualification if he false-started again).

Taking away reaction time, Burrell covered the 100 metres in 9.783 seconds, Lewis in 9.764. Lewis was actually the faster runner, but Burrell was the better "gunner".

Mental Chronometry

Subtractive Methodology

SIMPLE REACTION TIME (RT) TASK

STIMULUS DETECTION

RESPONSE EXECUTION

A simple reaction:

There is only one response to a single stimulus.

For example, a light goes on and the instruction is to press a key or a button as soon as possible after the onset of the stimulus. For Donders, this simple RT task (we will call it Task A) could be used as a baseline.

SIMPLE REACTION TIME (RT) TASK

STIMULUS DETECTION

RESPONSE EXECUTION

CHOICE REACTION TIME (RT) TASK

GO/NO GO REACTION TIME (RT) TASK

Simple RTChoice RT

Go/Nogo RT

Choice RT - Simple RT =

Choice RT - Go/Nogo RT =

A problem with the Go/NoGo task

Respond to Circle but not a Square

Go

What happens if the subject occasionally responds to the square?

Donders: If this happens once, the whole series must be rejected: for, how can we be sure that when they had to make the response and did make it, they had properly waited until they should have discriminated

NoGo

How can we be sure that when they had to make the response and did make it, they had properly waited until they should have discriminated.

The subject may simply have responded correctly without waiting to determine if the target is a circle ora square.

Go

If the subject responded incorrectly “Go” to the square, maybe he or she also sometimes responded correctly to the circle without allowing enough time to identify it. A kind of “false start”.

In other words, the participant may have changed the amount of time he or she allows before responding to the target in the go/nogo task, triggering on some trials very fast anticipatory responses before the stage of identification has been completed. If this were true, the components involved in Task C are not just those which determine performance in Task B minus the added stage of response selection.

Go/NoGo

Choice RT

The subtraction: Choice RT-Go/NoGo RT may notprovide a valid measure of

????????

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.

The Word Superiority Effect

Skilled readers are faster to identify any letter in a word than a single letter in isolation.

e.g. HAND ###Dvs

Cattell

HAND

HAND

###D

###D

A modern idea

380 JAMES L. MCCLELLAND AND DAVID E. RUMELHART

pie weighted average to yield a net input tothe unit, which may be either excitatory(greater than zero) or inhibitory. In math-ematical notation, if we let «,(<) representthe net input to the unit, we can write theequation for its value as

= 2 - 2 yikik(t), (1)

where ej(t) is the activation of an active ex-citatory neighbor of the node, each ik(t) isthe activation of an active inhibitory neigh-bor of the node, and a,j and yik are associatedweight constants. Inactive nodes have no in-fluence on their neighbors. Only nodes in anactive state have any effects, either excit-atory or inhibitory.

The net input to a node drives the acti-vation of the node up or down, dependingon whether it is positive or negative. Thedegree of the effect of the input on the nodeis modulated by the node's current activitylevel to keep the input to the node from driv-ing it beyond some maximum and minimumvalues (Grossberg, 1978). When the net in-put is excitatory, n,(0 > 0, the effect on thenode, fj(t), is given by

(2)where M is the maximum activation level ofthe unit. The modulation has the desiredeffect, because as the activation of the unitapproaches the maximum, the effect of theinput is reduced to zero. M can be thought

Figure 3. A few of the neighbors of the node for the letter T in the first position in a word, and theirinterconnections.

Features

Letters

Words

Bottom-up

Feed-forward

Excitatory Inhibitory

INTERACTIVE ACTIVATION MODEL, PART 1 383

all of the nodes in the system once each cycleon the basis of the values on the previouscycle. Obviously, this is simply a matter ofcomputational convenience and not a fun-damental assumption. We have endeavoredto keep the time slices "thin" enough so thatthe model's behavior is continuous for allintents and purposes.

Any simulation of the model involvesmaking explicit assumptions about the ap-propriate featural analysis of the input font.We have, for simplicity, chosen the font andfeatural analysis employed by Rumelhart(1970) and by Rumelhart and Siple (1974),illustrated in Figure 4. Although the exper-iments we have simulated employed differ-ent type fonts, we assume that the basic re-sults do not depend on the particular fontused. The simplicity of the present analysisrecommends it for the simulations, thoughit obviously skirts several fundamental issuesabout the lower levels of processing.

Finally, our simulations have been re-stricted to four-letter words. We haveequipped our program with knowledge of1,179 four-letter words occurring at leasttwo times per million in the Kucera andFrancis (1967) word count. Plurals, inflectedforms, first names, proper names, acronyms,abbreviations, and occasional unfamiliar en-tries arising from apparent sampling flukes

3CIEFGHIJKLMNDPQRBTU^WXYZ

wFigure 4. The features used to construct the letters inthe font assumed by the simulation program, and theletters themselves. (From "Process of Recognizing Ta-chistoscopically Presented Words" by David E. Ru-melhart and Patricia Siple, Psychological Review, 1974,81, 99-118. Copyright 1974 by the American Psycho-logical Association. Reprinted by permission.)

Figure 5. A hypothetical set of features that might beextracted on a trial in an experiment on word perception.

have been excluded. This sample appears tobe sufficient to reflect the essential charac-teristics of the language and to show howthe statistical properties of the language canaffect the process of perceiving letters inwords.

An Example

Let us now consider a sample run of oursimulation model. The parameter values em-ployed in the example are those used to sim-ulate all the experiments discussed in theremainder of Part 1. These values are de-scribed in detail in the following section. Forthe purposes of this example, imagine thatthe word WORK has been presented to thesubject and that the subject has extractedthose features shown in Figure 5. In the firstthree letter positions, the features of the let-ters W, O, and R have been completely ex-tracted. In the final position a set of featuresconsistent with the letters K and R have beenextracted, with the features that would dis-ambiguate the letter unavailable. We wishnow to chart the activity of the system re-sulting from this presentation. Figure 6shows the time course of the activations forselected nodes at the word and letter levels,respectively.

At the word level, we have charted theactivity levels of the nodes for the wordswork, word, wear, and weak. Note first thatwork is the only word in the lexicon consis-tent with all the presented information. Asa result, its activation level is the highest andreaches a value of .8 through the first 40time cycles. The word word is consistent withthe bulk of the information presented andtherefore first rises and later is pushed back


down below its resting level, as a result ofcompetition with work. The words wear andweak are consistent with the only letter ac-tive in the first letter position, and one of thetwo active in the fourth letter position. Theyare also inconsistent with the letters activein Positions 2 and 3. Thus, the activationthey receive from the letter level is quite

weak, and they are easily driven down wellbelow zero, as a result of competition fromthe other word units. The activations of theseunits do not drop quite as low, of course, asthe activation level of words such as gill,which contain nothing in common with thepresented information. Although not shownin Figure 6, these words attain near-mini-

word activations

work

Co• 1-1-po

OO

-0.40

letter activations

co

-POo

-0.40

Figure 6. The time course of activations of selected nodes at the word and letter levels after extractionof the features shown in Figure 5.









An Example











An Example











An Example






word activations

work

Co• 1-1-po

OO

-0.40

letter activations

co

-POo

-0.40





word activations

work

Co• 1-1-po

OO

-0.40

letter activations

co

-POo

-0.40



LETTERLEVEL

VISUAL INPUTFigure 2. The simplified processing system.

other nodes. The nodes to which a node con-nects are called its neighbors. Each connec-tion is two-way. There are two kinds of con-nections: excitatory and inhibitory. If twonodes suggest each other's existence (in theway that the node for the word the suggeststhe node for an initial t and vice versa), thenthe connections are excitatory. If two nodesare inconsistent with one another (in the waythat the node for the word the and the nodefor the word boy are inconsistent), then therelationship is inhibitory. Note that we iden-

tify nodes according to the units they detect,printing them in italics; stimuli presented tothe system are in uppercase letters.

Connections may occur within levels orbetween adjacent levels. There are no con-nections between nonadjacent levels. Con-nections within the word level are mutuallyinhibitory, since only one word can occur atany one place at any one time. Connectionsbetween the word level and letter level maybe either inhibitory or excitatory (dependingon whether the letter is a part of the wordin the appropriate letter position). We callthe set of nodes with excitatory connectionsto a given node its excitatory neighbors andthe set of nodes with inhibitory connectionsto a given node its inhibitory neighbors.

A subset of the neighbors of the letter tis illustrated in Figure 3. Again, excitatoryconnections are represented by the arrowsending with points, and inhibitory connec-tions are represented by the arrows endingwith dots. We emphasize that this is a smallsubset of the neighborhood of the initial t.The picture of the whole neighborhood, in-cluding all the connections among neighborsand their connections to their neighbors, ismuch too complicated to present in a two-dimensional figure.

Activation assumptions. There is asso-ciated with each node a momentary activa-tion value. This value is a real number, andfor node / we will represent it by a,(0- Anynode with a positive activation value is saidto be active. In the absence of inputs fromits neighbors, all nodes are assumed to decayback to an inactive state, that is, to an ac-tivation value at or below zero. This restinglevel may differ from node to node and cor-responds to a kind of a priori bias (Broad-bent, 1967) determined by frequency of ac-tivation of the node over the long term. Thus,for example, the nodes for high-frequencywords have resting levels higher than thosefor low-frequency words. In any case, theresting level for node / is represented by r,.For units not at rest, decay back to the rest-ing level occurs at some rate 0,.

When the neighbors of a node are active,they influence the activation of the node byeither excitation or inhibition, depending ontheir relation to the node. These excitatoryand inhibitory influences combine by a sim-

WORK

K on its own is quite confusable with R.

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 or variable if we wish to make use of it in an experiment.

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

Size

Familiarity

Stimulus Quality

Why might we want to vary a stimulus or response factor?

Stimulus Identification

Response Selection

Response Execution



Response Selection

Response Execution

Easy vs Hard to See is a Factor (Variable) that affects Stimulus Identification

Response Selection. Respond with the hand on the same side as the target object

Compatible Mapping

Response Selection. Respond with the hand on the opposite side to the target object

Incompatible Mapping



Response Selection

Response Execution

Easy vs Hard to See is a Factor (Variable) that affects Stimulus Identification Compatible vs Incompatible Mapping is a Factor (Variable) that affects Response Selection



Response Selection

Response Execution

Easy vs Hard to See is a Factor (Variable) that affects Stimulus Identification Compatible vs Incompatible Mapping is a Factor (Variable) that affects Response Selection

Varyingdifficulty

Varyingdifficulty

Examples of Compatible versus Incompatible Response Mappings.

Incompatible response mapping

Say white to Say black to

Incompatible response mapping

Respond with your left hand to

Respond with your right hand to

Respond with your left hand to

Respond with your right hand to

Compatible response mapping

Task: Respond to the direction of an arrow using a spatially corresponding keypress.

Right


Left


Left

Hard to See


Right

Hard to See

Compatible versus Incompatible Response Mappings?


Task: Respond to the direction of an arrow using a spatially opposite keypress.

Left




Right




Left


Hard to see



Right


Hard to see

EASY TO SEE HARD TO SEE

RT

500MS

550 MS

600 MS

COMPATIBLE RESPONSE

INCOMPATIBLE RESPONSE

650 MS

ADDITIVE EFFECTS

The Factors: Easy vs Hard to See and Compatible vs Incompatible have statistically independent effects on RT


Response Selection

Response Execution

Easy vs Hard to See

Compatible vs IncompatibleResponses

Letter Identification

Orthographic Lexicon

Phonological Lexicon

SPEECH OUTPUT

PRINT

Grapheme-phoneme

conversion rules

Semantic System



= 2 - 2 yikik(t), (1)





?????




SPEECH OUTPUT

PRINT

Grapheme-phoneme

conversion rules

Semantic System



= 2 - 2 yikik(t), (1)





A factor affecting Letter Identification?




SPEECH OUTPUT

PRINT

Grapheme-phoneme

conversion rules

Semantic System



= 2 - 2 yikik(t), (1)





A factor affecting Letter Identification? PencilEasy versus Hard to See Pencilvs




SPEECH OUTPUT

PRINT

Grapheme-phoneme

conversion rules

Semantic System



= 2 - 2 yikik(t), (1)





A factor affecting the Orthographic Lexicon (i.e.the speed of lexical access)?




SPEECH OUTPUT

PRINT

Grapheme-phoneme

conversion rules

Semantic System



= 2 - 2 yikik(t), (1)





A factor affecting the Orthographic Lexicon (i.e.the speed of lexical access)?

High Familiar vs Low Familiar Words (Familiarity)

Familiar Words: HAND, BOOK, TREE, LIFE

Less Familiar Words: PLUM, ROOK, SNIP, HIVE

Examples

Familiarity

Easy to see: HANDFAMILIAR

Hard to see: HAND

Easy to see: PLUMLESS FAMILIAR

Hard to see: PLUM

Task: Name the word as quicklyand as accurately as possible.

The image on the left depicts Cattell’s device for presenting a visual display to an observer. In the middle is the chronoscope and on the right the voice-activated device which is triggered by a spoken response. The vibration of the sound moved thin metal plates to generate an electronic signal which then stopped the chronoscope, providing a measure of the response time in milliseconds from the onset of the stimulus.

EASY TO SEE HARD TO SEE

RT

500MS

550 MS

600 MS

FAMILIAR WORDS

LESS FAMILIAR WORDS

650 MS

INTERACTIVE EFFECTS

The Factors: Easy vs Hard to See and Familiar vs Less Familiar Words do not have statistically independent effects on RT

naming latency

donders’ subtractive methodology -...

Documents