Verification of Donders' Subtraction Method - Semantic Scholar · Figure 1. Representation of simple and choice reactions according to Donders' insertion hypothesis. (The direction

Journal or Experimental ftychology:Human Perception and ftrformance1985, Vol. 11, No. 6, 765-776

Copyright 1985 by the American Psychological Association, Inc.0096-I523/85/J00.75

Verification of Donders' Subtraction Method

Robert Gottsdanker and G. Paul ShraggUniversity of California, Santa Barbara

In an experiment on 6 young adults advance (precued) information of the correctchoice response was utilized completely: (a) For precue-to-stimulus intervals (PSIs)clearly shorter than the difference between mean choice and simple reaction time(RT), median response latency (L) measured from precue onset was invariant; (b)For clearly longer PSIs, median RT was very near the value for simple RT. Thispretue-utilization effect would be expected if response actualization had been delayeduntil the response had been selected and if the requirement for discrimination andselection had no adverse effect on readiness to respond. Donders' (1868/1969) hy-pothesis in his initial application of the subtraction method, that choice and simplereactions are identical except for the serial insertion of discrimination and selectionoperations in the former, is thereby strongly supported. If this formulation is accepted,models that hold that response processing can overlap other processing stages maybe considered valid only for response selection, not response actualization.

In the analysis by Donders (1868/1969), achoice reaction takes longer than a simple re-action because of the required insertion of ad-ditional processing operations. He stated thatit takes longer to make a different-hand re-sponse in accordance with the foot that hasbeen stimulated than always to respond withthe same hand to a stimulus that is always onthe same side, because of the additional timerequired for "deciding which side had beenstimulated and for establishing the actions ofthe will on the right or left side" (p. 418). Don-ders called the first of these operations dis-crimination, and in current terminology thesecond operation would most often be calledresponse selection. The mean duration of theinserted operations is found by subtractingmean simple reaction time (RT) from meanchoice reaction time. This subtraction method

A partial report on the present experiment and on apreceding control experiment was given at the meeting ofthe American Psychological Association, in Toronto, Can-ada, August, 1984.

This research was supported by Grant 5 R01 AG00011to the University of California from the National Instituteon Aging and by a faculty research grant from the Uni-versity of California, Santa Barbara. Especial thanks aregiven to Bemadette Magee for her assistance in the collec-tion and analysis of data.

G. Paul Shragg is now at the Medical Center, Universityof California, San Diego.

Requests for reprints should be sent to Robert Gotts-dankei; Department of Psychology, University of California,Santa Barbara, California 93106.

is based on two assumptions. The first is thatthe inserted operations do not overlap in timewith the operation by which a response is ac-tualized, which is common to the simple andchoice reactions. The second is that the re-quirement of performing the inserted opera-tions does not reduce readiness to actualizethe response. Donders went on to apply thesubtraction method in a second way. Throughuse of a contingent reaction, where responseis required to only one of the possible stimuli,he estimated the duration of the response se-lection alone, by the difference between themeans for the choice and contingent reactions,and in so doing, the duration of discrimina-tion.

As noted by Steinberg (1969), althoughthere has been some revival in the use of thesubtraction method after it had fallen into dis-favor for perhaps more than a half century,"little is known about how to test the validityof any particular application of the subtractionmethod" (pp. 276-217). Contemporary criti-cism of the subtraction method has centeredupon the first assumption, that of strict serialityof operations (e.g., Miller, 1982). The earlycriticism challenged the second assumption,that of unimpeded readiness to respond,largely on the basis of introspective reports(Watt, 1905). In the present study we presentan augmentation of the subtraction methodthat can test the method's validity for Donders'initial application, the comparison of choice

765

766 ROBERT GOTTSDANKER AND G. PAUL SHRAGG

and simple RTs. Specifically, we test Donders1

assumption, for the case of a compatible left-right choice reaction. We split the informativeand imperative functions of the choice stim-ulus by presenting an informative visual stim-ulus as a precue and following it quickly onhalf the trials at random by an auditory im-perative stimulus. If, over very brief precue-to-stimulus intervals (PSIs), including simul-taneous presentation, average latency betweenprecue and onset of response is invariant, andif for somewhat longer PSIs average RT to theimperative stimulus is equal to average simpleRT, the assumptions underlying the subtrac-tion method are supported, as was the case inthe present experiment. This combined out-come of the augmented subtraction method istermed the precue-utilization effect becausethere is complete utilization of the precued in-formation in reducing average RT to the im-perative stimulus until it remains equal to av-erage simple RT.

Following is the rationale for the procedureemployed and the conclusions drawn from theprecue-utilization effect, Donders' insertionhypothesis for a choice reaction implies thatthe choice stimulus provides separate infor-mative and imperative contributions to the re-sponse. The informative contribution leads tothe discrimination among stimuli and selectionamong corresponding responses. The imper-ative contribution leads to the actualization ofa selected response. Thus, the effect of the im-perative contribution is delayed until a re-sponse has been selected. In a simple reaction,where the response has been selected long inadvance of stimulus occurrence, the stimulusprovides only an imperative contribution, andso leads directly to response actualization.

The main hypothesized events for a simpleand a choice reaction are represented in FigureI, in the top and bottom sections, respectively.For simple RT it is seen that the preselectedresponse is actualized as soon as the prelimi-

Simple RT

PreviousResponseSelection

Onset of Response

RTg = Encoding Stimulus + Premotor

Stimulus

I-

Choice RTOnset of Response

Discriminationand Response

Selection

Imperative Delay

RT,,

Response Actualization

-I

RTC = Encoding Stimulus + Discrimination and Response Selection + Premotor

RTC - RTS = Discrimination and Response Selection

Figure 1. Representation of simple and choice reactions according to Donders' insertion hypothesis. (Thedirection of time is shown by t—*. RT indicates the reaction time measured between the onset of the stimulus(S) and the onset of the response. RTS and RTC stand for simple reaction time and choice reaction time,respectively. The value of E indicates the proportional efficiency of an operation.)

VERIFICATION OF DONDER'S SUBTRACTION METHOD 767

nary processing of the stimulus (encoding) hasbeen completed. It will be noted that responseactualization is divided between premotor andmotor times. Here it is indicated that the mea-sured onset of the response occurs exactlywhen the movement starts. This is difficult toattain in practice. However, the same temporalpoint is used in the other examples to be pre-sented. For the choice reaction the only changeis in the insertion of the discrimination andresponse selection operations between encod-ing and actualization, with the delay in the im-perative contribution of the stimulus being in-dicated by the dotted line. The terms used forthe "boxes" should not be taken as more thanconvenient tables. For example, it need not besupposed that a comparison of possible re-sponses takes place in response selection. Also,the failure to use such terms as translation andretrieval does not imply that such processesare unimportant in the labeled operations. Inaddition to showing the events on single trials,the foregoing diagrams may just as well rep-resent mean values over a number of simpleand choice trials. In the subtraction method,the difference between mean choice and simpleRT thus gives the mean value of the insertedprocesses.

In these diagrams, as well as those in Figures2 and 3, an operation reaches completion whenthe "area" of the corresponding bar attains acriterion value. At any instant, the area is aproduct of the efficiency of the operation, E,and the time that the operation has been un-derway. In the cases just shown, efficiency hasbeen assumed to be at the maximum value ofI throughout. Models that hold that someprogress can be made toward response ac-tualization before the completion of discrim-ination and response selection have not insistedthat this can be done with maximum efficiency.It is very implausible for response acutalizationto proceed as rapidly before a response hasbeen selected as it can in a simple reaction,where the response has already been selectedbefore the stimulus is presented. In represent-ing the possibility of an overlap between re-sponse actualization and the other stages, then,the width of the bar will be shown as less than1 during the period of overlap.

If the depiction of a choice reaction in Figure1 is correct, and if actually different stimuliwere to be assigned to the informative and im-perative functions of the choice stimulus, the

imperative stimulus could trail the informativestimulus (or precue) without affecting latency,L, between precue and response, just as longas the imperative stimulus could be encodedbefore a response had been selected. Up to thatpoint, lengthening of PSI would simply shortenthe delay for the effect of imperative stimulus.This outcome, which is called Danders' Ex-pectation 1, is shown at the top of Figure 2 fora short intersignal interval (ISI) PSI. The dot-ted line represents the delay in the effect of theimperative stimulus. It should be noted thatthe encoding of the imperative stimulus isshown as proceeding concurrently with thediscrimination and selection operations. Thisis a reasonable assumption because withoutsome "trace" of the imperative stimulus therecould be no response. Interference betweenthe precue and the imperative stimulus wasminimized in the present experiment by useof different sense modalities. At the bottom ofFigure 2 is shown the expectation for a longPSI. Selection of the response has been com-pleted. Again, as in the case for the diagramsin Figure 1, the representations may be takento indicate the mean values obtained ratherthan the values for a single trial. It may benoted that mean RT for the long PSI is shownas equal to that for simple RT in Figure 1,because it is made of the same components.This outcome is termed Danders' Expecta-tion 2.

A first approximation of the longest PSI atwhich waiting would be required is given bythe difference between mean choice and simpleRT, because this is held to be the mean timerequired for the inserted operations. However,there are two reasons that the critical intervalfor testing Donders' model should be some-what shorter. First, the testing interval shouldbe reduced by the time that would be takenfor encoding the imperative stimulus. More-over, some trial-to-trial variation is to be ex-pected in the time required for the discrimi-nation and response-selection operations (andto a lesser extent for the more automatic en-coding operation). Thus, on a particular trialthe time for discrimination and selection mightbe very short, so that an imperative stimulusthat usually would occur during these opera-tions would now occur after the operations hadbeen completed. This poses no problem forPSIs that are clearly shorter than the mostrapid discrimination and response selection


that could take place on a trial, for example,a PSI of 30 ms (which was one of the valuesused in the present experiment). However, asPSIs begin to approach the mean differencebetween choice RT and simple RT, the inter-vening operations will have been completed

on some trials before the imperative stimulusoccurs, so the representation would be wrongfor those trials. Still, this limitation may beovercome to a considerable extent by the useof the median rather than the mean to describethe latency associated with a PSI. It may be

L with Short PSISInsertion Model

Onset of ResponseFsTPSL


Selection

Stimulus B

PSL

•-AorB

LA = Lg (mean or median)Donders (1)

RTP with Long PSIs

Insertion ModelOnset of Response

Enc.P

Discrimationand Response

Selection

tPrecue

Response Actualization

StimulusPSI RT,,

RT = RTS (mean or median)Donders (2)

Figure 2. Representation of precued reactions with short and long PSIs according to Donders' insertionhypothesis. (The direction of time is shown by t-». P stands for the informative precue. S stands for theimperative stimulus. Stimulus A (SA) and Stimulus B <SB) indicate the imperative stimulus presented at thedesignated instants. L indicates the latency between the onset of the precue and the onset of the response.LA and La stand for the latency when Stimulus A or Stimulus B is presented. PSI indicates the precue-to-stimulus interval. PSIA and PSIB represent the precue-to-stimulus interval when Stimulus A or Stimulus Bis presented. RT indicates reaction time measured between the onset of the imperative stimulus and the onsetof the response. KTP is the reaction time in the procedure in which a precue is presented. RTS stands forsimple reaction time, as shown in Figure 1. The value of E indicates the proportional efficiency of an operation.)


assumed that there is an appreciable correla-tion between overall RT and the duration ofdiscrimination and response selection opera-tions. Thus, the trials on which these opera-tions will already have been completed beforepresentation of the stimulus at the somewhatambiguous PSIs will, by and large, be thosewith RTs shorter than the median. The median,of course, is not affected by shifts that all takeplace at values on one side of it. Consequently,for the present analysis the median is preferableto the mean, which is affected by every changeof value. The same problem, in reverse, is en-countered in determining the shortest PSI atwhich no waiting is required. Now "safe" PSIsare those that are clearly longer than the dif-ference between mean choice and simple RT.

More valid estimates again may be made forborderline PSIs by use of medians rather thanmeans.

Alternative representations that reflect thecriticisms made of the subtraction method areshown in Figure 3. Again, mean values arerepresented. An interpretation of a continu-ous-flow model (Eriksen & Schultz, 1979), asapplied to the present paradigm, is shown inthe top two diagrams. With the onset of theimperative stimulus, a steady amount of re-sponse actualization with E < 1 takes placebefore the end of discrimination and selection,at which point there begins the full rate of re-sponse-actualization processing (E - 1). Thearea of response actualization required forreaching the criterion now is seen to be reached

L with Short PSIsOverlapping-Operatlons Model

Precue

Stimulus B

PSI-

LA < LB (mean or median)

vs. Bonders (1)

RTP with Long PSIs

Degraded-Preparation Model

Onset of Response

Enc.p


Selection

tPrecue

Stimulu

•PSI-

RT > RTS (mean or median)

vs. Donders (2)

Figure 3. Representation of precued reactions when Donders' assumptions are denied. (The terms are dennedin the same way as in Figure 2.)


earlier by the shorter of the two PSIs, shownin the topmost diagram. Thus, median latencyfrom precue to response will not be constantbut will increase with PSI in contradiction toDonders' Expectation 1. It is difficult to seewhy this would not be the case for any otherformulation of partial response actualizationduring the added operations. At the bottom ofFigure 3 the effect of reduced readiness to re-spond is shown by a thinner bar for responseactualization (E < 1). A longer time is nowrequired for the area to reach the criterionvalue. Consequently, the expectation is for RTto the imperative stimulus to be longer thansimple RT, in contradiction to Donders' Ex-pectation (2).

It is important to recognize that the aug-mented subtraction method is employed to testhypotheses that model events in procedures inwhich a single stimulus is given. It is notclaimed that a precise estimate can be madefor the duration of inserted operations for theaugmented procedure itself, as there is the un-known value of the additional encoding op-eration required for the separate imperativestimulus. However, if the conclusions of theaugmented subtraction method are accepted,the estimate can be made for the single-stim-ulus procedures through use of Donders' orig-inal subtraction method. Curiously, the use ofmedians in the augmented method appears tobe appropriate to test the hypothesis stated interms of means. As was noted previously, theonly effect that time for encoding the imper-ative stimulus has on testing the insertion hy-pothesis is on the longest value for which la-tency between precue and response should re-main constant. An auditory imperativestimulus was used in the present study to min-imize encoding interference, but it does notmatter whether this resulted in more or lessrapid encoding than that for the precue. Thequestion may still be raised as to whether re-sults obtained in a catch-trial procedure (re-quired because PSI was constant over a blockof trials) may be applied to ordinary choicereactions, which typically do not have catchtrials. An alternative method would have beento use varied PSIs over a block of trials, withfalse reactions being prevented by time uncer-tainty. However, this is a very risky procedurebecause choice RT is affected to a greater ex-tent by time uncertainty than is simple RT

(Simon & Slaviero, 1975). In the present study,subjective as well as objective time uncertaintywas essentially eliminated by the use of thetransit-signal method (Gottsdanker, 1970). Itmight even be argued that the usual proceduresin which choice and simple RT are comparedshould be modified to include the transit-signalmethod and catch trials to avoid confoundinginserted operations with time-uncertainty ef-fects. Still, it must be admitted that there isthe possibility of a differential effect of catchtrials on choice and simple RT. This remainsto be investigated. An additional caution is thatthe present procedure does not identify thenature of the inserted operations. Discrimi-nation and response selection may be sequen-tial or integral. Moreover, there is no guaranteethat response actualization starts instantly afterresponse selection has been completed in achoice reaction. Possibly time is taken inswitching from one operation to another. Forthis reason, the Donders' computation of thetime required for discrimination and selectionis a maximum estimate. A final point is thatany existence of conditions that are contraryto the present assumptions can lead only toresults that falsify Donders' expectations in thepresent study. If medians are indeed being af-fected by trials in which the precue sometimesoccurs after the completion of discriminationand selection, the effect would be for latencybetween precue and response to increase forthat PSI rather than to remain constant. Anydifferential effect of encoding the imperativestimulus on the efficiency of the discriminationand selection operations would also destroy theinvariance of the latency.

Method

Subjects. Six subjects were used, I male and 5 femaleuniversity students. Ages ranged from 19 to 22 years. Onefemale subject replaced another whose data could not beused because of a computer malfunction. Subjects werepaid participants recruited by a notice posted in the psy-chology building.

Tasks. Two tasks were used, a precued choice reactionand a simple reaction, each with the transit-signal method(Gottsdanker, 1970). On a precued choice reaction, twolight horizontal bars ascended the display, side by side, andreached a suitably gapped reference line in 3 s. Just beforethen (or at the same instant) either the left- or right-handbutton was to be pressed, provided a tone sounded at theinstant of transit. A representation of the display and re-sponse buttons is shown in Figure 4. The interval between

onset of the precue (brightening of one of the bars) and

VERIFICATION OF BONDER'S SUBTRACTION METHOD 771

the onset of the imperative stimulus (tone) was constant

over a block of trials at one of the following values: 0, 30,

60,90, 120, or 150 ms. The left and right precue came on

equally often at random. Similarly, the tone occurred on

half of the trials at random. In the simple reaction only

one bar ascended the display, randomly on the right or left

side, so the subject knew 3 s in advance which response to

make, provided the tone occurred. Thus the brightening

stimulus was uninformative. Again, the tone for response

occurred on half of the trials at random.

Procedure. There were six blocks of 64 trials in each

daily session of about 50 min. There was an intertrial in-

terval of 10 s and a 2-min rest between blocks. On each

session there were first two blocks on the simple reaction,

the first of which was regarded as practice. There were

then four blocks of precued trials, the first of which was

regarded as practice. Subjects were tested over six sessions,

each on a different day. PSI was constant through a session.

A balanced Latin-square design was used, with each subject

having a different order of PSIs, with each appearing once

on each test day, and with each preceded once by every

other PSI. Feedback on RT and errors was provided on the

display immediately after each response. Questions were

encouraged after each block of trials.

Technical details. All programming of the display,

measurement and recording of RTs and errors, and the

providing of feedback were controlled by means of a Digital

Equipment Corporation PDF 11/03 DECLAB computer.

Determination of side of stimulus was done by random

allocation with no constraints. A different allocation was

made for each block of trials. A Hewlett-Packard I304A

Cathode-Ray Display was employed with a display area 20

cm high and 25 cm wide. The ascending left and right bars

were about 1.5 cm long. A short center bar, 0.5 cm long,

also ascended the screen at the same time. This was in-

cluded to provide a left-right landmark for the simple RT

task, on which only one stimulus bar ascended the screen.

The distance from the display to the subject was about 65

Display

t T

— P Tone= .5

Response Buttons

Figure 4. Schematic representation of the experimental

setup. (The brightening of a bar is shown by its thickening.

The filled circle shows the correct button to press, provided

the imperative tone occurred on that trial. P indicatesprobability; sec indicates seconds.)

Table 1Mean Values of Median and Mean ReactionTimes for Precued Responses and SimpleResponses on Corresponding Test Days

PSI

Mean of medians Mean of means

Precued Simple Precued Simple

0

306090120150

235204174

159155

153

154154154154150148

244214178164156

156

155157154154150

150

Note. All values are in milliseconds. PSI = precue-to-stim-

ulus interval.

cm. The subject sat in a sound-shielded room, in subdued

light, with forearms resting on a felt covered table and with

the two forefingers resting lightly on the response buttons.

A red light above each button came on when the subject

exerted sufficient pressure for response. This was made use

of only when the subjects were learning the task. A force

of about 0.6 N and a throw of 2 mm were sufficient to

operate the microswitches to which the buttons were

mounted. Both precue and imperative stimuli had dura-

tions of 50 ms. The tone, heard through a headset, had a

frequency of 1000 Hz and a power of 70 dB, 20 <<N/

m! (SPL).

Results

Mean values on correct trials across subjectsof the individual median and mean RTs (fromthe onset of the imperative stimulus) are shownin Table 1. There were 96 possible responsesat each PSI for each subject and 32 possiblecorresponding simple responses. Variation bytest day proved inconsequential for either sim-ple or precued RTs, with a range of only 4 msfor medians, so results are collapsed over days.

It can be seen that medians and means arein close agreement in their relation to PSI. Thepredicted drop of 30 ms between PSI = 0 andPSI = 30 ms is met almost exactly by each ofthe measures. However, the relation is slightlymore regular for medians, and the "elbow" inthe curve occurs a little sooner (as would beexpected from the previous discussion of thepreferability of medians). Consequently, thetest of Donders' two expectations is carried outin terms of medians. These tests are showngraphically in Figure 5. According to Expec-tation 1, for PSIs clearly shorter than the dif-ference between mean choice RT (with no ad-


vance information) and simple RT, the valueof L, latency of start of response from onsetof precue, should be invariant. The presentcomparable choice and simple means are thevalues at PS1 = 0, seen in Table 1 to be 244and 135 ms, with a difference of 79 ms. Thus,it is expected that median L should be constantover PSIs 0, 30, and 60 ms. It appears in Figure5 that this is so, in accordance with Donders'Expectation 1. Their values are 235, 234, and235 ms, respectively. The validity of this com-parison is enhanced by the fact that mediansimple RT was identical to the nearest milli-second for PSIs 0 through 90 ms; All were 154ms. Furthermore, individual subjects werequite consistent as seen in the 95% confidence

300

250

~ 200

£

fe 150t-o_i

100

50

Donders Expectation (1)

L=C

Donders Expectation (2)

PRECUED REACTIONS

D L: Latency measured from

• RT

precue onset

: RT measured fromstimulus onset

RTS: Simple RTi _ i i

30 60 90 120

PSI (msec)

150

Figure 5- Mean of median latencies and reaction times inmilleseconds as a function of precue-to-stimulus interval(PSI). (L indicates the latency between the onset of theinformative precue and the onset of the response. C standsfor a constant value. RT indicates reaction time measuredbetween the onset of the imperative stimulus and the onsetof the response. RTP is the reaction time in the procedurein which a precue is presented. RTS stands for simple re-action time.)

interval for each of the three differences be-tween means of medians over this range ofPSIs. The intervals were -2.63 to +3.68 msfor the 0-30 ms difference, -4.27 to +6.27 msfor the 0-60 ms difference, and -8.88 to +6.54ms for the 30-60 ms difference. The hypoth-esized value of 0 clearly falls within each range,and no other specific hypothesis appreciablydifferent from 0 is tenable. The stability of RTfor the two longest PSIs, which are clearly lon-ger than the difference between choice RT andsimple RT of 79 ms, is equally evident, themeans of medians being 155 and 153 ms forthe 120- and 150-ms PSIs, respectively. How-ever, it may be seen that there is a slight (5 ms)difference between precued and simple RT atthose PSIs and at the 90 ms PSI also. A two-way repeated measures analysis of variance wasperformed for precued and simple RT overthese three longest PSIs. The 5-ms differencefor conditions was significant, F(l, 10) =14.25, p < .01. Also, the effect of PSI was sig-nificant, F(2, 10) = 6.99, p < .025. The inter-action between condition and PSI was not sig-nificant (F < 1). This is because simple RTdropped slightly (and inexplicably) as did pre-cued RT for PSIs 120 ms and 150 ms on thosetesting days. It will be recalled that this was adifferent actual day for each subject. Thus,Donders' Expectation 2 was not quite met. Itwas off by the very small (but statistically sig-nificant) amount of 5 ms.

It seems likely that the discrepancy betweenprecued and simple RTs at the long PSIs wasdue to operation at different points on thespeed-accuracy trade-off function. There werealmost no wrong-direction errors at the 120-or 150-ms PSIs nor, of course, for simple RTon corresponding days (3 out of 2,972 trialsfor the three conditions combined). However,the overall percentages of anticipations andfalse alarms were consistently higher for thesimple reactions than for the precued reactionson corresponding days for the three longestPSIs: 6.51% vs. 0.87% at PSI = 90; 2.60% vs.1.48% at PSI = 120, and 5.73% vs. 3.04% atPSI = 150. It is proposed that the discrepancybetween about 5% and 2% errors could wellaccount for much larger differences than 5 ms.Unfortunately, there appear to be no data ex-tant on speed-accuracy trade-off for contingentsimple reactions, and most studies of choicereaction have induced much higher error rates.


However, two of the error rates produced inthe Pachella and Pew (1968) study on theirDay 3 are somewhat comparable. There, anincrease in error rate of about 5% to 8% be-tween conditions resulted in about 20-msshortening in RT. A further analysis of errorshelps to substantiate the conclusions reachedconcerning the short ISIs. There was no ten-dency for subjects to "jump the gun" on sometrials and commit themselves to a response onappearance of the precue, thereby sharpeningthe decline in RT with PSI. In fact, there werefewer wrong-direction errors at PSI = 30 andPSI = 60 than at PSI = 0, 2.52% and 1.65%as compared with 3.12%. Anticipations andfalse alarms were below 1 % at all three of thesePSIs.

Discussion

The prediction of invariance of median pre-cue-to-response latency (or equivalently a — 1slope of median RT) over PSIs whose valuesare clearly less than the difference betweenmean choice and simple RT was confirmedalmost exactly. The slight increment of RT atthe longer PSIs over simple RT seems almostcertainly due to the higher error rate for thelatter. These findings, as has been explained,lend very strong support to Donders' assump-tion in use of the subtraction method that ina choice reaction additional operations havebeen inserted into a simple reaction.' Of great-est interest at the present day is the evidencethat actualization of a response cannot beginbefore response selection has been completed.The use of the subtraction method is justifiedfor this application, provided it is stipulatedthat neither the nature or number of insertedoperations is revealed. The other use of thesubtraction method by Donders is, in fact, anattempt to separate the durations for stimulusdiscrimination and action selection. In thatapplication a contingent (or c) reaction is ob-tained for comparison with the choice (or b)reaction and the simple (or a) reaction. Theassumption is that response selection is notrequired to the "correct" stimulus, only dis-crimination. This assumption is challenged byrecent evidence that there are, in fact, "motorprocesses" associated with not responding tothe "wrong" stimulus (Richer, Silverman, &Beatty, 1983), so a kind of response selection

must be involved. There appears to be no clearway, using the present augmented subtractionmethod, to separate the hypothesized stages ofdiscrimination and response selection.

The assigning of response actualization tooperations that do not overlap with responseselection has bearing on previous examinationsof the issue of discrete processing stages. Intheir "continuous flow model," Ericksen andSchultz (1979) hold that in visual search "cer-tain responses become primed over other re-sponses" (p. 252). They also state that "whenthe priming for ... [a] response reaches theevocation threshold, the [prior] inhibition isremoved and the response occurs" (p. 252).From the present conclusions it would insteadbe stated (provided their basic conception iscorrect) that when inhibition is removed, re-sponse selection occurs. Whether a response isactualized depends on the utilization of theimperative component of the stimulus. Miller'sconclusion that "partial information about astimulus was transmitted to response activa-tion before the stimulus was uniquely identi-fied" (1982, p. 273) would similarly be refor-mulated in terms of response selection. Thebasis for his interpretation was the advantagefor identification RT when the initial characterof a pair was assigned to two fingers of thesame hand rather than to two fingers of thedifferent hands. However, Reeve and Proctor(1984) have recently shown that there is thesame advantage when the initial character isassigned to adjacent overlapping fingers of thedifferent hands. Thus, there would appear tobe more efficient selection of an action withina limited movement space rather than moreefficient response preparation of fingers on onehand.

1 It is important in testing the insertion hypothesis by

means of the augmented subtraction method to rule outpossible stimulus artifacts related to the presentation ofthe precue. Such possibilities were examined in studiesthat preceded the present experiment. First, using a sampleof 24 men and women ranging from 21 to 78 years of age,it was shown that an advance precue that is uniniformativedoes not affect simple RT (Gottsdanker & Shragg, 1981).Second, the possibility was tested that RT is reduced withlengthening of PSI in part because of the increasing con-spicuity of the brightening precue as it occurs farther fromthe reference line. However, increasing the contrast of theprecue by reducing the brightness of the reference line byabout half did not shorten RT at PSI = 0 for a sample of18 college men and women (Gottsdanker & Shragg, 1984).


The issue of serial-stage versus continuousmodels was also investigated through use of aprecue method by Meyer, Yantis, Osman, andSmith (1984). Although their overall conclu-sion agreed with that arrived at in the presentstudy, the methods and logic were quite dif-ferent. The precues were not the stimuli forresponse that would occur in the nonprecuedtask as is required in a test of the Dondershypothesis. They were incompatible words ornonwords that were followed by the actualcompatible stimuli rather than by a neutralimperative stimulus. Moreover, except forPSI = 0, there were much longer times betweenonset of the precue and the onset of the con-firming stimulus, about 785 ms for the "me-dium" delay. The logic was that at short delaysRTs would all be choice reactions, at long de-lays they would all be simple reactions, whileat some medium value there would be a mix-ture of choice and simple reactions, with aconsequent increase in the variance of the RTdistribution. In the present procedure, inwhich it was assumed that the same processingrequired in a nonprecued case would start withthe onset of the precue, there would be quitea different expectation concerning RT distri-butions. For a PSI on which there is a delayon some but not all trials, the distribution ofwaiting times would be truncated. Conse-quently, RT distributions would have a con-stant variance until PSIs were reached at whichvariance would be gradually reduced as trun-cation of waiting times increases until finallya reduced RT is reached when no waiting-timedelay is required on any response. Experimentsusing finely graded random PSIs are now beingconducted by one of the present investigatorsto test this expectation. It should be noted thatMeyer et al. (1984) make the assumption that"This contingency betweeen the prime and teststimulus allows the subject to prepare his orher response fully in advance, depending onhow long the delay is between the two stimuli"(p. 72). Following Donders, the present viewis that an absolute precue allows the subjectto select a response, not to make any progresstoward actualizing one. Perhaps the distinctionmade by Meyer et al. between response pro-gramming and program loading is parallel.

There is also a resemblance between thepresent paradigm and that used to study abilityto inhibit RT responses. In the latter paradigm

the first stimulus instructs the subject to makethe required simple or choice reaction with anoccasional trailing stimulus giving the instruc-tions not to respond. In the model of Logan,Cowan, and Davis (1984) there is a race be-tween response and inhibition processes. Be-cause simple as well as choice reaction may beprevented, it may be concluded—if the modelis accepted—that commitment to a responsedoes not occur until some time after the re-sponse-actualization process has started. Therewould thus be two major premovement stagesof response actualization. It should be noted,despite the similarity to the present paradigm,that the inhibition procedure does not addressthe issue posed by the subtraction method.Further, in the foregoing study, only one in-terval shorter than 100 ms was used, and therewas some success in stopping a response evenwith an interval of 400 ms.

A perhaps closer resemblance is seen in ex-periments on the psychological refractory pe-riod (PRP). Typically in these studies twostimuli are given in rapid order, each requiringits own response. Interest is centered on thelengthening of RT as interstimulus interval(ISI) is reduced (or conversely how it is short-ened as ISI increases). According to the single-channel hypothesis (Welford, 1959), thereshould be a -1 slope since the processing ofStimulus 2 must be delayed until the processingof Stimulus 1 has been completed. That hy-pothesis is not the same as that investigated inthe present study even though it is isomorphicwith it. Two separate responses are made inthe typical PRP study, so the interference isbetween these responses or even between thesame stage of the two responses. In the presentmethod of critical precues, there is only oneresponse, and it is hypothesized that a stage ofthis response cannot start until another stageof the same response has been completed. Still,the distinction blurs in those PRP experimentswhere no response is required to the first stim-ulus. Usually, in such studies the first stimulusis irrelevant to the response and can only beregarded as distracting (e.g., Davis, 1959).However, Nickerson (1967) used the same par-adigm as that of the present study, but withvaried ISIs, and considered the lengthening ofRT as PSI was shortened as an indicator ofpsychological refractoriness. A much morereasonable interpretation is that RT was in-


flated at the short ISIs because of low momen-tary probability of stimulus occurrence(Gottsdanker, 1975), not because of psycho-logical refractoriness. This conclusion isstrengthened by the fact that in Nickerson'sstudy, an ISI (or PSI) of almost 400 ms wasrequired for RT to descend to the level of sim-ple RT. Here, no more than 90 ms or 120 mswas required.

In addition to its present use, the augmentedsubtraction method may be applied wheneverit is possible to split stimulus contributions thathave different hypothesized functions into twoparts. One example is the programming of as-pects of a response (or, according to presentevidence, selection of aspects of a response).Rosenbaum (1980) showed that RT was re-duced in accordance with the number and kindof precued dimensions. It should be noted thathe used very long PSIs, 3 s and 5 s. His inter-pretation was that part of the programmingwas done in advance, so less had to be donewhen the stimulus exactly specifying the re-sponse appeared. An important point is thata precue that did not specify a dimension butsimply reduced the number of response alter-natives did not reduce RT. However, Goodmanand Kelso (1980) found that with compatibleprecues and stimuli for response, RT was ef-fectively reduced by such "ambiguous" pre-cues. They attributed Rosenbaum's results toproblems of translation. More generally, theuse of very long PSI can never lead to definitiveresults because of the many possibilities thatexist for reorganization of preparation. On theother hand, the serial expectancies of Rosen-baum can be put to a direct test by use of thepresent augmented subtraction method. Theexpectation is, of course, that RT will diminishexactly by the amount PSI is increased untila constant value is reached. Such study was,in fact, carried out in the Santa Barbara lab-oratory by Reed (1984) using compatible pre-cues but with both compatible and incompat-ible response stimuli. The — 1 slope that wouldsupport Rosenbaum's formulation was notfound. Instead, there was only a small reduc-tion of RT at the short PSIs that was possiblyan automatic facilitation. Only when the PSIwas long enough to allow repreparation, about300ms (Gottsdanker, 1975; Sanders, 1971) wasthere appreciable reduction of RT. The impli-cation, in present terms, is that actions are se-

lected by an integral rather than serial process.Another possible application is on the questionof whether a complex stimulus is analyzed byseparate aspects or globally. Here one aspector another is precued, and the course of re-duction of RT with PSI is again determined.

A by-product of the present experiment isa possible way of measuring simple RT, with-out the complication of error rate. At PSI =120 ms there were virtually no wrong-choiceerrors (as occur in typical choice reactions) andonly a few false alarms and anticipations (asoccur in typical simple reactions with littletime uncertainty). Yet RT was only 5 ms longerthan simple RT. Apparently, there was justenough time to make an unhurried choice, butnot enough time to establish a bias toward oneof the alternatives.

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Received May 10, 1984Revision received May 28, 1985

Documents

Verification of Donders' Subtraction Method - Semantic Scholar · Figure 1. Representation of simple and choice reactions according to Donders' insertion hypothesis. (The direction