Automatic Aftereffects in Two-Choice Reaction Time: A...

Journal of Experimental Psychology:Human Perception and Performance1984, Vol. 10, No; 4, 581-598

Copyright 1984 by theAmerican Psychological Association, Inc.

Automatic Aftereffects in Two-Choice Reaction Time:A Mathematical Representation of Some Concepts

Eric Soetens, Michel Deboeck, and Johan HuetingUniversity of Brussels, Brussels, Belgium

A mathematical model is developed to describe sequential effects in two-choicereaction time experiments with a short response-stimulus interval. Evidence isbriefly discussed that in conditions with short response-stimulus intervals, automaticaftereffects dominate sequential effects, and the influence of subjective expectancycan be neglected. In these conditions the model premises three components ofautomatic aftereffects—facilitation, inhibition, and noise, with a common decayfactor. Influence of response-stimulus interval and practice on sequential effectsare examined and related to parameter changes in the proposed single-decay model.The decrease of automatic aftereffects with increasing response-stimulus intervalis primarily ascribed to an increasing decay factor. The parameter representationof the model also clarifies the issue of the disappearance of automatic aftereffectswith practice. It shows a gradual fading of inhibition in the initial stages of practice,together with a slower decrease of the facilitation effect. The single-decay modelprovides a satisfactory explanation for the processes involved in compatible two-choice reaction time with short response-stimulus interval.

During the presentation of a series of ran-dom binary stimuli, subjects react as if certainsequences are more likely to occur than others.Remington (1969) demonstrated that a re-action time (RT) in a two-choice task dependsupon the specific sequence of the precedingstimuli. Influences caused by events dating onetrial back are called first-order effects, whereasinfluences caused by earlier trials are calledhigher order effects. Several efforts have beenmade to develop theories relevant to sequentialeffects. In general, two main categories of the-ories can be distinguished: theories based onstrategies and expectancies on the one handand theories based on automatic aftereffectson the other. The aim of the present article isto develop a mathematical model for only onecategory, namely, automatic aftereffects.

There is disagreement in the literature con-cerning the nature of automatic aftereffects.Some authors argue that it is a form of ex-

The authors are very grateful to J. Duncan from theMedical Research Council, Applied Psychology Unit,Cambridge, England, and L. C. Boer, from the Institutefor Perception TNO, Soesterberg, the Netherlands, for theirvaluable comments on revising this article.

Requests for reprints should be sent to Eric Soetens,Laboratory of Experimental Psychology, Waverse steenweg1077, B-1160 Brussels, Belgium.

pectancy, whereas others claim that automaticeffects are different and independent concepts.Recent data obtained in our laboratory seemto support the notion of separate concepts.The methods and conditions separating au-tomatic aftereffects from expectancy are stud-ied in a separate report (Soetens, Boer, &Hueting, 1984). In the present article we as-sume that both concepts are different. Someof the differentiating aspects will be brieflydiscussed.

Subjective expectancy is an explanatoryconcept with respect to subjects' expectanciesconcerning a specific stimulus and their prep-aration for this event (Bertelson, 1961, 1963;Kirby, 1976; Laming, 1968). Typical for ex-pectancy is its two-sided effect: It has a costand a benefit. If an expectancy is confirmed,a short RT follows; if it is not, RT is prolonged.The effect is easy to detect in a two-choicetask, where high expectancy of one stimulusimplies low expectancy of the alternative. Ex-pectancy can explain a first-order alternationeffect, that is, faster reactions to a differentstimulus when compared to reactions to a re-peated stimulus. The effect is described as thesubjects' tendency to expect more alternationsthan repetitions, in a way analogous to thegambler's fallacy phenomenon (Jarvik, 1951).Expectancy can also explain some higher order

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582 E. SOETENS, M, DEBOECK, AND J. HUETING

sequential effects. Higher order expectancy ef-fects can be described as the subjects' pref-erence for a continuation of an unbroken runof identical events, that is, alternations or rep-etitions (Kirby, 1976,1980). For example, aftera series of alternations, another alternation isexpected. The longer the preceding alternationrun, the stronger the expectancy. When theexpectancy is confirmed, a short RT ensues,but when it is discontinued, RT is long. Thesame reasoning applies to repetition runs.

Expectancy effects are mostly reported inexperiments with a relatively long response-stimulus interval (RSI; Hale, 1967; Kirby,1972; Williams, 1966). Vervaeck and Boer(1980) suggested that the process of buildingup an expectancy needs a critical minimumtime. This time can be estimated by reviewingthe literature on first-order sequential effects.First-order alternation effects are usually foundwith RSIs of more than '/z s. Kirby (1980)remarks, however, that there could be seriousconfounding of RSI influences with compat-ibility. Results of pilot studies in our laboratorysuggest that the critical minimum RSI for ex-pectancy in a spatially compatible two-choicetask is about 100 ms. Kirby (1976), however,reported subjective expectancy in experimentswith RSIs of 1-50 ms, but his actual RSI waslonger because his subjects had a "time-on-key" period between the reaction and the onsetof RSI. The RT counter stopped when thetelegraph key was pushed down, but RSIstarted at the moment that the key was re-leased. Thus, subjects could delay the onset ofRSI by keeping the key down. The time onkey can be estimated by consulting Welford(1977), who reports an average of 150-200ms, using a similar, if not the same, apparatus.The actual RSI of Kirby would then probablyexceed 200 ms, which explains the finding ofan expectancy effect. The same confusingmethodology was also used by other research-ers (e.g., Bertelson & Renkin, 1966), andsometimes the actual RSI was additionallyprolonged with the warming-up time of thepresented stimuli when incandescent lampswere used (Keele & Boies, 1973). Apart frommethodological differences, the influence ofRSI has often been compounded with the in-fluence of other variables, such as stimulus-response compatibility, practice, and numberof alternatives. For a detailed analysis con-

cerning the interactions of some of these vari-ables we refer to Soetens et al, (1984).

The second category, automatic aftereffects,is usually associated with short RSI experi-ments. Automatic aftereffects are assumed tobe short-lived automatic consequences of pro-cessing a stimulus. In contrast with subjectiveexpectancy, automatic aftereffects seem towork only in one direction, namely, a gain inprocessing speed. Several researchers foundthat in short RSI conditions, RT to a repeatedstimulus was faster than RT to a differentstimulus (Bertelson, 1961, 1963; Hyman,1953). This effect was called the repetition ef-

fect and was originally observed as a first-ordereffect. The effect, later renamed automatic fa-cilitation, has been replicated repeatedly (e.g.,Hale, 1967; Kirby, 1976). The repetition effectalso appeared in experiments with relativelylong RSIs (Bertelson, 1963; Bertelson & Ren-kin, 1966; Entus & Bindra, 1970), but thiswas probably due to the interaction of stim-ulus-response compatibility. The effect alsoincreases when the number of alternatives isincremented (Hoyle & Gholson, 1968; Hyman,1953; Remington, 1969, 1971). Automatic fa-cilitation is said to decay over time but hasnot necessarily disappeared with the arrival ofthe next stimulus. Therefore, an accumulationcan take place, thus creating higher order fa-cilitation effects (Kirby, 1976; Remington,1969). The effects of earlier trials are pro-gressively less influential, suggesting that theydecay over time. The fact that facilitation oc-curs only with short RSIs is also an indicationthat it dissipates with time. Moreover, severalauthors found decreasing repetition effectswith increasing RSIs (Bertelson, 1961; Ber-telson & Renkin, 1966; Smith, 1968; Umilta,C. Snyder, & M. Snyder, 1972), supporting thenotion of a decaying repetition effect.

According to Laming (1968), facilitation isa general phenomenon, not limited to a specificstimulus. His results suggest that at short RSIs,after a sequence of repetitions, there is alwaysa facilitation effect, no matter whether thestimulus to come is a repetition or an alter-nation. Suppose, for example, that P and Qare the two possible alternatives in a two-choicetask. Let us consider as a typical example amultiple repetition sequence PPPP. Lamingobserved that RT is short when the repetitionsequence is continued, but more important,

AUTOMATIC AFTEREFFECTS IN TWO-CHOICE REACTION TIME 583

when an alternation occurs, RT is also shorterthan after any other alternation sequence. Inother words, RTPPppQl is shorter than any otherRT...PQ, This one-sided effect is clearly anti-expectancy.

Vervaeck and Boer (1980) discovered thatLaming's general facilitation effect changedinto a stimulus-specific effect after extensivetraining. They concluded that this develop-ment can not be explained by facilitationalone. Therefore, an alternative model wassuggested, drawing a clear line between facil-itation as a stimulus-specific effect on the onehand and a second concept, namely inhibition,on the other hand. The model assumes twochannels or pathways, one for each of the twostimuli, going from stimulus intake to responseexecution, and the influence of automatic af-tereffects, facilitation and inhibition, is locatedsomewhere along these pathways. Each chan-nel is assumed to have a neutral state, whichcan be changed from extreme excitation toextreme inhibition. When a particular stimulusis presented, its corresponding "home" chan-nel will be used, causing the excitation of thatchannel. The critical assumption of the modelof Vervaeck and Boer concerns the influenceof stimulus processing on the "alternative"channel. It is proposed that an alternation tothe home channel inhibits the alternativechannel, whereas repetitions on the homechannel do not modify the state of the alter-native channel. As an analogy of the model,consider the electrical induction phenomenon.Alternations can be compared with abruptchanges in electrical potential, which causeinduction in nearby channels. In the model,inhibition is comparable to induction and in-hibits the processing on the alternative channel.Repetitions on the home channel can be com-pared to small changes in potential, thus notaffecting the state of the alternative channel.It is further assumed that inhibition, similarto facilitation, decays over time. In this way,repetitions on the home channel allow the dis-sipation of inhibition on the alternative chan-nel. Vervaeck and Boer argued that the in-hibition effect could, in fact, explain the samephenomenon as the general facilitation effectproposed by Laming (1968). Indeed, the dis-sipation of inhibition on the alternative chan-nel seems to work as a facilitation. It shouldbe noted that the inhibition effect is stimulus

specific, because an alternation from the al-ternative channel to the home channel inducesno inhibition on the home channel.

A third concept associated with sequentialeffects in short RSI experiments is suggestedby Laming (1968). He proposes the existenceof an internal standard to identify the incomingsignals. When a series of repetitions is pre-sented, the standard becomes sharp and en-ables the subject to detect either signal withrelative ease. When the signals are alternated,the image becomes blurred and the identifi-cation of either signal is more difficult. Thisblurring of the standard can be described asnoise in the process of identifying the stimulus.Laming used this noise to explain the slowingdown of RTs to either stimulus after sequenceswith many alternations.

All three concepts mentioned earlier haveproven useful in explaining part of the dataobtained in two-choice RT-tasks with shortRSI, but their mutual relationship is not welldefined. For example, does an inhibition over-rule a preceding facilitation, vice versa, or arethey approximately equal in strength? Whatis the speed of decay of such effects as facil-itation, inhibition, and noise? Are these con-cepts redundant, and if so, to what extent? Itmight be rewarding, therefore, to establish re-lationships between the components of au-tomatic aftereffects by means of a mathemat-ical model.

In the model that we propose no parameterfor subjective expectancy is incorporated.Therefore, the model applies only to sequentialdata caused by automatic aftereffects. In aseparate report Soetens et al. (1984) foundthat in short RSI conditions (RSI < 100 ms)the influence of subjective expectancy is neg-ligible. Briefly, the argumentation is as follows:A repetition-alternation function is derived,representing the effects of each particular se-quence of preceding stimuli on the RT to thenext event that is either a repetition or analternation. Figure 1, Panel a shows an ex-ample of a repetition-alternation scattergram,based on Kirby (1972). For each precedingsequence of stimuli, RT to a repetition is set

' The presentation order of stimuli is given by the leftto right reading order. The right-most letter denotes thecurrent stimulus.

584 E. SOETENS, M. DEBOECK, AND J. HUETING

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275 300 425 450 475 500 525 550

repetition RT (msec)

Figure 1. Repetition-alternation scattergram based on data of Kirby (1972), representing an expectancycondition in the left panel, and data of Vervaeck and Boer (1980), representing automatic aftereffects inthe right panel. (The crosses stand for reaction times [RTs] after a sequence of three alternations; the plussigns stand for RTs after a sequence of three repetitions. [From Soetens, Boer, & Hueting, 1984])

out along the abscissa, and RT to an alternationis set out along the ordinate. Kirby assumedthat expectancy was dominant in these data.The cross in Figure 1, Panel a represents RTsafter three alternations. Subjects expect a con-tinuation of this run. Hence, RT to a subse-quent alternation is relatively short, whereasRT to an unexpected repetition is long. Theplus sign in Figure 1, Panel a represents RTsafter a run of three repetitions. A continuationof this run is expected. Hence, RT to a rep-etition is short. The repetition-alternationfunction for expectancy data thus describesthe negative trading relation between expectinga particular event and not expecting the al-ternative event (cf. Kinchla, 1980). Audley(1973) predicted this time exchange relationwith a slope of —45° on the assumption thatthere is a linear relationship between expec-tancy and two-choice RT.

Positive slopes are predicted for the repe-tition-alternation function of automatic af-tereffects data. In contrast to expectancy, au-tomatic aftereffects are one-sided, so that somesequences create a benefit for either of thesubsequent events. Figure 1, Panel b shows arepetition-alternation scattergram based ondata of Vervaeck and Boer (1980). Vervaeckand Boer assumed that automatic aftereffectswere dominant here. The plus sign representsRTs after three previous repetitions. It is ap-parent that RT is short whether the next eventhappens to be a repetition or an alternation.The other points form a positive slope in therepetition-alternation function, except for thepoint marked by the cross. This represents

RTs after three previous alternations. Soetenset al. (1984) showed that this point is an ex-ception, indicating the breakthrough of ex-pectancy. We therefore decided to omit thispoint in the analysis of the present experimentsin order to avoid traces of expectancy. Withoutthe discrepant point, correlation in Figure 1,Panel b is .99, and the slope of the best-fittingstraight line is 34°. The general prediction ofautomatic aftereffects is a positively slopedrepetition-alternation function that contrastssubstantially with the negatively sloped repe-tition-alternation function predicted for anexpectancy condition.

In the following experiments, the repetition-alternation function is tested for a positiveslope and a high correlation as a check on thedominance of automatic aftereffects.

A General ModelThe information flow from the perception

of stimulus P to its corresponding response iscalled the P channel and, for stimulus Q, thethe Q channel. In the case of two similar stimuliit is assumed that both channels have similarcharacteristics and, consequently, it can be as-sumed that the time needed for informationto flow through each channel is equal. This iscalled the neutral time T0. The absolute valueof T0 depends upon the complexity of thestimulus-response relation and can vary fromsubject to subject. More permanent changeswithin one subject, such as learning effects,can also influence this neutral time. The valueof To is estimated as a function of the overallmean RT.


If, in this neutral state, a P stimulus is pre-sented, then, in case of a correct response, theP channel is triggered. The result is a facili-tation for a following P stimulus if RSI is nottoo long. This can be represented as a decreasein processing time for a following P stimuluswith a factor/ with 0 «/< 1. So

r?-TO-/TO, (i)where Tp is the time needed for processing aP stimulus after the arrival of a P stimulus,the subscript relating to the preceding stimulus,the superscript to the appropriate channel.

On the Q channel on the contrary, this Pstimulus can give rise to an inhibition effect,which, according to this concept, results in anincrease of processing time for a subsequentQ stimulus with a factor say »', with / > 0.Inhibition effects on the Q channel appear onlywhen switching from the Q to the P channel.This happens only in 50% of all P stimuli.This means that the actual increase of pro-cessing time is i/2. Processing time on the Qchannel is as follows:

T$ = To + iTo/2, (2)

where T$ is the processing time needed onthe Q channel after the arrival of a P stimulus,the subscript relating to the preceding stimulusand the superscript to the appropriate channel.

Both effects, facilitation and inhibition, de-cay over time. The decay factors are nameddf and d\, respectively. Both have a positiverelation with time (d{, d\> 1). The momentthe next stimulus is about to arrive, the neededprocessing times of Equations 1 and 2 havechanged to

T$ = To + i

(3)

(4)

Following the same reasoning, the situationon the P channel after a second P stimuluswill be

T0- fTo/dt -

where TpP is the needed processing time onthe P channel (superscript) after the stimulussequence PP (subscripts). Note that the facil-itation caused by the last P stimulus exerts itsinfluence on the momentary processing timebefore this stimulus had arrived, this being

Tp. After decay, processing time will be thefollowing:

TpPp=T0-fT0/df

2~fn/d(. (6)According to the two-channel theory, the

arrival of this second P stimulus does not in-duce an inhibition effect on the Q channel.So, apart from decay, no changes occur on theQ channel.

If, on the contrary, the second stimulus wereto be Q, an alternation, then an increase ofthe general noise level is predicted. Again thisnoise effect will decay over time. Because thenoise influence is not channel specific, it willbe found in both channels. Besides this noiseeffect, there will be an inhibition in the Pchannel. Processing time in this channel afterthe sequence PQ and after decay can be derivedfrom Equation 3:

Tin = T0 - fT0/d(2 + (iftk + n/dn)T$, (7)

where i is the inhibition parameter with itsdecay d\, and n represents the influence on thenoise level with its decay dn (n ** 0 and dn **1). Note again that inhibition and noise exerttheir influence on the momentary necessaryprocessing time Tp. The influence on noiselevel, caused by the alternation PQ, can alsobe found in the Q channel, where, moreover,a facilitation occurs. Integrating this influencein Equation 4, processing time on the Q chan-nel after sequence PQ and after decay can beexpressed as follows:

r& = To + iT0/2d2 + (n/dn -f/df)T$, (8)

with noise («) and facilitation (/) exerting theirinfluence on the momentary necessary pro-cessing time on the Q channel, T$.

If this reasoning is continued and the modellimited to sequences of four stimuli, 16 for-mulas are obtained, representing 16 states ofa channel, each corresponding to a specificsequence of events.

(5) Model Predictions

The general model predicts sequence effectsdepending on the values of the parameters.These parameters can be influenced by factorssuch as practice, RSI, and other task variables.Some restrictions can be set for the parametersapart from those already mentioned in de-


veloping the model. In short RSI experimentsit can be expected that a first-order facilitationeffect will occur. This means/> «, becauseotherwise the noise effect caused by an alter-nation overrules the first-order facilitation ef-fect. To have a better idea how the model pre-dicts the differences in RT as a function ofthe sequence, arbitrary values can be given tothe parameters and the predictions comparedwith data from a short RSI experiment. For/ and /' a value of 0,5 was chosen and fornoise n = 0.2. All decay factors were given thevalue 3.

Figure 2 shows how RTs are predicted aspercentages of the neutral processing time T0.Sequences on the horizontal axis are in theorder of increasing RT prediction. The curveis divided into two parts according to the first-order effect. The first part, with first-order rep-etitions, is termed the repetition curve, whereasthe second part, with first-order alternations,the alternation curve. Throughout the articlethe same order of sequences is maintained inall figures. In this way, it is easy to compare

the evolution of the data with the predictionsin Figure 2. Decreasing parameter i (inhibi-tion) from 0.5 to 0.2 and plotting the predictedvalues (see Figure 2) cause a change in theslope of the alternation curve, whereas therepetition curve is practically unaffected. De-creasing parameter/(facilitation) from ,5 to.25 results in a shift in the repetition curvewith respect to the alternation curve. Increas-ing the d parameter flattens both repetitionand alternation curve, bringing them closer tothe 100% level. For clarity, the latter is notshown in Figure 2. The predictions are com-pared with the data of Vervaeck and Boer(1980), who used an RSI of approximately 55ms. A comparison of the observed RTs withthe model predictions shows that the modelforetells fairly well which sequences causeshorter RTs and which cause the longer RTs.

Experiment 1

To make predictions, arbitrary values wereset for the model parameters in the prior sec-

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MODEL PREDICTIONS d=3f - 0 . 5 & i=0.5f » 0 . 5 & i=0.2f = 0.25&i=0.5

0.2

A-& DATA OF VERVAECK & BOER (1980EXPERIMENT 2)

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P Q Q P Q P P Q Q P P Q P Q Q PP P Q Q Q Q P P Q Q P P P P Q QP P P P Q Q Q Q Q Q Q Q P P P Pp p p p p p P P Q Q Q Q Q Q Q Qp p p p p p p p p P P P P P P P

S T I M U L U S S E Q U E N C E S

Figure 2. Predicted reaction time of the general model, as a function of stimulus sequences, with two valuesfor facilitation (/) and inhibition (/')• (P is the current stimulus and Q the alternative. Read the strings inchronological order from top to bottom. The lowest letter denotes the current P stimulus. Predictions areexpressed in percentages of the neutral processing time and compared with data of Experiment 2 of Vervaeckand Boer—"Sequential effects in two-choice reaction time: Subjective expectancy and automatic aftereffectat short response-stimulus intervals" by K. R. Vervaeck and L. C. Boer, 1980, Ada Psychologica, 44, 175-190. Adapted by permission of the authors.)


tion. The optimum values for these parameterscan be calculated by comparing model pre-dictions with medians of a large data set andchanging the parameter values by means of agrid search. The data set in this experimentcontains approximately 1,100 RTs per stimulussequence.

The general model, as proposed, containstoo many parameters. Some of the treatedconcepts could be redundant. In Experiment1 an attempt is made to eliminate redundantconcepts by comparing the experimental datawith approximations obtained from threesimplified forms of the general model.

In a first submodel, it is assumed that decayis independent of whatever effect caused it.Expressed in parameters, this means df - d\ =dn. This is termed the single-decay model. Thefacilitative influence of repetitions has beenascertained so many times that the facilitationparameter is considered to be indispensablein all models. The concepts of noise and in-hibition are more open to question. For thisreason, two other submodels are analysed, eachleaving out one of these concepts. The secondsubmodel eliminates the noise factor. Thismodel can be compared to the two-channelrepresentation as proposed by Vervaeck andBoer (1980). Translated in parameters of thegeneral model, this means n = 0 and dn = 1,leaving the possibility of different decay factorsfor facilitation and inhibition. This model isreferred to as the model without noise. In athird submodel, inhibition is eliminated,meaning / = 0 and d\ = 1, and a possibilityfor different decay factors for facilitation andnoise. This is called the model without inhi-bition.

To obtain comparable values between modelpredictions and median RTs, a value for T0has to be chosen. A reasonable approximationis to keep T0 constant for every experimentalcondition, with a value of T0 = MRT/A/T,where MT is the mean of all computed rvaluesand MKT the mean of the median RTs persequence.

In the present experiment, the influence ofsubjective expectancy was kept to a minimumby applying very short RSIs. To reduce theremaining traces of expectancy, we tested themodels without RTs after three alternations.Moreover, before applying the model to theobserved data, we calculated the slope and

correlation of the repetition-alternation func-tion.

MethodSubjects. Twenty subjects volunteered for the exper-

iment. They were all unfamiliar 'with RT tasks.Apparatus. Stimuli were presented by means of two

7-segment light emitting diodes (LED), displaying thecharacter 0. Each LED measured IS mm X 16 mm andtheir centers were set 45 mm apart on a black verticalpanel. The panel was placed 2.6 m from the subject, re-sulting in a between-stimulus visual angle of 1°. A whitevertical line separated the two displays, Before the startof each 100-trial-block of stimuli, a third LED, placed 45mm to the left of the left stimulus and displaying thecharacter 8, was used as a warning signal. The room wassemidarkened to make the stimuli clearly visible. Two pushbuttons connected to microswitches, which were to bemanipulated by the subject's forefingers, were placed ona horizontal response panel in front of the subject. Theleft hand operated the left key in response to the left LED,and the right hand operated the right key in response tothe right LED. The experiment was controlled by anHP2100A minicomputer.

Procedure. RT was recorded as the time between stim-ulus onset and the moment that either of the responsekeys was switched down. This switching terminated stim-ulus exposure and started RSI, which lasted 20 ms. Thus,"time on key" overlapped RSI.

Complete randomization of all stimulus sequences wasaccomplished by basing the chance of exposure of a par-ticular stimulus on the value of the RT to the previousstimulus. When this RT, in ms, was an even number, theleft stimulus was presented on the subsequent trial. WhenRT was odd, the right stimulus was presented on the sub-sequent trial. With this procedure, after eliminating errorsand error sequences, each stimulus sequence occurred onaverage 55 times per 1,000 stimuli, with a standard de-viation of 3.08. No error correction was possible.

Each subject participated in one 15-min session. Duringall trial blocks, stimuli succeeded at a pace depending onthe subject's RTs. After two 50-trial practice blocks, duringwhich the subject was instructed to keep the error rateless than or equal to 4% he or she ran through 10 exper-imental blocks, each consisting of 100 trials. Between blocksthere was a 30-s rest period, during which the subject wasinformed of the error rate in the immediately precedingblock.

Results and Discussion

Errors amounted to h88% and were posi-tively correlated with median RT across se-quences. Thus an explanation of sequentialeffects in terms of speed/accuracy trade-off isruled out. Median RTs were calculated persequence per subject and averaged over sub-jects. Figure 3 shows median RTs and errorpercentages as a function of stimulus se-quences.


The analysis of the repetition-alternationfunction revealed a high correlation (.95 withRTs after three alternations excluded), indi-cating considerable linearity in the scatter-gram. The slope of the best-fitting straight linewas 43°. This slope clearly indicates a dom-ination of automatic aftereffects.

In general the trend of the data in Figure3 corresponds with the predictions of Figure

2 and with the data of Vervaeck and Boer(1980). An ANOVA with first-order and higherorder effects as within-subjects factors revealedsignificant main effects, F(\, 19) = 8.52, p <0.01, for first-order effects, and F(l, 133) =10.97, p < 0.001, for higher order effects.

The minimum standard error of estimatewas computed between the median RTs foreach of the 16 sequences of four consecutive

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P Q Q P Q P P Q Q P PP P Q Q Q Q P P Q Q PP PP P

Q Q Q QP P P P

Q Q Q QQ Q Q Q

Q P Q QP P P Q

PQ

P P P PQ Q Q QP P P P

S T I M U L U S S E Q U E N C E S

Figure 3. Results of Experiment 1: median correct reaction time and error percentage as a function ofpreceding stimulus sequences. (The order of sequences on the horizontal axis is the same as in Figure 1.Each point on the reaction time [RT] curve represents approximately 1,100 RTs.)


Table 1Goodness of Fit for Different Modelsto the Data of Experiment 1

Model S. % var

Single decayWithout noiseWithout inhibition

9.29(11.37)15.55 (17.88)9.89(11.47)

.953 (.929)

.869 (.826)

.947 (.927)

Note. Numbers in parentheses give the results of the modelswhen the point with three alternations is included (/trQpQpP,RTpQpQp); Se = standard error of estimate in milliseconds;% var = percentage of variance accounted for.

stimuli and its corresponding value in one ofthe models by using the following formula:

"e ~

/ 2 (RTn - rn)2

n=l

~Nwith rn

, (9)where MT is the mean of all computed rvaluesand MRT the mean of the median RTs persequence. TO is the estimated neutral pro-cessing time. N is the number of sequencesused in the analysis (14 without the sequencesafter three alternations and 16 with all se-quences). RTn is the median RT per sequence,and Tn is the calculated rvalue per sequence.By means of a computer program, a gridsearch was performed on all parameters of themodel. For every combination of parametervalues, T values and standard error were cal-culated. After the grid search, a minimumstandard error indicated the best model ap-proximation. Table 1 shows the computedminimum standard errors and percentage ofvariance accounted for by the respectivemodels.

Table 1 indicates that a model without noiseis the least appropriate to explain automaticaftereffects in the present data. Although allmodels explain more than 85% of the variance,there still is a sizeable difference between themodel without noise and both other models.Apparently, inhibition and facilitation aloneare not sufficient to explain all sequential ef-fects with short RSI.

Single decay seems to be the most promisingmodel, although the difference between it andthe model without inhibition is small. In the

latter, however, facilitation is equal to one. Notethat in the development of the model, / = 1has been denned as the maximum toleratedvalue for the facilitation parameter. Probably,the best approximations of the model withoutinhibition will predict / values greater thanone. This implies that the model predicts thepossibility for negative RTs. This also raisesdoubts about the value of the model withoutinhibition. Other parameter values are n =.55, da = 3.5, and d{ = 6.5. The single-decaymodel generated the following optimum pa-rameter values: facilitation/= .45, inhibitioni - .50, noise n = .20, with a common decayd = 3.0. A further evaluation of both remainingmodels is made in Experiment 2.

Experiment 2

In this experiment RSI was systematicallymanipulated. It is predicted that the strengthof the decay parameter increases as RSI is pro-longed. Automatic aftereffects are assumed tobe short-lived automatic consequences of theprocessing of a stimulus. This implies theirdecay over time. An indication of the presenceof decay is the fact that automatic effects seemto appear only in experiments with relativelyshort RSI. Moreover, the aftereffects of earliertrials are progressively less influential. Exper-imental support for the notion of decay hasbeen found by several researchers who ob-served decreasing repetition effects with an in-creasing RSI (Bertelson, 1961; Bertelson &Renkin, 1966; Hale, 1967; Smith, 1968; Um-ilta et al., 1972). There are, however, otherresearchers who found little or no effect of achanging RSI on the repetition effect (Keele,1969; Keele & Boies, 1973; Schvaneveldt &Chase, 1969). These seemingly conflicting re-sults can be ascribed to other variables suchas stimulus-response compatibility, practice,and number of alternatives, whose influencesare often compounded with RSI influences.The interaction of some of these variables isstudied by Soetens et al. (1984).

Both remaining models were tested undereach RSI condition. In the single-decay modelit is expected that the common decay factorwill rise with an increasing interval, leavingthe other parameters unchanged. In the modelwithout inhibition, both decay factors, df anddn, are expected to increase. An increase of


decay will make first-order effects more im-portant in relation to higher order effects. Ingeneral, an increase of decay means a decreaseof all automatic aftereffects.

RSI manipulation was limited to a maxi-mum of 100 ms in order to minimize expec-tancy. The risk that expectancy will surfaceincreases as RSI is increased. Therefore, thedata were tested for traces of expectancy bymeans of the repetition-alternation functionbefore applying the, models.

MethodUnless otherwise mentioned, the experiment was iden-

tical to Experiment 1. RSIs were 20, 30, 50, 70, and 100ms. In each RSI condition 10 subjects participated—atotal of 50 subjects.


Errors amounted to 2.09% and were posi-tively correlated with median RT across se-quences. Figure 4 represents median RTs forfive different RSIs and overall error percentagesas a function of stimulus sequences.

The repetition-alternation function dis-played positive slopes between 30° and 40°and a correlation between .80 and .98 for the20-70-ms RSI conditions. Thus, it can be as-sumed that in these conditions the influenceof expectancy is of minor importance. In the100-ms RSI condition, however, the slope is26° and the correlation drops to .48. This wasinterpreted as a growing influence of expec-tancy.

The increasing influence of expectancy isalso visible in Figure 4, where the three right-most points of the repetition and the alter-nation curve in the 100-ms condition deviatefrom the monotonically increasing course ob-served in the other conditions. The gradualdisappearance of the first-order repetition ef-fect, which has been found in other studies(e.g., Bertelson & Renkin, 1966), is not veryclear from Figure 4. Only after RSI = 50 msdoes first-order repetition gradually diminish.If RSI is continually prolonged, the alternationcurve will probably drop beneath the level ofthe repetition curve. This represents a changefrom a first-order repetition effect to a first-order alternation effect, which has often beenascertained in two-choice RT experiments withlonger RSIs (Entus & Bindra, 1970; Hale,

1967; Williams, 1966). An experiment dem-onstrating this change in first-order effect wascarried out by Soetens et al. (1984).

An ANOVA was carried out on the data ofExperiment 2 with RSI as between-subjectsfactor and first-order and higher order effectsas within-subjects factors. All main effects weresignificant. There was no interaction betweenfirst-order effect and RSI, F(4,45) = 1,02. Thefirst-order repetition effect remains in all RSIconditions. On the other hand, interaction be-tween RSI and higher order effects was sig-nificant,>(28, 315) = 1.82, p < 0.01. Thissupports the notion of decaying higher ordereffects with increasing RSI, which is also visiblein Figure 4. The 20-ms RSI condition displaysthe steepest slope, whereas in the 100-ms RSIcondition, the slope has virtually disappearedin the alternation curve.

Table 2 shows that in all RSI conditions,both models account for more than 80% ofthe variance. As it turns out, there is no clearexplanation for the results of the model with-out inhibition. Facilitation maintains a valueof 1.0. The noise parameter is about 0.30 ex-cept for RSI = 20 ms, where noise is 0.60.Noise decay varies around 3.0, and decay offacilitation is very unstable. Moreover, severalcomparable minima were generated by thecomputer program, with diverging parametervalues, indicating an instability in the model.This, together with the prediction of negativeRTs after facilitation (/> 1.0), also disqualifiesthe model without inhibition.

An explanation in terms of the single-decaymodel appears more likely. Standard error ofestimate is smaller in all conditions, exceptfor RSI = 100 ms. The computer programgenerated only one clear minimum standarderror of estimate in all conditions. Parametervalues are rather stable over different RSI con-ditions. Facilitation fluctuates around .50, in-hibition around 0.50, and noise around 0.20.Diverging values of noise and inhibition in the100-ms RSI condition can be explained as theincreasing influence of expectancy. Thiswas already apparent from the correlation ofthe repetition-alternation function, whichdropped to .48 in the 100-ms RSI condition.Table 2 further shows that the single-decaymodel predicts an increasing decay with in-creasing RSI. Although the change in decayfactor is not spectacular, there is a positive


relation with RSI. According to the modelpredictions, an increasing d parameter is re-flected by a flattening of both repetition andalternation curves and a diminishing first-ordereffect. The former is visible in Figure 4, espe-cially if the data that can be ascribed to ex-pectancy are not considered. The latter man-ifests itself only in the longer RSI conditions.

The d parameters in the general model wereoriginally proposed as time-dependent param-eters. A closer look at the data in the presentexperiment, however, shows that the numberof intervening stimulus-response cycles alsoaffects d. To explain this influence, considerfirst the data of the 100-ms RSI condition.Figure 4 and the analysis with the repetition-

480

460

440

420

400

360

340

320

300

RSI 20msecRSI 30msec

D D RSI 50msecRSI 70msecRSI 100msec

3

1 1 1 I I I I

P Q Q P Q P P Q Q P P Q P Q Q PP P Q O Q Q P P Q Q P P P P Q Qp p p p o . a a o . a o . Q o . P P P PP P P p p p p p Q Q Q a a a a aP P P P P P P P P P P P P P P P

S T I M U L U S SEQUENCES

Figure 4. Results of Experiment 2: median correct reaction time (RT) and overall error percentage as afunction of preceding stimulus sequences with response-stimulus interval as parameter. (Each point on theRT curves represents approximately 550 RTs.)


Table 2Goodness of Fit and Parameter Values for Different Response-StimulusInterval (RSI) Conditions of Experiment 2

RSI S. i var

Single-decay model

20305070

100

8.437.107.017.288.10

.96

.95

.98

.90

.86

.46

.34

.60

.50

.50

0.600.450.600.500.10

0.200.200.150.150.30

3.203.503.504.005.50

Model without inhibition

20305070

100

9.898.09

13.289.697.92

.95

.93

.92

.82

.87

.00

.00

.00

.00

.00

0.600.350.300.300.20

6.808.004.005.509.50

3.603.002.503.003.00

Note. Se = standard error of estimate in milliseconds; % var = percentage of variance accounted for;/= facilitation;(' = inhibition; n = noise; d = decay; d; = decay of facilitation; dn = decay of noise.

alternation function indicate that higher orderautomatic effects have almost disappeared after100 ms. On the other hand, the experimentshows that third- and fourth-order automaticaftereffects exist in the short RSI conditions,indicating that their influence extends over aperiod of four interstimulus intervals, togetherlasting over more than 1 s. It is clear that theintervening stimulus-response cycles prolongthe existence of automatic effects. This ap-parent contradiction can be explained by as-suming that monitoring, or the stimulus-re-sponse cycle itself, protects existing aftereffectsor at least hampers their decay. With this as-sumption, the decay factor of the single decaymodel is not only related to time but also toevent rate.

It can be concluded that the single-decaymodel gives the best approximations to thepresent data. The proposed common decayfactor has a tendency to increase with increas-ing RSI. The decay factor seems to depend onevent rate as well as on time.

Experiment 3

The aim of this experiment is to examinethe influence of practice on automatic after-effects, particularly on the parameters of thesingle-decay model. Many researchers have in-vestigated the influence of practice on choice

RT (e.g., Hale, 1968, 1969;Teichner&Krebs,1974). Uniformly, it has been established thatRT decreases with practice. However, reduc-tion rate is not always the same and seems todepend on other variables such as RSI andstimulus-response compatibility. The reduc-tion phenomenon has been explained by someauthors as a change of strategy (Fletcher &Rabbitt, 1978), whereas others attribute it toshortcuts becoming "built into" the centralmechanism on frequently used channels(Kirby, 1980, p. 103; Welford, 1968). Again,it is important to make a distinction betweenpractice effects occurring in conditions withdominating expectancy influences and practiceeffects in conditions with dominating auto-matic effects.

The influence of practice on sequential ef-fects has been studied in other reports (Kirby,1976; Soetens et al., 1984; Vervaeck & Boer,1980). These studies show that sequential ef-fects fade out with practice. Theoretically, itis often assumed that a change of strategy takesplace so that subjects cease to favor one stim-ulus above the other as a consequence of theprevious stimulus sequence. However, this ex-planation applies only to practice influence onsequential effects in expectancy conditions, notin automatic aftereffects conditions prevailingat short RSIs. Yet in an experiment with shortRSI, Vervaeck and Boer (1980) found a dis-


appearing slope of the alternation curve. Thiswas explained as a change from a general rep-etition effect to a stimulus-specific one, whichin the present model corresponds with the dis-appearance of inhibition. If we look at thepredictions in Figure 2, this can indeed beexpected. Decreasing the inhibition parameter/ results in a disappearing slope in the alter-nation curve. In Vervaeck's article it was men-tioned that 1 subject was trained to an evenhigher practice level (30,000 trials), resultingin a disappearance of all higher order sequen-tial effects, including facilitation. As predictedby the general model, the decline of facilitation(/) results in a shift of the repetition curve inrelation to the alternation curve. In short, itcan be expected that both effects, inhibitionand facilitation, will diminish with practice,inhibition disappearing somewhat faster thanfacilitation.

MethodUnless otherwise mentioned, Experiment 3 was identical

to Experiment 1. RSI was 50 ms. Six subjects participatedin seven individual testing sessions. A session consisted of10 experimental blocks of 100 trials. Each session waspreceded by a 50-trial warming-up block. The frequencyof testing was about one session every 7 days.


Error rate amounted to 3% approximatelyand was correlated with median RT acrosssequences as in the other experiments. Max-imum differences of mean error rate betweendifferent sessions was 1.3%. In Figure 5 medianRTs and error percentages are plotted as afunction of stimulus sequences for seven prac-tice sessions. For clarity, Sessions 4-5 and 6-7 are combined and only the overall error curveis drawn. Error curves parallel median RT forall sessions.

The repetition-alternation function againdisplayed positive slopes going from 55° forunpracticed subjects to 30° for experiencedsubjects, with correlations of at least .85. Itcan be safely assumed that the data are de-termined only by automatic aftereffects.

An ANOVA with three within-subjects fac-tors—practice (7 levels), first-order effects (2levels), and higher order effects (8 levels)—yields a highly significant practice effect, F(6,30) = 16.52, p < 0.001. The decrease of RTwith practice is evident. Overall median RT

changes gradually from 355 ms for unpracticedsubjects to 281 ms for highly practiced sub-jects. In the single-decay model this is projectedas a decreasing neutral processing time (T0 =MRT/MT). This points to more permanentchanges in the frequently used stimulus-re-sponse channels. The ANOVA further reveals aminimally significant first-order effect, F(l,5) = 9.06, p < 0.05. The first-order repetitioneffect demonstrated in the 50-ms RSI condi-tion of Experiment 2 is tempered by practice.This is supported by an interaction betweenpractice and first-order effect, F(6, 30) = 3.60,p < 0.01. First-order effects are significant forunpracticed subjects, F(l, 5) = 16.52, p <0.01, but not for practiced subjects, F(l, 5) =5.37. The disappearing first-order effect is alsovisible in Figure 5, where the level of the rep-etition curve shifts in the direction of the levelof the alternation curve. In the final practicesession the difference between both levels isminimal. In the model prediction of Figure 2it has been shown that such a shift correspondsto a decreasing facilitation.

Remarkable is the change of the slope ofthe alternation curve with practice. This de-velopment is different from the change of theslope of the repetition curve. An interactionbetween practice, first-order effects, and higherorder effects in the ANOVA supports this dif-ferentiating effect, F(42, 210) = 2.14, p <0.001. The slope of the regression line for thealternation curve gradually diminishes to apractically horizontal course in the final ses-sion. Coefficients of regression are shown inTable 3. In Figure 2 the model predictionsindicated that such a change of the slope ofthe alternation curve can be associated witha diminution of the inhibition parameter inthe single-decay model.

Table 3 shows that the model accounts for98% of the variance on all practice levels. Notethat the model scales all RTs relative to T0,so that no parameter changes can be attributedto the decrease of sequential effects propor-tionally to the overall baseline RT. All param-eters evolve as expected. Facilitation and in-hibition decrease with every session. Inhibitioneven disappears completely for highly prac-ticed subjects, as could be predicted from theevolution of the slope of the alternation curve.The evolution of the facilitation parameter inTable 3 suggests the disappearance of facili-


tation after extensive practice. Decay and noiseremain constant over all practice levels andare approximately at the same level as in the50-ms RSI condition of Experiment 2. Thevery low standard errors of estimate for allpractice levels are striking. The single-decaymodel approximates the experimental datawithin a range of a few milliseconds.

General Discussion

In the present study a mathematical modelhad been proposed, describing the supposedcomponents of automatic aftereffects in serialtwo-choice RT experiments. It is assumed thatsequential effects are caused by two indepen-dent processes, namely, automatic aftereffects

TRIALS

1-10001001-2000

2001-3000

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Figure 5. Results of Experiment 3: median correct reaction time (RT) and overall error percentage as afunction of preceding stimulus sequences with level of practice as parameter. (Each point on the RT curvesrepresents approximately 550 RTs.)


Table 3Goodness of Fit and Parameter Values of the Single Decay Model for Different Practice Levels

Practicelevel

1234567

£

6.156.234.203.484.372.822.22

% var

.99

.99

.99

.99

.98

.98

.98

d

3.503.103.003.003.153.453.50

/

.60

.61

.52

.52

.47

.37

.36

i

0.600.400.300.300.200.150.00

n

0.150.200.150.150.200.150.20

Slope'

34.029.016.316.015.611.74.3

Note. S, = standard error of estimate in ms; % var = percentage of variance accounted for; d = decay;/= facilitation;(' = inhibition; n = noise." slope = slope of the alternation curve, expressed as increase of median reaction time in milliseconds per sequence.

and subjective expectancy. Automatic afteref-fects are usually associated with short RSI ex-periments, whereas subjective expectancy isassociated with long RSI experiments. Soetenset al. (1984) showed how both concepts canbe separated. The proposed mathematicalmodel is specifically intended to describe au-tomatic aftereffects. Before applying the model,we checked the data on the influence of ex-pectancy.

The proposed single-decay model was aptto explain sequential effects in a two-choiceRT task with short RSI. The model suggestedthe existence of three different components ofautomatic aftereffects, namely, facilitation, in-hibition, and noise. Attempts to explain theresults of the present experiments without oneof these components failed. This was dem-onstrated in Experiment i, where we at-tempted to rule out noise or inhibition.

In Experiment 2 we studied the relation be-tween automatic aftereffects and RSI. Theprediction that automatic aftereffects woulddiminish with increasing RSI, due to an in-creasing decay, was supported by the data. Theresults are in agreement with earlier studies(Bertelson, 1961; Bertelson & Renkin, 1966),where a decreasing repetition effect was foundwith increasing RSI. An exception is the resultsof Schvaneveldt and Chase (1969), who didnot find any indications for decaying sequentialeffects in a two-choice task where subjects hadto press lighted buttons. It might well be that,because of the extreme compatibility of thetask, expectancy is already dominating in thereshortest RSI condition (100 ms). Their se-

quential data indeed showed expectancy pat-terns. However, there is no obvious explanationfor the absence of decay in their incompatiblearrangement. It is not clear whether this canbe attributed to a transfer of training effect(the subjects participated in several condi-tions), to the value of RSI (it is unclear whetherRSI include time on key), or to the role of eyemovements as a consequence of eccentricstimulus presentation.

In the results of Experiment 2 the effect ofdecaying automatic aftereffects is visualized inFigure 4 as a flattening of both repetition andalternation curve with increasing RSI. Thechange of the first-order repetition effect withincreasing RSI is not so clear, except for agradually diminishing effect from RSI = 50ms on. This trend was confirmed by Soetenset al. (1984), who employed an RSI of 250ms with a completely identical experimentalmethod. They observed a complete disap-pearance of the first-order repetition effect.Some researchers (Entus & Bindra, 1970; Hale,1967; Kirby, 1976) even found that an orig-inally first-order repetition effect changed intoa first-order alternation effect with rising RSI,indicating the increasing influence of expec-tancy on the first-order effect. This seems tohappen only when RSI becomes sufficientlylong. Welford (1977) suggests that an individ-ual needs time to build up expectancies. Theincreasing influence of subjective expectancywhen RSI is prolonged can also be found inthe higher order sequential effects of Experi-ment 2, even with the short RSIs used there.

Changes in the parameters of the single-


decay model due to RSI manipulation give theopportunity to be more explicit about thechanges in automatic aftereffects with increas-ing RSI. The model shows that all but one ofthe parameters have a constant value with achanging RSI. Only the decay parameter isresponsible for the decrease in repetition ef-fects. The original strength of facilitation, in-hibition, and noise evoked by previous stim-ulus processing is independent of the subse-quent interval. Although the decay parameterincreases monotonically as RSI increases, thisdoes not necessarily imply that the rate ofdecay is independent of the interval. The datain Experiment 2 showed that, whereas auto-matic aftereffects seem to disappear at a rapidrate without intervening events in the 100-msRSI condition, they seem to persist much lon-ger with intervening events in the short RSIconditions. The intervening stimulus-responsecycles hamper the decay of automatic after-effects. The rate of decay is thus slowed downin the short RSI conditions. It can be con-cluded that the proposed d parameter is notonly a function of time but also of the numberof intervening events.

Experiment 3 demonstrated the dissipationof automatic aftereffects with practice. Thegradual rotation of the alternation curve inFigure 5 is an indication of a dissipating in-hibition effect, as is demonstrated with themanipulation of the inhibition parameter inFigure 2. The decreasing inhibition with prac-tice is also supported by the predictions of thesingle-decay model. The calculated inhibitionparameter gradually diminishes to a value ofzero. Also the slower decrease in facilitation,which Vervaeck and Boer (1980) detected afterextensive training of one subject, is demon-strated adequately in the same analysis withthe single-decay model. The decay parameterremained constant over all training levels.

The decrease of automatic aftereffects withpractice can be related to a decreasing mon-itoring time as proposed by Welford (1968).Monitoring, as denned by Welford, is a processduring which subjects check for errors afterresponses are executed. Subjects already fa-miliar with a particular task need not checkfor correct responses, or at least checking be-comes superficial (Annett, 1966). Experiencedsubjects, then, do not need monitoring.Checking for correct responses can happen

only if the preceding stimulus-response cyclehas left some residual neural activity. Auto-matic aftereffects can be regarded as such re-siduals. Kirby (1980, pp. 146-147) observedthat it is not too farfetched to assume thatmonitoring is the primary function of auto-matic aftereffects, and not the facilitation ofsome subsequent stimulus-response cycle.Now, if monitoring becomes superfluous withpractice, automatic aftereffects such as facil-itation and inhibition lose their function andgradually disappear.

The overall reduction of RT with practicehas been explained in two ways. The first the-ory proclaims a change of strategy. For ex-ample, Fletcher and Rabbitt (1978) found ev-idence suggesting that with increasing practice,subjects tended to respond in terms of changeor constancy between successive displays. Thisis very unlikely to happen in short RSI ex-periments because processing rate is much toohigh to give subjects the opportunity to developstrategies or expectancies. An alternative the-ory suggests a change in stimulus-responsemapping. In other words, changes occur in thefrequently used channels, and shortcuts be-come built into the central mechanism. Thisidea is better suited to a high-speed processingexperiment and also fits into the ideas of thepresent model. The disappearance of someprocessing fraction during the stimulus-re-sponse cycle is not impossible. Possibly some-thing similar happens to monitoring, althoughthis stage of processing is situated during RSI.

Some conclusions can also be drawn aboutthe locus of automatic aftereffects in the pro-cessing system. If it is assumed that a part ofthe RT process cannot be influenced by thecomponents of automatic aftereffects, thisshould result in an invariable fraction of RT.The analysis of the data with the single-decaymodel was repeated with different values foran invariable RT fraction. All results werenegative, that is, standard errors increased withan increasing invariable RT fraction, whereasthe percentage of variance, accounted for bythe model, decreased. This means that the sin-gle-decay model predicts automatic aftereffectson all processes of the stimulus-response cycle.This is in accordance with the information-reduction paradigm developed by Bertelson(1965). The results of his experiments implythat part of the repetition effect is due to the


repetition of the signal, but the main influenceis due to the repetition of the response. Thecomplexity of the results in other studiesstrongly suggests that more complex centralmechanisms are involved. Rabbitt (1968), forexample, found that an initially strong stim-ulus effect changed into a strong response ef-fect. Rabbitt and Vyas (1973) provided evi-dence of repetition effects on five out of sixprocessing stages: perceptual identification,signal coding, signal-response mapping, re-sponse selection, and response programming.On the whole, the literature on the locus ofsequential effects is highly controversial.Moreover, some researchers found that theimpact of the effects on the different processingstages changed with RSI (Eichelman, 1970)and stimulus-response mapping (Peeke &Stone, 1972). To confirm the predictions ofthe present model with respect to the locationof automatic aftereffects, further research isnecessary.

The single-decay model is specifically de-signed to explain sequential data arising fromautomatic aftereffects in two-choice tasks.Generalization of the results to multiple-choiceexperiments is difficult. It is known that in-crementing the number of alternatives givesrise to stronger repetition effects (Hale, 1969;Hoyle & Gholson, 1968; Hyman, 1953; Rem-ington, 1969, 1971) that extend over longerRSIs. This might be an indication for strongerautomatic aftereffects, but still the RSI seemsto be sufficiently long for building up expec-tancy. Expectancy in a two-choice task has atwo-sided effect that distinguishes it from au-tomatic effects, but expectancy in multiple-choice tasks is more complex, as can be derivedfrom results in guessing experiments (Schva-neveldt & Chase, 1969). Identifying uniquedata patterns for automatic aftereffects, as op-posed to expectancy effects, might well turnout to be extremely difficult in multiple-choiceexperiments. There is definitely a need to re-solve the complex issues inherent in multiple-choice experiments. For example, why is itthat some researchers did find decreasing rep-etition effects with increasing RSI (Smith,1968; Umilta et al., 1972), suggesting a decay,whereas others did not find any indicationsfor decay (Keele, 1969; Keele & Boies, 1973;Schvaneveldt & Chase, 1969)?

The merit of the single-decay model is that

it offers a quantitative approach to the analysisof automatic aftereffects. Many studies on se-quential effects have often been limited to theobservation of one isolated component anddid not show its relationship to the other com-ponents involved. The mathematical modelshows the mutual relationship between thecomponents of automatic aftereffects and howthey change with experimental manipulation.The single-decay model provides a satisfactoryexplanation for the processes involved incompatible two-choice RT tasks with shortRSI. In future applications, the model can helpto identify the presence of automatic afteref-fects in other RT research.

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Received March 31, 1983Revision received March 21, 1984

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