Verification of Donders' Subtraction Method

Transcription

1 Journal or Experimental ftychology: Human Perception and ftrformance 1985, Vol. 11, No. 6, Copyright 1985 by the American Psychological Association, Inc I523/85/J00.75 Verification of Donders' Subtraction Method Robert Gottsdanker and G. Paul Shragg University of California, Santa Barbara In an experiment on 6 young adults advance (precued) information of the correct choice 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. This pretue-utilization effect would be expected if response actualization had been delayed until the response had been selected and if the requirement for discrimination and selection had no adverse effect on readiness to respond. Donders' (1868/1969) hypothesis in his initial application of the subtraction method, that choice and simple reactions are identical except for the serial insertion of discrimination and selection operations in the former, is thereby strongly supported. If this formulation is accepted, models that hold that response processing can overlap other processing stages may be considered valid only for response selection, not response actualization. In the analysis by Donders (1868/1969), a choice reaction takes longer than a simple reaction because of the required insertion of additional processing operations. He stated that it takes longer to make a different-hand response in accordance with the foot that has been stimulated than always to respond with the same hand to a stimulus that is always on the same side, because of the additional time required for "deciding which side had been stimulated and for establishing the actions of the will on the right or left side" (p. 418). Donders called the first of these operations discrimination, and in current terminology the second operation would most often be called response selection. The mean duration of the inserted operations is found by subtracting mean simple reaction time (RT) from mean choice reaction time. This subtraction method A partial report on the present experiment and on a preceding control experiment was given at the meeting of the American Psychological Association, in Toronto, Canada, August, This research was supported by Grant 5 R01 AG00011 to the University of California from the National Institute on Aging and by a faculty research grant from the University of California, Santa Barbara. Especial thanks are given to Bemadette Magee for her assistance in the collection and analysis of data. G. Paul Shragg is now at the Medical Center, University of California, San Diego. Requests for reprints should be sent to Robert Gottsdankei; Department of Psychology, University of California, Santa Barbara, California is based on two assumptions. The first is that the inserted operations do not overlap in time with the operation by which a response is actualized, which is common to the simple and choice reactions. The second is that the requirement of performing the inserted operations does not reduce readiness to actualize the response. Donders went on to apply the subtraction method in a second way. Through use of a contingent reaction, where response is required to only one of the possible stimuli, he estimated the duration of the response selection alone, by the difference between the means for the choice and contingent reactions, and in so doing, the duration of discrimination. As noted by Steinberg (1969), although there has been some revival in the use of the subtraction method after it had fallen into disfavor for perhaps more than a half century, "little is known about how to test the validity of any particular application of the subtraction method" (pp ). Contemporary criticism of the subtraction method has centered upon the first assumption, that of strict seriality of operations (e.g., Miller, 1982). The early criticism challenged the second assumption, that of unimpeded readiness to respond, largely on the basis of introspective reports (Watt, 1905). In the present study we present an augmentation of the subtraction method that can test the method's validity for Donders' initial application, the comparison of choice 765

2 766 ROBERT GOTTSDANKER AND G. PAUL SHRAGG and simple RTs. Specifically, we test Donders 1 assumption, for the case of a compatible leftright choice reaction. We split the informative and imperative functions of the choice stimulus by presenting an informative visual stimulus as a precue and following it quickly on half the trials at random by an auditory imperative stimulus. If, over very brief precueto-stimulus intervals (PSIs), including simultaneous presentation, average latency between precue and onset of response is invariant, and if for somewhat longer PSIs average RT to the imperative stimulus is equal to average simple RT, the assumptions underlying the subtraction method are supported, as was the case in the present experiment. This combined outcome of the augmented subtraction method is termed the precue-utilization effect because there is complete utilization of the precued information in reducing average RT to the imperative stimulus until it remains equal to average simple RT. Following is the rationale for the procedure employed and the conclusions drawn from the precue-utilization effect, Donders' insertion hypothesis for a choice reaction implies that the choice stimulus provides separate informative and imperative contributions to the response. The informative contribution leads to the discrimination among stimuli and selection among corresponding responses. The imperative contribution leads to the actualization of a selected response. Thus, the effect of the imperative contribution is delayed until a response has been selected. In a simple reaction, where the response has been selected long in advance of stimulus occurrence, the stimulus provides only an imperative contribution, and so leads directly to response actualization. The main hypothesized events for a simple and a choice reaction are represented in Figure I, in the top and bottom sections, respectively. For simple RT it is seen that the preselected response is actualized as soon as the prelimi- Simple RT Onset of Response Previous Response Selection RT g = Encoding Stimulus + Premotor Discrimination and Response Selection Choice RT Onset of Response Stimulus I- Imperative Delay RT,, Response Actualization -I RT C = Encoding Stimulus + Discrimination and Response Selection + Premotor RT C - RT S = Discrimination and Response Selection Figure 1. Representation of simple and choice reactions according to Donders' insertion hypothesis. (The direction 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. RT S and RT C stand for simple reaction time and choice reaction time, respectively. The value of E indicates the proportional efficiency of an operation.)

3 VERIFICATION OF DONDER'S SUBTRACTION METHOD 767 nary processing of the stimulus (encoding) has been completed. It will be noted that response actualization is divided between premotor and motor times. Here it is indicated that the measured onset of the response occurs exactly when the movement starts. This is difficult to attain in practice. However, the same temporal point is used in the other examples to be presented. For the choice reaction the only change is in the insertion of the discrimination and response selection operations between encoding and actualization, with the delay in the imperative contribution of the stimulus being indicated by the dotted line. The terms used for the "boxes" should not be taken as more than convenient tables. For example, it need not be supposed that a comparison of possible responses takes place in response selection. Also, the failure to use such terms as translation and retrieval does not imply that such processes are unimportant in the labeled operations. In addition to showing the events on single trials, the foregoing diagrams may just as well represent mean values over a number of simple and choice trials. In the subtraction method, the difference between mean choice and simple RT thus gives the mean value of the inserted processes. In these diagrams, as well as those in Figures 2 and 3, an operation reaches completion when the "area" of the corresponding bar attains a criterion value. At any instant, the area is a product of the efficiency of the operation, E, and the time that the operation has been underway. In the cases just shown, efficiency has been assumed to be at the maximum value of I throughout. Models that hold that some progress can be made toward response actualization before the completion of discrimination and response selection have not insisted that this can be done with maximum efficiency. It is very implausible for response acutalization to proceed as rapidly before a response has been selected as it can in a simple reaction, where the response has already been selected before the stimulus is presented. In representing the possibility of an overlap between response actualization and the other stages, then, the width of the bar will be shown as less than 1 during the period of overlap. If the depiction of a choice reaction in Figure 1 is correct, and if actually different stimuli were to be assigned to the informative and imperative functions of the choice stimulus, the imperative stimulus could trail the informative stimulus (or precue) without affecting latency, L, between precue and response, just as long as the imperative stimulus could be encoded before a response had been selected. Up to that point, lengthening of PSI would simply shorten the delay for the effect of imperative stimulus. This outcome, which is called Danders' Expectation 1, is shown at the top of Figure 2 for a short intersignal interval (ISI) PSI. The dotted line represents the delay in the effect of the imperative stimulus. It should be noted that the encoding of the imperative stimulus is shown as proceeding concurrently with the discrimination and selection operations. This is a reasonable assumption because without some "trace" of the imperative stimulus there could be no response. Interference between the precue and the imperative stimulus was minimized in the present experiment by use of different sense modalities. At the bottom of Figure 2 is shown the expectation for a long PSI. Selection of the response has been completed. Again, as in the case for the diagrams in Figure 1, the representations may be taken to indicate the mean values obtained rather than the values for a single trial. It may be noted that mean RT for the long PSI is shown as equal to that for simple RT in Figure 1, because it is made of the same components. This outcome is termed Danders' Expectation 2. A first approximation of the longest PSI at which waiting would be required is given by the difference between mean choice and simple RT, because this is held to be the mean time required for the inserted operations. However, there are two reasons that the critical interval for testing Donders' model should be somewhat shorter. First, the testing interval should be reduced by the time that would be taken for encoding the imperative stimulus. Moreover, some trial-to-trial variation is to be expected in the time required for the discrimination and response-selection operations (and to a lesser extent for the more automatic encoding operation). Thus, on a particular trial the time for discrimination and selection might be very short, so that an imperative stimulus that usually would occur during these operations would now occur after the operations had been completed. This poses no problem for PSIs that are clearly shorter than the most rapid discrimination and response selection

4 768 ROBERT GOTTSDANKER AND G. PAUL SHRAGG that could take place on a trial, for example, a PSI of 30 ms (which was one of the values used in the present experiment). However, as PSIs begin to approach the mean difference between choice RT and simple RT, the intervening operations will have been completed on some trials before the imperative stimulus occurs, so the representation would be wrong for those trials. Still, this limitation may be overcome to a considerable extent by the use of the median rather than the mean to describe the latency associated with a PSI. It may be L with Short PSIS Insertion Model Onset of Response FsT PSL Discrimination and Response Selection Stimulus B PSL -AorB L A = L g (mean or median) Donders (1) RT P with Long PSIs Insertion Model Onset of Response Enc. P t Precue Discrimation and Response Selection PSI Stimulus RT,, Response Actualization RT = RT S (mean or median) Donders (2) Figure 2. Representation of precued reactions with short and long PSIs according to Donders' insertion hypothesis. (The direction of time is shown by t-». P stands for the informative precue. S stands for the imperative stimulus. Stimulus A (S A ) and Stimulus B <S B ) indicate the imperative stimulus presented at the designated instants. L indicates the latency between the onset of the precue and the onset of the response. LA and L a stand for the latency when Stimulus A or Stimulus B is presented. PSI indicates the precue-tostimulus interval. PSI A and PSI B represent the precue-to-stimulus interval when Stimulus A or Stimulus B is presented. RT indicates reaction time measured between the onset of the imperative stimulus and the onset of the response. KT P is the reaction time in the procedure in which a precue is presented. RT S stands for simple reaction time, as shown in Figure 1. The value of E indicates the proportional efficiency of an operation.)

5 VERIFICATION OF DONDER'S SUBTRACTION METHOD 769 assumed that there is an appreciable correlation between overall RT and the duration of discrimination and response selection operations. Thus, the trials on which these operations will already have been completed before presentation of the stimulus at the somewhat ambiguous PSIs will, by and large, be those with RTs shorter than the median. The median, of course, is not affected by shifts that all take place at values on one side of it. Consequently, for the present analysis the median is preferable to the mean, which is affected by every change of value. The same problem, in reverse, is encountered in determining the shortest PSI at which no waiting is required. Now "safe" PSIs are those that are clearly longer than the difference between mean choice and simple RT. More valid estimates again may be made for borderline PSIs by use of medians rather than means. Alternative representations that reflect the criticisms made of the subtraction method are shown in Figure 3. Again, mean values are represented. An interpretation of a continuous-flow model (Eriksen & Schultz, 1979), as applied to the present paradigm, is shown in the top two diagrams. With the onset of the imperative stimulus, a steady amount of response actualization with E < 1 takes place before the end of discrimination and selection, at which point there begins the full rate of response-actualization processing (E - 1). The area of response actualization required for reaching the criterion now is seen to be reached L with Short PSIs Overlapping-Operatlons Model Precue Stimulus B LA < LB (mean or median) vs. Bonders (1) RTP with Long PSIs Degraded-Preparation Model Onset of Response Enc. p t Precue Discrimination and Response Selection PSI- PSI- Stimulu RT > RTS (mean or median) vs. Donders (2) Figure 3. Representation of precued reactions when Donders' assumptions are denied. (The terms are denned in the same way as in Figure 2.)

6 770 ROBERT GOTTSDANKER AND G. PAUL SHRAGG earlier by the shorter of the two PSIs, shown in the topmost diagram. Thus, median latency from precue to response will not be constant but will increase with PSI in contradiction to Donders' Expectation 1. It is difficult to see why this would not be the case for any other formulation of partial response actualization during the added operations. At the bottom of Figure 3 the effect of reduced readiness to respond is shown by a thinner bar for response actualization (E < 1). A longer time is now required for the area to reach the criterion value. Consequently, the expectation is for RT to the imperative stimulus to be longer than simple RT, in contradiction to Donders' Expectation (2). It is important to recognize that the augmented subtraction method is employed to test hypotheses that model events in procedures in which a single stimulus is given. It is not claimed that a precise estimate can be made for the duration of inserted operations for the augmented procedure itself, as there is the unknown value of the additional encoding operation required for the separate imperative stimulus. However, if the conclusions of the augmented subtraction method are accepted, the estimate can be made for the single-stimulus procedures through use of Donders' original subtraction method. Curiously, the use of medians in the augmented method appears to be appropriate to test the hypothesis stated in terms of means. As was noted previously, the only effect that time for encoding the imperative stimulus has on testing the insertion hypothesis is on the longest value for which latency between precue and response should remain constant. An auditory imperative stimulus was used in the present study to minimize encoding interference, but it does not matter whether this resulted in more or less rapid encoding than that for the precue. The question may still be raised as to whether results obtained in a catch-trial procedure (required because PSI was constant over a block of trials) may be applied to ordinary choice reactions, which typically do not have catch trials. An alternative method would have been to use varied PSIs over a block of trials, with false reactions being prevented by time uncertainty. However, this is a very risky procedure because choice RT is affected to a greater extent by time uncertainty than is simple RT (Simon & Slaviero, 1975). In the present study, subjective as well as objective time uncertainty was essentially eliminated by the use of the transit-signal method (Gottsdanker, 1970). It might even be argued that the usual procedures in which choice and simple RT are compared should be modified to include the transit-signal method and catch trials to avoid confounding inserted operations with time-uncertainty effects. Still, it must be admitted that there is the possibility of a differential effect of catch trials on choice and simple RT. This remains to be investigated. An additional caution is that the present procedure does not identify the nature of the inserted operations. Discrimination and response selection may be sequential or integral. Moreover, there is no guarantee that response actualization starts instantly after response selection has been completed in a choice reaction. Possibly time is taken in switching from one operation to another. For this reason, the Donders' computation of the time required for discrimination and selection is a maximum estimate. A final point is that any existence of conditions that are contrary to the present assumptions can lead only to results that falsify Donders' expectations in the present study. If medians are indeed being affected by trials in which the precue sometimes occurs after the completion of discrimination and selection, the effect would be for latency between precue and response to increase for that PSI rather than to remain constant. Any differential effect of encoding the imperative stimulus on the efficiency of the discrimination and selection operations would also destroy the invariance of the latency. Method Subjects. Six subjects were used, I male and 5 female university students. Ages ranged from 19 to 22 years. One female subject replaced another whose data could not be used because of a computer malfunction. Subjects were paid participants recruited by a notice posted in the psychology building. Tasks. Two tasks were used, a precued choice reaction and a simple reaction, each with the transit-signal method (Gottsdanker, 1970). On a precued choice reaction, two light horizontal bars ascended the display, side by side, and reached a suitably gapped reference line in 3 s. Just before then (or at the same instant) either the left- or right-hand button was to be pressed, provided a tone sounded at the instant of transit. A representation of the display and response buttons is shown in Figure 4. The interval between onset of the precue (brightening of one of the bars) and

7 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 interval 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 included 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 t Display T Response Buttons P Tone =.5 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 indicates probability; sec indicates seconds.) Table 1 Mean Values of Median and Mean Reaction Times for Precued Responses and Simple Responses on Corresponding Test Days PSI Mean of medians Mean of means Precued Simple Precued Simple Note. All values are in milliseconds. PSI = precue-to-stimulus 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 durations 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 subjects of the individual median and mean RTs (from the onset of the imperative stimulus) are shown in Table 1. There were 96 possible responses at each PSI for each subject and 32 possible corresponding simple responses. Variation by test day proved inconsequential for either simple or precued RTs, with a range of only 4 ms for medians, so results are collapsed over days. It can be seen that medians and means are in close agreement in their relation to PSI. The predicted drop of 30 ms between PSI = 0 and PSI = 30 ms is met almost exactly by each of the measures. However, the relation is slightly more regular for medians, and the "elbow" in the curve occurs a little sooner (as would be expected from the previous discussion of the preferability of medians). Consequently, the test of Donders' two expectations is carried out in terms of medians. These tests are shown graphically in Figure 5. According to Expectation 1, for PSIs clearly shorter than the difference between mean choice RT (with no ad-

8 772 ROBERT GOTTSDANKER AND G. PAUL SHRAGG vance information) and simple RT, the value of L, latency of start of response from onset of precue, should be invariant. The present comparable choice and simple means are the values at PS1 = 0, seen in Table 1 to be 244 and 135 ms, with a difference of 79 ms. Thus, it is expected that median L should be constant over PSIs 0, 30, and 60 ms. It appears in Figure 5 that this is so, in accordance with Donders' Expectation 1. Their values are 235, 234, and 235 ms, respectively. The validity of this comparison is enhanced by the fact that median simple RT was identical to the nearest millisecond for PSIs 0 through 90 ms; All were 154 ms. Furthermore, individual subjects were quite consistent as seen in the 95% confidence ~ 200 fe 150 t- o _i Donders Expectation (1) L=C Donders Expectation (2) PRECUED REACTIONS D L: Latency measured from precue onset RT : RT measured from stimulus onset RT S: Simple RT i _ i i PSI (msec) 150 Figure 5- Mean of median latencies and reaction times in milleseconds as a function of precue-to-stimulus interval (PSI). (L indicates the latency between the onset of the informative precue and the onset of the response. C stands for a constant value. RT indicates reaction time measured between the onset of the imperative stimulus and the onset of the response. RT P is the reaction time in the procedure in which a precue is presented. RT S stands for simple reaction time.) interval for each of the three differences between means of medians over this range of PSIs. The intervals were to ms for the 0-30 ms difference, to ms for the 0-60 ms difference, and to ms for the ms difference. The hypothesized value of 0 clearly falls within each range, and no other specific hypothesis appreciably different from 0 is tenable. The stability of RT for the two longest PSIs, which are clearly longer than the difference between choice RT and simple RT of 79 ms, is equally evident, the means of medians being 155 and 153 ms for the 120- and 150-ms PSIs, respectively. However, it may be seen that there is a slight (5 ms) difference between precued and simple RT at those PSIs and at the 90 ms PSI also. A twoway repeated measures analysis of variance was performed for precued and simple RT over these three longest PSIs. The 5-ms difference for conditions was significant, F(l, 10) = 14.25, p <.01. Also, the effect of PSI was significant, F(2, 10) = 6.99, p <.025. The interaction between condition and PSI was not significant (F < 1). This is because simple RT dropped slightly (and inexplicably) as did precued RT for PSIs 120 ms and 150 ms on those testing days. It will be recalled that this was a different actual day for each subject. Thus, Donders' Expectation 2 was not quite met. It was off by the very small (but statistically significant) amount of 5 ms. It seems likely that the discrepancy between precued and simple RTs at the long PSIs was due to operation at different points on the speed-accuracy trade-off function. There were almost no wrong-direction errors at the 120- or 150-ms PSIs nor, of course, for simple RT on corresponding days (3 out of 2,972 trials for the three conditions combined). However, the overall percentages of anticipations and false alarms were consistently higher for the simple reactions than for the precued reactions on corresponding days for the three longest PSIs: 6.51% vs. 0.87% at PSI = 90; 2.60% vs. 1.48% at PSI = 120, and 5.73% vs. 3.04% at PSI = 150. It is proposed that the discrepancy between about 5% and 2% errors could well account for much larger differences than 5 ms. Unfortunately, there appear to be no data extant on speed-accuracy trade-off for contingent simple reactions, and most studies of choice reaction have induced much higher error rates.

9 VERIFICATION OF DONDER'S SUBTRACTION METHOD 773 However, two of the error rates produced in the Pachella and Pew (1968) study on their Day 3 are somewhat comparable. There, an increase in error rate of about 5% to 8% between conditions resulted in about 20-ms shortening in RT. A further analysis of errors helps to substantiate the conclusions reached concerning the short ISIs. There was no tendency for subjects to "jump the gun" on some trials and commit themselves to a response on appearance of the precue, thereby sharpening the decline in RT with PSI. In fact, there were fewer wrong-direction errors at PSI = 30 and PSI = 60 than at PSI = 0, 2.52% and 1.65% as compared with 3.12%. Anticipations and false alarms were below 1 % at all three of these PSIs. Discussion The prediction of invariance of median precue-to-response latency (or equivalently a 1 slope of median RT) over PSIs whose values are clearly less than the difference between mean choice and simple RT was confirmed almost exactly. The slight increment of RT at the longer PSIs over simple RT seems almost certainly due to the higher error rate for the latter. These findings, as has been explained, lend very strong support to Donders' assumption in use of the subtraction method that in a choice reaction additional operations have been inserted into a simple reaction.' Of greatest interest at the present day is the evidence that actualization of a response cannot begin before response selection has been completed. The use of the subtraction method is justified for this application, provided it is stipulated that neither the nature or number of inserted operations is revealed. The other use of the subtraction method by Donders is, in fact, an attempt to separate the durations for stimulus discrimination and action selection. In that application a contingent (or c) reaction is obtained for comparison with the choice (or b) reaction and the simple (or a) reaction. The assumption is that response selection is not required to the "correct" stimulus, only discrimination. This assumption is challenged by recent evidence that there are, in fact, "motor processes" associated with not responding to the "wrong" stimulus (Richer, Silverman, & Beatty, 1983), so a kind of response selection must be involved. There appears to be no clear way, using the present augmented subtraction method, to separate the hypothesized stages of discrimination and response selection. The assigning of response actualization to operations that do not overlap with response selection has bearing on previous examinations of the issue of discrete processing stages. In their "continuous flow model," Ericksen and Schultz (1979) hold that in visual search "certain responses become primed over other responses" (p. 252). They also state that "when the priming for... [a] response reaches the evocation threshold, the [prior] inhibition is removed and the response occurs" (p. 252). From the present conclusions it would instead be stated (provided their basic conception is correct) that when inhibition is removed, response selection occurs. Whether a response is actualized depends on the utilization of the imperative component of the stimulus. Miller's conclusion that "partial information about a stimulus was transmitted to response activation before the stimulus was uniquely identified" (1982, p. 273) would similarly be reformulated in terms of response selection. The basis for his interpretation was the advantage for identification RT when the initial character of a pair was assigned to two fingers of the same hand rather than to two fingers of the different hands. However, Reeve and Proctor (1984) have recently shown that there is the same advantage when the initial character is assigned to adjacent overlapping fingers of the different hands. Thus, there would appear to be more efficient selection of an action within a limited movement space rather than more efficient response preparation of fingers on one hand. 1 It is important in testing the insertion hypothesis by means of the augmented subtraction method to rule out possible stimulus artifacts related to the presentation of the precue. Such possibilities were examined in studies that preceded the present experiment. First, using a sample of 24 men and women ranging from 21 to 78 years of age, it was shown that an advance precue that is uniniformative does not affect simple RT (Gottsdanker & Shragg, 1981). Second, the possibility was tested that RT is reduced with lengthening of PSI in part because of the increasing conspicuity of the brightening precue as it occurs farther from the reference line. However, increasing the contrast of the precue by reducing the brightness of the reference line by about half did not shorten RT at PSI = 0 for a sample of 18 college men and women (Gottsdanker & Shragg, 1984).

10 774 ROBERT GOTTSDANKER AND G. PAUL SHRAGG The issue of serial-stage versus continuous models was also investigated through use of a precue method by Meyer, Yantis, Osman, and Smith (1984). Although their overall conclusion agreed with that arrived at in the present study, the methods and logic were quite different. The precues were not the stimuli for response that would occur in the nonprecued task as is required in a test of the Donders hypothesis. They were incompatible words or nonwords that were followed by the actual compatible stimuli rather than by a neutral imperative stimulus. Moreover, except for PSI = 0, there were much longer times between onset of the precue and the onset of the confirming stimulus, about 785 ms for the "medium" delay. The logic was that at short delays RTs would all be choice reactions, at long delays they would all be simple reactions, while at some medium value there would be a mixture of choice and simple reactions, with a consequent increase in the variance of the RT distribution. In the present procedure, in which it was assumed that the same processing required in a nonprecued case would start with the onset of the precue, there would be quite a different expectation concerning RT distributions. For a PSI on which there is a delay on some but not all trials, the distribution of waiting times would be truncated. Consequently, RT distributions would have a constant variance until PSIs were reached at which variance would be gradually reduced as truncation of waiting times increases until finally a reduced RT is reached when no waiting-time delay is required on any response. Experiments using finely graded random PSIs are now being conducted by one of the present investigators to test this expectation. It should be noted that Meyer et al. (1984) make the assumption that "This contingency betweeen the prime and test stimulus allows the subject to prepare his or her response fully in advance, depending on how long the delay is between the two stimuli" (p. 72). Following Donders, the present view is that an absolute precue allows the subject to select a response, not to make any progress toward actualizing one. Perhaps the distinction made by Meyer et al. between response programming and program loading is parallel. There is also a resemblance between the present paradigm and that used to study ability to inhibit RT responses. In the latter paradigm the first stimulus instructs the subject to make the required simple or choice reaction with an occasional trailing stimulus giving the instructions not to respond. In the model of Logan, Cowan, and Davis (1984) there is a race between response and inhibition processes. Because simple as well as choice reaction may be prevented, it may be concluded if the model is accepted that commitment to a response does not occur until some time after the response-actualization process has started. There would thus be two major premovement stages of response actualization. It should be noted, despite the similarity to the present paradigm, that the inhibition procedure does not address the issue posed by the subtraction method. Further, in the foregoing study, only one interval shorter than 100 ms was used, and there was some success in stopping a response even with an interval of 400 ms. A perhaps closer resemblance is seen in experiments on the psychological refractory period (PRP). Typically in these studies two stimuli are given in rapid order, each requiring its own response. Interest is centered on the lengthening of RT as interstimulus interval (ISI) is reduced (or conversely how it is shortened as ISI increases). According to the singlechannel hypothesis (Welford, 1959), there should be a -1 slope since the processing of Stimulus 2 must be delayed until the processing of Stimulus 1 has been completed. That hypothesis is not the same as that investigated in the present study even though it is isomorphic with it. Two separate responses are made in the typical PRP study, so the interference is between these responses or even between the same stage of the two responses. In the present method of critical precues, there is only one response, and it is hypothesized that a stage of this response cannot start until another stage of the same response has been completed. Still, the distinction blurs in those PRP experiments where no response is required to the first stimulus. Usually, in such studies the first stimulus is irrelevant to the response and can only be regarded as distracting (e.g., Davis, 1959). However, Nickerson (1967) used the same paradigm as that of the present study, but with varied ISIs, and considered the lengthening of RT as PSI was shortened as an indicator of psychological refractoriness. A much more reasonable interpretation is that RT was in-

11 VERIFICATION OF DONDER'S SUBTRACTION METHOD 775 flated at the short ISIs because of low momentary probability of stimulus occurrence (Gottsdanker, 1975), not because of psychological refractoriness. This conclusion is strengthened by the fact that in Nickerson's study, an ISI (or PSI) of almost 400 ms was required for RT to descend to the level of simple RT. Here, no more than 90 ms or 120 ms was required. In addition to its present use, the augmented subtraction method may be applied whenever it is possible to split stimulus contributions that have different hypothesized functions into two parts. One example is the programming of aspects of a response (or, according to present evidence, selection of aspects of a response). Rosenbaum (1980) showed that RT was reduced in accordance with the number and kind of precued dimensions. It should be noted that he used very long PSIs, 3 s and 5 s. His interpretation was that part of the programming was done in advance, so less had to be done when the stimulus exactly specifying the response appeared. An important point is that a precue that did not specify a dimension but simply reduced the number of response alternatives did not reduce RT. However, Goodman and Kelso (1980) found that with compatible precues and stimuli for response, RT was effectively reduced by such "ambiguous" precues. They attributed Rosenbaum's results to problems of translation. More generally, the use of very long PSI can never lead to definitive results because of the many possibilities that exist for reorganization of preparation. On the other hand, the serial expectancies of Rosenbaum can be put to a direct test by use of the present augmented subtraction method. The expectation is, of course, that RT will diminish exactly by the amount PSI is increased until a constant value is reached. Such study was, in fact, carried out in the Santa Barbara laboratory by Reed (1984) using compatible precues but with both compatible and incompatible response stimuli. The 1 slope that would support Rosenbaum's formulation was not found. Instead, there was only a small reduction of RT at the short PSIs that was possibly an automatic facilitation. Only when the PSI was long enough to allow repreparation, about 300ms (Gottsdanker, 1975; Sanders, 1971) was there appreciable reduction of RT. The implication, in present terms, is that actions are selected by an integral rather than serial process. Another possible application is on the question of whether a complex stimulus is analyzed by separate aspects or globally. Here one aspect or another is precued, and the course of reduction of RT with PSI is again determined. A by-product of the present experiment is a possible way of measuring simple RT, without the complication of error rate. At PSI = 120 ms there were virtually no wrong-choice errors (as occur in typical choice reactions) and only a few false alarms and anticipations (as occur in typical simple reactions with little time uncertainty). Yet RT was only 5 ms longer than simple RT. Apparently, there was just enough time to make an unhurried choice, but not enough time to establish a bias toward one of the alternatives. References Davis, R. (1959). The role of attention in the psychological refractory period. Quarterly Journal of Experimental Psychology, 11, Donders, F. C. (1969). Over de snelheid van psychische processen [On the speed of psychological processes]. (W. Koster, Trans.), In W. Koster, (Ed.), Attention and performance: II. Amsterdam: North-Holland. (Original work published 1868) Eriksen, C. W., & Schullz, D. W. (1979). Information processing in visual search: A continuous flow conception and experimental results. Perception & Psychophysks, 25, Goodman, D., & Kelso, J. A. S. (1980). Are movements prepared in parts? Not under compatible (naturalized) conditions. Journal of Experimental Psychology: General. 109, Gottsdanker, R. (1970). A transit-signal methodology for studying reaction time. Behavior Research Methods and Instrumentation, 2, 6-8. Gottsdanker, R. (1975). The attaining and maintaining of preparation. In P. Rabbitt & S. Dornic (Eds.), Attention and performance V (pp ). New York: Academic Press. Gottsdanker, R., & Shragg, G. P. (1981, August). Motor priming and age. Paper presented at the 89th meeting of the American Psychological Association, Los Angeles, CA. Gottsdanker, R., & Shragg, G. P. (1984, August). Verification of Danders' subtraction method. Paper presented at the 92nd meeting of the American Psychological Association, Toronto, Canada. Logan, G. D., Cowan, W. B., & Davis, K. A. (1984). On the ability to inhibit simple and choice reaction time responses: A model and a method. Journal of Experimental Psychology: Human Perception and Performance, Meyer, D. E., Yantis, S., Osman, A., & Smith, J. E. K. (1984). Discrete versus continuous models of response preparation: A reaction-time analysis. In S. Kornblum

12 776 ROBERT GOTTSDANKER AND G. PAUL SHRAGG & J. Requin (Eds.), Preparatory states and processes (pp ). Hillsdale, NJ: Erlbaum. Miller, J. (1982). Discrete versus continuous stage models of human information processing: In search of partial output. Journal of Experimental Psychology: Human Perception and Performance, 8, Nickerson, R. S. (1967). Psychological refractory phase and the functional significance of signals. Journal of Experimental Psychology, 73, PacheUa, R. C, & Pew, R. W. (1968). Speed-accuracy tradeoff in reaction time: Effect of discrete criterion times. Journal of Experimental Psychology, 76, Reed, P. S. (1984, June). A timecourse analysis of movement precue utilization. Unpublished doctoral dissertation, University of California, Santa Barbara. Reeve, T. G., & Proctor, R. W. (1984). On the advance preparation of discrete finger responses. Journal of Experimental Psychology: Human Perception and Performance. 10, Richer, E, Silverman, C., & Beatty, J. (1983). Response selection and initiation in speeded reactions: A pupillometric analysis. Journal of Experimental Psychology: Human Perception and Performance, 9, Rosenbaum, D. (1980). Human movement initiation: Specification of arm, direction, and extent. Journal of Experimental Psychology: General, Sanders, A. F. (1971). Probabilistic advance information and the psychological refractory period. Ada Psychologica.35, Simon, J. R., & Slaviero, D. (1975). Differential effect of a foreperiod countdown procedure on simple and choice reaction time. Journal of Motor Behavior, 7, Steinberg, S. (1969). The discovery of processing stages: Extensions of Donders' method. In W. Koster(Ed-), Attention and performance //(pp ). Amsterdam: North-Holland. Watt, H. J. (1905). Experimentelle Beitrage zu einer Theorie des Denkens [Experimental contribution to a theory of thinking]. Archivjtir die Gesamle Psychologie. 4, Welford, A. T. (1959). Evidence of a single-channel decision mechanism limiting performance in a serial reaction task. Quarterly Journal af Experimental Psychology, 11, Received May 10, 1984 Revision received May 28, 1985