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The information hypothesis and non-repetitions
Actu psvclto~o~ica
Attention and Performance 11 f W, (I;. Koster, ed.) 1969, 37-53 @JNorth-Holland Pubhkhing Company, Amsterdam
university of Oregon, Eugene, Ore., U.S.A.
and
Lstituto di Psicotogiu della Facaltci
edica dell’ Wniversitci di Bologna, Italy
WRACT
The information hypothesis specifies that equi-information conditions will yield the same mean R provided that S can and does take advantage of all the information available to him prior to the occurrence of each new signal. KORNBLUM'S recent experiment (1968) demonstrated RT was not the same for equi-information conditions differing in propotiion of repetitions. Qne can conclude with Kornblum that his findings disconfirm the information hypothesis or one can look: for factors in the experimental situation that may have im ability to profit from information in alternations. VZhen we repeated Kornblum’s conditions in a choice reac:tion experiment designed to give S more opportunity to use the information from alternations, the overAl results were more compatible with :he information hypothesis. This result suggests that a fruitful way to study the microstructure of T is to isolate the factors that differentiate situatioils in which the infor hypothesis holds from those in which it does not. ‘ XNTR~D~ICTI~N
In 1953 Hyman published results in support of the idea that reaction
time (.RT) was a function of stimulus information @I) regarless of how the information in a stimulus (‘message’) was varied - by varying the number of different alternat ves froj!n which the message is selected, the probabilities with which the different messages can occur, or the sequential constraints between the successive occurrences of any two messages. These results, in addition to those of ICI& (1952) on and transmitted information, provided the initial basis for what has since been called the “information hypothesis’. 1 This study was conducted at the Istituto di Psicologia, 1Jniversiti di Bologna, Bologna, Italy during the academic year 1967-8 while the senior author was a Fulbright-Hays Research Scholar. We are indebted to Professor Renzo Canestrari, Director of the Istituto, for providing us with facilities and financial suppoti. 37
33
IL HYMAN ANDC, UMlL'd
In its stricter form the information hypothesis has recently stated as fiiollows: ‘all other things being equal (such as stimulusresponse compatibihty, training, discriminability, and elrror rate), equiinformation conditions must produce equal overall mean L~DM[, 1963). A weaker version would be the following: ‘equal increments in inform&on produce equal increments in RT’ (Kam~m, ibid.). 1.1.
The stricter version of the information hypothesis was disconfirmed even in Hyman’s original study. Three out of the 24 conditions in that study yielded RTs that were significantly, although slightly. too high. The:6 t&z conditions had in common the fact that sequential cons&a&s were introdu& by the simple expedient of not allowing a stimulus to immediately repeat itself. This ‘non-repetition’ constraint, according to the information hypothesis, should make a situation with 5 possible alternatives equivalent to a situation in which four alter&&es have an equal probability of occurring on each trial. Instead, this restriction yieided RTs that were systematically too high. %~~LUM (1963) recently attempted to pit the inforha&on hypothesis against an alternative possibility. His argument is based on the fact, air&y clear in Ifyman’s study, that the RT to a stimulus tends to faster when &at stimulus has just keen preceded by itself rather than by another stimulus. Kornbfum claims that most previous studies on information and RT have generally increased the probability of a response reptition whenever they dwreased the value of I-I.2 Since mean RT can be expected to decrease whenever the proportion of rep&ions in a series increases, Karnblum argues, the evidence for the variation of RT with M’is confounded with the possibility that the data CIect the variation of RT with proportion of repetitions. omblum’s simple, but ingenious, confrontation of the information es& with the repetitions-hypothesis involves separately varying rtion of repetitions and H. He gen,erates equi-information pairs of conditions in which one member has a higher than normal proportion of repetitions and the other member has a Power than normal rtion. In aU three of his equLir&rmation pairs, the high repetition 2
&p-at exception is Mm’s study (1953) in vuhich seven of the eight e&a1 conditions were generated by decreasing the probabmty of a rep titksn. See the discussion.
INFORMATION HYPOTHESIS ANDNON-REPETITIONS
39
condition yields a significantly lower T than does its low repetition counterpart. Furthermore, although the RT to low repetition conditions seems to be constant across different values of HI, the RT to high repetition conditions increases in the familiar linear fashion with H. ornblum concludes that ‘the information hypothesis must be rejected erroneous and misleading interpretation of serial choice RT data’. His footnote to his conclusion and his preceding discussion of the literdturc makes it clear that he expects his conclusions to be valid also for the non-serial choice reaction experiments. 1.2.
Erroneous hypothesis or non-optimal conditions
Since the information hypothesis specifies equivalent conditions only under conditions in which S has processed all the information available to him prior to the occurrence of each new stimulus, before we accept any apparent discrepancies from the hypothesis as actual disconfirmations, we must ask if the conditions were optimal for such anticipatory processing on the part of S. 0n the other hand, the information hypothesis would be of doubtful utility, if after reasonable efforts to achieve optimal conditions, Ss still do not tend to respond to informationally equal conditions with the same effectiveness. The objective of WYMAN’Searly study (1953) was to see if the information hypothesis, in fact, could be consi ered as useful in psycholo&al research on RT. To achiev; a positive answer, it was necessary to demonstrate that when the situation was made reasonably ‘ideal’, cqui-information conditions which intuitively appeared different, would indeed tend to yield the same mean RTs. In that experiment, reasonably ‘ideal’ conditions included a response-stimulus interval of approximately 9 to 10 set, preliminary pnictice prior to every series, and highly motivated and experienced Ss, each of whom participatti in a minimum of 40 separate. experimental sessions over a period of three months. By and large the results gave a positive answer. The discrepancies that we have already mentioned, although significant, were not too large in the oj/eralI picture, It seemed more reasonable at the tiime to look upon the case of non-repetitions as due to special circumstances of the experiment rather than to inadequacies inherent in the information hypothesis. It could be the case, for example, that the type of strategy optimal for this special case was quite different from the type of strategies that functioned well for the other cases. Since the three
40
R. HYMAN AND C.UMIETA
special cases aforementioned occurred near the end of the experiment, S:S’rather extensive experience with the other conditions might have the adoption of a new strategy specifically for this new coniraped d&ion. This argument in no way lessens the importance of the difficulty o!! this condition, but 2 places the burden upon factors &at may have impeded optimal processing rathear than upon some defect in the information hypothesis. The possibility of interference among the different conditions that S must master seems especially high in KORNBLUM'S experiment (1968) sinas each S had to deal with all 8 corztiitions within the short span of each session. But an even more important impediment upon Ss’ ability rm optimally, in our opinion, was the fact that the interval the termination of one response and the initiati stGmuluswas only 140 msec. This hardly seems sufficient prepare for the next signal. When we contr& this response-stimulus ~18erval of MO msec with the 9 set of Hyman’s experiment, a ratio cxf more than 60 to I, we can appreciate the necessity for extreme caution in generalizing from Kornblum’s findings to the traditional e,hoice reaction experiment. 2.3.
RatioMalefor present experiment
The present experiment was undertaken to provide a confrontation between the information and repetition hypotheses under conditions stBmewhat more ‘ideal’ than those provided by either HYMAN(1953) or KORNBLUM (1968). For this purpose we employed three of Kornblum’s eight conditions - one pair of cqui-information conditions consisting CAone high and one low repeQ&n situation and one condition of four E! le alternatives without sequential constraints. By choosing (I itions easily discriminable from each other and by restricting the total set to just three conditions, we hoped to minimize possible conor interference between conditions. The connection between uh~s and response was natural without being too compatible. And most importantly, the interval between response and succe t sufficiently large to enable S to prepare fully for the next f;timulrms. er these more optimal conditions the same diflerences between lcw repetition members of equi-information co indeed, the usG.~lness of the information hyp c~btful. If, on the other hand, the differences observed by
INFORMATION
HYPOTHESIS AND NON-REPETITIONS
1
ornblum tend to disappear, or actua?ry disappear, then this would seem to support the case for the continued usefulness of the information hypothesis. ne immediate use, for example, would be to ask what ges would be required to transform Kornblum’s situation i which S could use the information in alternations as we11 as ils.
2.
ETHOD
el, 15 X 34.5 cm, was ocated approximately 80 cm ight aInd slightly below eye level. The panel contained ws of rectangles, 5 X 4 cm, each rectangle composed a translucent plastic while the rest of he panel was a opaque grey. arabic numeral (3 cm high, 1.8 cm at widest level, in black lines cm in thickness) was printed upon each rectangle. The numerals were ‘1’ through ‘8’ inclusive, the top row consisting of *I’ through ‘4’ in order, xnd the bottom row consisting of ‘5’ through ‘13’in order. ‘Each rectangle CQUd be illuminated by a small light immediately behind it. The m~:ured intensity of light on the panel was 5 Sux; the measured intensity of a rectangle when illuminated was 250 lux. S sat a!ane in an anaechoic chamber facing the display panel. From ropriate instructions by an adjoining room E provided S with selected the appropriate means of an intercom. Before each tsia Iight by means of a control switch and pressed a button which simultaneously actived a warning buzzer and an interval timer. seconds after the warning buzzer had sound the appropriate numera was illuminated and, at the same time, a voice key and reaction timer were activated, S’s verbal response #ailing aloud the name of the illuminated numeral) simultaneously terminated the light and the timer. The accuracy of S’s response was monitored by means of the intercom. RT was recorded to the nearest one hundredth of a second. E cmployed an average of 5.5 set to record, reset, select the next stimulus, and initiatt: the next cycle, Between ihe termination of one response and the occurrence of the next stimulus there was an average interval of approximately 7.5 sec. 2.2. Stimulus coditions Three different stimulus con,ilitisns, corresponding to three of eight conditions of KOWBLUM'S expermrent #68), were used. mch con-
42
R. HYMAS AND C. UMILTA
dition consisted of four alternatives with equal frequencies of occurrence h S always dealt with the same four alternatives thrcs;lghout the nt; four different combinations of alternatives %~o Ss for ezich combination. The combinations were: ‘1’ ‘5’ through 9’; ‘2’, ‘3’, ‘6’; ‘7’; and ‘l’, ‘4, “S, ‘8’). In c there were no sequential constraints, the probability of a re 0.25. and the average amount of information per stimul bits. lu condition A2 [high alternation) no repetitions were allowed so that the average amount of information pzr stimulus was reduced to 1.5243 bits. IIn condition A3 (high repetition) the probability that a stimulus would repeat itself on the next trial was 0.61 and t&e average amount of information also 1.58 bits. 2.3. ExpeCrmtai
sessions
S was given all three conditions in each session. For each session, condition consisted of 120 trials divided into groups of 40 trials. T se:;sion its& was divided into three blocks with a five minute rest tween ea& block. In each block S received one series of each con&ion; the order of conditions varied from block to block such that the orq&r af conditions within and across blocks formed a Latin Square. Before ach series S was given complete information about the statistical structure of the series he was about to encounter; in addition, this information was supplemented with 10 practice trials prior to each cond&ion in the first block. The series within each condition were constructed with tables of ra:~!om numbers (RAND CORPORATION, 1955). A new randomization s used for every session and S and no series was ever repealed. Every series within a block contained 5 extra trials to serve as replacements n case of errors. 2.4.
Eight Ss, six males and two females, each participated in four complete sessions, Two Ss who had previously served through 8 sessions of a veq sir&lar experiment received a different set of four alternatives for this lexperiment. With the exception of the two Es the Ss were ents at the University of Bologna; they were paid for their services. t one of the Ss were native-speaking Italians. The response for Ss c~~~&ted in calling out the English name of the illuminated ‘two’, etc.). For the remaining English-speaking S, the
INFO
ATION HYPO
SIS AND NON-REPETITIOIVS
43
e response was to call out the Italian name of the illuminated numeral (‘uno’, “due’, etc.).
3.1.
T lo conalitions
he results of session I were used as a practice session. our major conclusions are b on averages taken across the last three ince the effects of practice were approximately the same for nditionr, it turns out that our conclusions would with or without the inclusion of the first session. The actup he four sessions were 58, 64 and 53 msec for conditions A 1, 2 and A3 respectively. Although tk gain is largest alternation condition and lowest for the l-CgE;repetirion condition the differences are not statistically significant (although, as we will see, later evidence suggests that these differences may be real). Approximately 62 s of this total reduction is accounted for bv the reduction from first to second :iession. Table 1 presents the mean overall RTs to each condition. All three l
TABLE
1 Overall mean RT arid other informatiorl average across the last three sessions and all eight 5s. The data for each condition are based on 2,880 responses.
Al No constraints 2.00 bits
Condition A2 High alternation I .58 bits
A3 High repetition 1.58 bits
430 msec 430
416 msuc 353 508
_~___
.-
Total condition Repetitions Alternations
455 msec 411 460
Proportion of errors: Tota% condition 0.020 Proportion of errors 0.011 after a repcltition Proportion of errors after an a&em~ation 0.022 --
0.025
0.017
0.02s
0,025
means differ significantly from each other. For every S, the meaz ior the high alternation condition is less than for Al, clearly indicating that
Ss are using the information in the alternations. This average reductio I
of about 25 msec corresponds to an average gain of about 60 msec for each bit. The reduction for the high repetition conditi S, is larger than for the high alternation condition, 39 msec for the high repetition condition corresponds to a 93 msec for every bit. Although the average difference between A2 and A3 d 22: msec for the fist two sessions to 12 msec for the last two sessions, this gradual reduction is not statistica\Iy significant. There seem to be iarge individual differences. y the fourth session, two of the eight Ss were faster under the high a!iternation condition a for five of the eight Ss (including the two whose Ts were faster for A2) the actual difference between high and low repetition equi-information conditions appears to be negligible (an absolute difference of 8 msec or less). 3.2. Mean RT to alternuthm crnd repetitions Table I also presents the mean RTs separately to the repetition and alternation components of rach condition averaged across the last three sessions. Fig. 1 depicts thr, mean RT to repetitions as a function of H, the information in %heoccurrence of a repetition. The means are nlotted
SESSION
I
r”Lr 337+72.3
H
SESSION IV ;lV=296+68.4
I
0
Pig.
1.
1.0 INFORMATION
I
2.0 IN 817’S (II)
H
I
3.0
mean RT to repetitions as a function of IS. Means and equations are plotted separately for sessions I and IV.
NON-REPETITIONS
INFORMAFION
nd IV to illustrate th t the total reductio as a result of sessions was a roximate1-y the Same fc,q bth levels of 49 msec for the low and high information lopes of 72 and 68 msec are not signific s are significarntly different SESSION
I
^yI= 394+ 55.0 H
SESSION
IV
$lV=336+52,9
0
I!0 INFORMATION
Fig. 2.
210
H
3!0
IN BtTS 3Hl
The meau RT to alternations as a fu &on of H. Means and equations are plotted separately for sessions 1 and IV.
for alternations as a function of N for both sessions I and IV. Again, t significantly different but the the two slopes of 56 and 53 are average reduction of 64 msec at each level of In addition, the average reduction o ponents is significantly greater than for the repetition components. This greater average reduction for alternations seems to hold from session to session: 38 for alternations MC! 34 for repetitions from sessions I to I ; 8 and 0 from sessions I and 18 and 12 from sessions III to IV. etitions and alternatio Fig. 3 depicts the average W aged across the last three sessi squares estimates) of 56 and 68 for al peetively, are not statistically significan slopes are quite large, two Ss having slopes which were consisteziliy larger for tbs: alternations across all three sessions. he 95 $%confidence
$6
R. HYMAN AND C. UMILTii
% ALTERNATIONS $~=343+56.3H 0 REPE71TIOW 9 R= 304+ 68.4 N
SITES
T
0
I
LO INFORMATlON
I
2.0 tN GrlTS (H)
1
3.0
Pig. 3. The mean RT to both alternations and repettions alId the quations averaged across sessions II through IV. Also shown are the predicted values, on the basis of the predictions from the repetitions and alternations compuneuts, for conditions Al (2.00 bits), A2 (1.58 bits) Cno repetitions), A3 (1.58 bits, high proportion of repetitions). At 1.58 hits the point with the higher RT represents AZ.
limits for the average difference in slopes are from -8.5 to 33 msec in favor of the repetitions. The: bulk of the difference between RT to alternations and &arepetitions seems to be due to a constant dLplacement of the two functions along the vertical axis. Fig. 3 also illus,.rates how this constant displacement accounts for the differences in the overall mean RT. The greater the absolute difference in intercepts between. the alternation and repetition functions, the greater will appear the differences in slopes of the information function based on overall mean RTs to conditions in hkh information is varied by increasing alternations as compared with overall mean RTs to conditions in which information is varied by increas,ing repetitions. 3.3,
Analysis of errors
Table I also contains the overall proportion of errors for each cond&ion as well as the conditional p&abilities of an error for alternations this experiment, the repetitions. Across the totA of 11,519 trials mar rate was 2 %. For individual Ss, this rate varied from a low of
SIS AND NON-REPETITIONS
he error rate vari
47
significantly with conditions,
ference in error rate for co
either for alternations nor for
e average error rate of 0
4. DISCWSKIN Just which aspects of our findings are due to the amount of time S has between successive occurrence of stimuli, to the particular comn of stimulus-response employed, to the small number o conditions, or to other features of our particular situation is dihlicult to y. But it does seem rcasonablz to claim, whatever else may be different, that our situation provides Ss with more opportunity to process rnations than does orrainformation from both repetitions and imal conditions, however, %s blum’s situation. Even under our more still appear to have greater difficulty in using the information from alternations than from repetitions. The probability of an error for an alternation is twice that for a repetition. This difference in error rates does not change with practi to the occurrence of an alternation is Furthermore, the mean higher than to the occurren a repetition. There is also the hat RT to variations in W is somewhat more sensitive for r s is not statistical y sigkficant. ere seems little doubt that the information On the other hand, hypothesis is much more compatible with our results than with those of Kornblum’s. The relative difference between the alternation and repetition condition is much less in our study; furthermore, the effect of practice is much more pronoumced on the alternations, suggesting that with extended practice, the differences between these conditions will disappear entirely. Indeed, after four sessions, the differences ham?
48
R. HYMAN
AND C. IJMILTii
completely disappeared for at least two of our Ss, and ossibly for as many as five out of the eight. Furthermore, the results suggest that much, if no all, of the initial difference between alternations and repetitions in our experiment can be conceived of as difference in vertical displacement of the RTfunction; practice across the four sessions affects only this vertical displacement, leaving t e slope of RT against N unchanged. ta from a pilot study with two Ss confirms this effect of practice across eight sessions. In ou.!r situation, then, there seems to be no indication that continued practice will reduce the slope of RT on H.
Whether the so~~~4ledinformation hy othesis has been useful up to now or can be. useful in the future is a matter which cannot be settled appeal to ‘critical tests’ or by any objeztijve decision rules. Like any other conceptual tool, the usefulness of this hypoth& will depend greatly upon who applies it, to what it is aIqAied, and $3~ it is applied. One of the first argumentj against the information hypothesis occurred wb,en it was discovered that under som+3conditions the function of RT to rr:jmt the on 1Ytends to be constant. Instead of using this o D (1961) has information hypotbiesis, it has been productive, as illustrated, to search for differences in conditions and psychological process that obtain when the function of RI’ on H is and is not a constant. Now KORWLUM (1968) has brought forth another type of cha The previous challenge, based on the situations in which there is presumed S-R compa.tibility, does not deny that RT is a single-valued functicn ~8 H. but rather points to the possibility that under some conditions this single-valued function becomes a constant. Kornblum uses his findings to argue that RT 5 not even a single-valued function H tile same value of H can produce different mean RTs. In one sense Kornblu~~ is correct. Under many conditions, the same value of W can give rise to different mean RTs We have sett:nexamples of this in HYMAN’Searly study (1953) and KORNBLUVI'S recent one (1968). Kornblum’s findings do present a challenge. Rut we would argue tbat the )nature of the challenge does not concern the usefulness or correctness of the inftirmation hypothesis - a question which is ly best left to history - but rather it concerns the discovery and
WESlS AND NON-REPETITIONS
specification of
9
recesses and conditions that are operative when the tends to be inadequate. ions, one thecmtical and the
time to process only wh, S bus fully extracted all the infcmzation available to hint rbr to tht+foccurrence of each new signal. henever serve a situation in ui-information conditions yield s either S, because ( f impediments in the situa easons, ma:1 not have bee I extracting all the inform to the occurrence of each new signal under one or more of the conditions, or the information hypothesis might be in error because it lumps togetl- er as equivalent conditions that are psychology distinct even under ‘ideal’ conditions. Since one can always argue that conditions were somehow not ideal, this theoretical feature of the information hypothesis seems to preclude critical empirical tests of’ the hypothesis” Nevertheless, there do seem to bl: pragmatic bases, based on e 1 datn,, for arguing for or uthesis. Wkle it seems imagains’ %e utility of the information conditions were ideal, it seems possible to say in any absolute sense t plausible to order situations in terms of their tendency to approximate an ideal situation. When we order two or more experimental situations in terms of their relative tendencies to approximate the ideal, we should feel justified in claiming continued utility for the information hypothesis only if the agreemeni of data to the hypothesis improves with increasing tendency towards the ideal situation. If, in our relatively more ideal circumstances, the mean R equi-information conditions had shown the same rektive discrepancies fl*omthe information hypothesis as they had for .Kornblum”s experiment. tiile continued usefuIness of this conceptual tool would indeed be under question. Since, however, our data strongly suggest that the information hypothesis tends to hold true the more we approximate ideal CO@ &ions, the issue: before us is no1:‘the continued usefulness of this tool, but rather the search for the mechanisms of information processing that enable the hypth& to hold in one condition and not in the other.
50
R. EIWvlAN AND C. UMILTk
4.2. TP’hereptdtions ,hypotlze5fs M[(I~LPJM (1967, 1968) suggests that the repetitio,.ls hypothesis
It serve as an explanatory alternative to the informat on it could very well be the case that in a serial rerrctio tl,ta his, the major consideration is whether or not a stin~ulus has just repeated itself; while in 0 r situation, in which S has s jfficieat reen trials to consider all the alternatives and to .set himself for information in possibilities other than a rep&ition, it could be that the stimuh~s occurrence is the major d(eterminant of We are quite accustomed to multi-process theories today and we neeh not feel any iscomfort in postulating at least two levels at which processing of the input sign& occur - one of which becomes more prominent und certain restrictions. But before wq can fully assess the role of repetit!ons in the search for mechanisms underlying serial and choice RT, some important difficulties must be resolved. The basic argument as presenterS by Kornblum is attra&iely simple. Since RT to a repetition is faster Bhan to an alternation, as we &ease tile proportion of repetitions in a stimulus series the average RT to this series should diminish. And Kornblum’s findings clearly demojlstrate this to be the case. But, by the same logic, we should expect that as we decrease the proportion of repetitions the average RT to a series should increuse. Yet, when Kornblum lowe the probability of a repetition from 0.25 to 0.00, meIn RI’ did not rise as the repetitions hypothesis demands, instead it remained constant over this range. Clearly the: simple argument of the repetitions hypothesis, by its&, .isnot sufficient to account for even Kornblum’s results. Some other unexplained difficulties with the repetitions hypothesis arise when we also consider an earlier experiment of KORNBLUM'S (1967). In that experkment RT to a repetition apparently varied with the prokbility of a reptition but RT to an alternation was independent of the probability of an alternation. This was true only when the number of alternatives was held constant. In contrast, in the second experiment, under very similar collditions, Kornblwm reports that RT varied as a n&ion of the probakrility of occurrence of both l&natives and repetitions. Thus, even wWn Kornbltlm’s particular serial reaction condition, tie role of rep&ions needs to be clarified. aturagy, the argument for the repetitions hypothesis becomes even more tenuous as we eJltend it beyond Kornblum’s very special situation. ornblum claims that ‘with rare exceptions it can be shown that, for a
D iVON-REPET.ITIBNS
51
als, the sequences of signals on which the sed were construct ormation increas simultaneously with the probabi~ty es not list these ‘rare excep AN’S
( 195 3)
eXperiInent.
rvations with respect to sequences rd with my ow an’s results are blum’s conclusions. eight different conditions in the situation in which ing sequential constrai n all but one of thet the probability of a re for the same number of alterhus, seven out of eight seornblum would call high alternation conditions. And yet, only three of these conditions - the S ial cases of ‘no repetition’, gave significantly high RTs. The other four high alternation conditions, along with the one high repetition condition, all behaved ust as they should according to the information sis (if anythi g, Ss were somewhat too f.zst to these conditions, 1: scquen tial conditions s could be explained by the fact tha came late in the experiment). iscrepancies ir! Hyman’s experiment, then, cannot be inter T as a difference between high repetition and low repetitian, but rather as a special difficulty entaille by the non-repetition condition. A consts a sideration of the task dema s under the various conditions s conreason for the special difficulty. The conditions with se that, straints differ from the other conditions of yman’s experiment & trial, the su ective probability distribution on th;e possible on alternatives could change as a function of the receding stimu conditions with no sequential constraints, S faces the &samep distribution on the given alternatives in every trial. constraint requires S to keep track of the precedi trial. In addition to tl& memory I task, S has to generate I& subjective pro&&&y distribution for each new stimulus. the simpler the type of distribution, the easier it wil! this task. si The five sequenti 1 conditions with the 1
R. WYMAN AND C. uMII.Ti
52
periment all had these two features in common: (1) on each trial S was presented with a unimodal subjective probability distribution such while the that one alternative was always relatively highly pro’ remaining n- 1 alternatives had equal and relative y low probabilities of occurrence; and (2) the shifting mode was always easy ‘to trac tiaP (being either a repetition of the preceding stimuPus or re preceding stimulus by a simple spatial rule). The three no conditions, on the other hand, always confronted S with a distribution with n-1 modes dividing the probabili y space equally among themselves and on which the particular set vr-4 modes always shifted after every stimulus. These considerations suggest that, the initial difficulty that Ss in our resent experiment had with the non-repetition condition was not so much a matter of the proportion of repetitions or alternations, but rather the type of changing distribution on each trial and the ease of le to us that a repetition has an important status for ,wo reasons. One reason is that it represents a very easy way to keep track of the most probable response. Another reason is that there may be something inherent in n repetition, independent of S’s expectancies and strategies, that tends to facilitate the response, It also $ausibk that this latter factor may well be the more important con+ &nent in Kornblum’s situation, but before we could draw such a conclusior+,,we would want to see these factors of type of distribution, of kee~ping track of the more probable response, and pure repcIns unconfounded in Kornblum’s situation. 5.
C~N~.LUSI~NS hat
evidence we now have Tuvithrespect to choice reactio the infomation hypothesis, w h specifies equivalent the assumption that S can ii es profit from all1the information aivailable to him prior to each new signal, tends to be a closer and closer approximation to the empirical data as the conditions of respondthe ideal. As long as this tendency re:mains reasonable, en the information hypothesis can be used as a point of departure how S processes information by seeking to define the paramake a differeact between the situations under which the on hypothesis holds and those under which it does noit. As we ‘complicate’ the ideal condition, in the spirit of Donders’ corn-
IN
ATIONWYPQTHESI
AND NON-REPETITIONS - -’
53
ould hopefully discover a hierarchy of diffithat produce deviations from the equivalences esis. Some of these ty_pesof gested =- keeping track of the high probaw several eq 1 modes instead of one an alternation i mation hypothes s is to be abandon mature to do so on
ain of information.
Quart. .I. exp. Psychol. 4,
ulus information 85 a determinant of reaction time. J. exp. tion time for repetitions and non-repetitions: a nlnrmation hypothesis. In: Attention and per, m-w. A. F. Sanders (ed.), Acta Psychol. rial-choice reaction-time: inadequacies of the infornnation ,432---434.
ion time experiments and information theory. ondun. Butterworths. In: C. Chcrr;l (ed.), Mormation theory. 137---146. atical theory of communiSHANNON, C. E. and W. WEAVER, 1949. The mat cation. Urbana: Univ. of Illinois Press. The Rand Cor ration, 1955. A million random digits. Glencoe, Illinois: The Free Press.
Attention and Performance 11 f W, (I;. Koster, ed.) 1969, 37-53 @JNorth-Holland Pubhkhing Company, Amsterdam
university of Oregon, Eugene, Ore., U.S.A.
and
Lstituto di Psicotogiu della Facaltci
edica dell’ Wniversitci di Bologna, Italy
WRACT
The information hypothesis specifies that equi-information conditions will yield the same mean R provided that S can and does take advantage of all the information available to him prior to the occurrence of each new signal. KORNBLUM'S recent experiment (1968) demonstrated RT was not the same for equi-information conditions differing in propotiion of repetitions. Qne can conclude with Kornblum that his findings disconfirm the information hypothesis or one can look: for factors in the experimental situation that may have im ability to profit from information in alternations. VZhen we repeated Kornblum’s conditions in a choice reac:tion experiment designed to give S more opportunity to use the information from alternations, the overAl results were more compatible with :he information hypothesis. This result suggests that a fruitful way to study the microstructure of T is to isolate the factors that differentiate situatioils in which the infor hypothesis holds from those in which it does not. ‘ XNTR~D~ICTI~N
In 1953 Hyman published results in support of the idea that reaction
time (.RT) was a function of stimulus information @I) regarless of how the information in a stimulus (‘message’) was varied - by varying the number of different alternat ves froj!n which the message is selected, the probabilities with which the different messages can occur, or the sequential constraints between the successive occurrences of any two messages. These results, in addition to those of ICI& (1952) on and transmitted information, provided the initial basis for what has since been called the “information hypothesis’. 1 This study was conducted at the Istituto di Psicologia, 1Jniversiti di Bologna, Bologna, Italy during the academic year 1967-8 while the senior author was a Fulbright-Hays Research Scholar. We are indebted to Professor Renzo Canestrari, Director of the Istituto, for providing us with facilities and financial suppoti. 37
33
IL HYMAN ANDC, UMlL'd
In its stricter form the information hypothesis has recently stated as fiiollows: ‘all other things being equal (such as stimulusresponse compatibihty, training, discriminability, and elrror rate), equiinformation conditions must produce equal overall mean L~DM[, 1963). A weaker version would be the following: ‘equal increments in inform&on produce equal increments in RT’ (Kam~m, ibid.). 1.1.
The stricter version of the information hypothesis was disconfirmed even in Hyman’s original study. Three out of the 24 conditions in that study yielded RTs that were significantly, although slightly. too high. The:6 t&z conditions had in common the fact that sequential cons&a&s were introdu& by the simple expedient of not allowing a stimulus to immediately repeat itself. This ‘non-repetition’ constraint, according to the information hypothesis, should make a situation with 5 possible alternatives equivalent to a situation in which four alter&&es have an equal probability of occurring on each trial. Instead, this restriction yieided RTs that were systematically too high. %~~LUM (1963) recently attempted to pit the inforha&on hypothesis against an alternative possibility. His argument is based on the fact, air&y clear in Ifyman’s study, that the RT to a stimulus tends to faster when &at stimulus has just keen preceded by itself rather than by another stimulus. Kornbfum claims that most previous studies on information and RT have generally increased the probability of a response reptition whenever they dwreased the value of I-I.2 Since mean RT can be expected to decrease whenever the proportion of rep&ions in a series increases, Karnblum argues, the evidence for the variation of RT with M’is confounded with the possibility that the data CIect the variation of RT with proportion of repetitions. omblum’s simple, but ingenious, confrontation of the information es& with the repetitions-hypothesis involves separately varying rtion of repetitions and H. He gen,erates equi-information pairs of conditions in which one member has a higher than normal proportion of repetitions and the other member has a Power than normal rtion. In aU three of his equLir&rmation pairs, the high repetition 2
&p-at exception is Mm’s study (1953) in vuhich seven of the eight e&a1 conditions were generated by decreasing the probabmty of a rep titksn. See the discussion.
INFORMATION HYPOTHESIS ANDNON-REPETITIONS
39
condition yields a significantly lower T than does its low repetition counterpart. Furthermore, although the RT to low repetition conditions seems to be constant across different values of HI, the RT to high repetition conditions increases in the familiar linear fashion with H. ornblum concludes that ‘the information hypothesis must be rejected erroneous and misleading interpretation of serial choice RT data’. His footnote to his conclusion and his preceding discussion of the literdturc makes it clear that he expects his conclusions to be valid also for the non-serial choice reaction experiments. 1.2.
Erroneous hypothesis or non-optimal conditions
Since the information hypothesis specifies equivalent conditions only under conditions in which S has processed all the information available to him prior to the occurrence of each new stimulus, before we accept any apparent discrepancies from the hypothesis as actual disconfirmations, we must ask if the conditions were optimal for such anticipatory processing on the part of S. 0n the other hand, the information hypothesis would be of doubtful utility, if after reasonable efforts to achieve optimal conditions, Ss still do not tend to respond to informationally equal conditions with the same effectiveness. The objective of WYMAN’Searly study (1953) was to see if the information hypothesis, in fact, could be consi ered as useful in psycholo&al research on RT. To achiev; a positive answer, it was necessary to demonstrate that when the situation was made reasonably ‘ideal’, cqui-information conditions which intuitively appeared different, would indeed tend to yield the same mean RTs. In that experiment, reasonably ‘ideal’ conditions included a response-stimulus interval of approximately 9 to 10 set, preliminary pnictice prior to every series, and highly motivated and experienced Ss, each of whom participatti in a minimum of 40 separate. experimental sessions over a period of three months. By and large the results gave a positive answer. The discrepancies that we have already mentioned, although significant, were not too large in the oj/eralI picture, It seemed more reasonable at the tiime to look upon the case of non-repetitions as due to special circumstances of the experiment rather than to inadequacies inherent in the information hypothesis. It could be the case, for example, that the type of strategy optimal for this special case was quite different from the type of strategies that functioned well for the other cases. Since the three
40
R. HYMAN AND C.UMIETA
special cases aforementioned occurred near the end of the experiment, S:S’rather extensive experience with the other conditions might have the adoption of a new strategy specifically for this new coniraped d&ion. This argument in no way lessens the importance of the difficulty o!! this condition, but 2 places the burden upon factors &at may have impeded optimal processing rathear than upon some defect in the information hypothesis. The possibility of interference among the different conditions that S must master seems especially high in KORNBLUM'S experiment (1968) sinas each S had to deal with all 8 corztiitions within the short span of each session. But an even more important impediment upon Ss’ ability rm optimally, in our opinion, was the fact that the interval the termination of one response and the initiati stGmuluswas only 140 msec. This hardly seems sufficient prepare for the next signal. When we contr& this response-stimulus ~18erval of MO msec with the 9 set of Hyman’s experiment, a ratio cxf more than 60 to I, we can appreciate the necessity for extreme caution in generalizing from Kornblum’s findings to the traditional e,hoice reaction experiment. 2.3.
RatioMalefor present experiment
The present experiment was undertaken to provide a confrontation between the information and repetition hypotheses under conditions stBmewhat more ‘ideal’ than those provided by either HYMAN(1953) or KORNBLUM (1968). For this purpose we employed three of Kornblum’s eight conditions - one pair of cqui-information conditions consisting CAone high and one low repeQ&n situation and one condition of four E! le alternatives without sequential constraints. By choosing (I itions easily discriminable from each other and by restricting the total set to just three conditions, we hoped to minimize possible conor interference between conditions. The connection between uh~s and response was natural without being too compatible. And most importantly, the interval between response and succe t sufficiently large to enable S to prepare fully for the next f;timulrms. er these more optimal conditions the same diflerences between lcw repetition members of equi-information co indeed, the usG.~lness of the information hyp c~btful. If, on the other hand, the differences observed by
INFORMATION
HYPOTHESIS AND NON-REPETITIONS
1
ornblum tend to disappear, or actua?ry disappear, then this would seem to support the case for the continued usefulness of the information hypothesis. ne immediate use, for example, would be to ask what ges would be required to transform Kornblum’s situation i which S could use the information in alternations as we11 as ils.
2.
ETHOD
el, 15 X 34.5 cm, was ocated approximately 80 cm ight aInd slightly below eye level. The panel contained ws of rectangles, 5 X 4 cm, each rectangle composed a translucent plastic while the rest of he panel was a opaque grey. arabic numeral (3 cm high, 1.8 cm at widest level, in black lines cm in thickness) was printed upon each rectangle. The numerals were ‘1’ through ‘8’ inclusive, the top row consisting of *I’ through ‘4’ in order, xnd the bottom row consisting of ‘5’ through ‘13’in order. ‘Each rectangle CQUd be illuminated by a small light immediately behind it. The m~:ured intensity of light on the panel was 5 Sux; the measured intensity of a rectangle when illuminated was 250 lux. S sat a!ane in an anaechoic chamber facing the display panel. From ropriate instructions by an adjoining room E provided S with selected the appropriate means of an intercom. Before each tsia Iight by means of a control switch and pressed a button which simultaneously actived a warning buzzer and an interval timer. seconds after the warning buzzer had sound the appropriate numera was illuminated and, at the same time, a voice key and reaction timer were activated, S’s verbal response #ailing aloud the name of the illuminated numeral) simultaneously terminated the light and the timer. The accuracy of S’s response was monitored by means of the intercom. RT was recorded to the nearest one hundredth of a second. E cmployed an average of 5.5 set to record, reset, select the next stimulus, and initiatt: the next cycle, Between ihe termination of one response and the occurrence of the next stimulus there was an average interval of approximately 7.5 sec. 2.2. Stimulus coditions Three different stimulus con,ilitisns, corresponding to three of eight conditions of KOWBLUM'S expermrent #68), were used. mch con-
42
R. HYMAS AND C. UMILTA
dition consisted of four alternatives with equal frequencies of occurrence h S always dealt with the same four alternatives thrcs;lghout the nt; four different combinations of alternatives %~o Ss for ezich combination. The combinations were: ‘1’ ‘5’ through 9’; ‘2’, ‘3’, ‘6’; ‘7’; and ‘l’, ‘4, “S, ‘8’). In c there were no sequential constraints, the probability of a re 0.25. and the average amount of information per stimul bits. lu condition A2 [high alternation) no repetitions were allowed so that the average amount of information pzr stimulus was reduced to 1.5243 bits. IIn condition A3 (high repetition) the probability that a stimulus would repeat itself on the next trial was 0.61 and t&e average amount of information also 1.58 bits. 2.3. ExpeCrmtai
sessions
S was given all three conditions in each session. For each session, condition consisted of 120 trials divided into groups of 40 trials. T se:;sion its& was divided into three blocks with a five minute rest tween ea& block. In each block S received one series of each con&ion; the order of conditions varied from block to block such that the orq&r af conditions within and across blocks formed a Latin Square. Before ach series S was given complete information about the statistical structure of the series he was about to encounter; in addition, this information was supplemented with 10 practice trials prior to each cond&ion in the first block. The series within each condition were constructed with tables of ra:~!om numbers (RAND CORPORATION, 1955). A new randomization s used for every session and S and no series was ever repealed. Every series within a block contained 5 extra trials to serve as replacements n case of errors. 2.4.
Eight Ss, six males and two females, each participated in four complete sessions, Two Ss who had previously served through 8 sessions of a veq sir&lar experiment received a different set of four alternatives for this lexperiment. With the exception of the two Es the Ss were ents at the University of Bologna; they were paid for their services. t one of the Ss were native-speaking Italians. The response for Ss c~~~&ted in calling out the English name of the illuminated ‘two’, etc.). For the remaining English-speaking S, the
INFO
ATION HYPO
SIS AND NON-REPETITIOIVS
43
e response was to call out the Italian name of the illuminated numeral (‘uno’, “due’, etc.).
3.1.
T lo conalitions
he results of session I were used as a practice session. our major conclusions are b on averages taken across the last three ince the effects of practice were approximately the same for nditionr, it turns out that our conclusions would with or without the inclusion of the first session. The actup he four sessions were 58, 64 and 53 msec for conditions A 1, 2 and A3 respectively. Although tk gain is largest alternation condition and lowest for the l-CgE;repetirion condition the differences are not statistically significant (although, as we will see, later evidence suggests that these differences may be real). Approximately 62 s of this total reduction is accounted for bv the reduction from first to second :iession. Table 1 presents the mean overall RTs to each condition. All three l
TABLE
1 Overall mean RT arid other informatiorl average across the last three sessions and all eight 5s. The data for each condition are based on 2,880 responses.
Al No constraints 2.00 bits
Condition A2 High alternation I .58 bits
A3 High repetition 1.58 bits
430 msec 430
416 msuc 353 508
_~___
.-
Total condition Repetitions Alternations
455 msec 411 460
Proportion of errors: Tota% condition 0.020 Proportion of errors 0.011 after a repcltition Proportion of errors after an a&em~ation 0.022 --
0.025
0.017
0.02s
0,025
means differ significantly from each other. For every S, the meaz ior the high alternation condition is less than for Al, clearly indicating that
Ss are using the information in the alternations. This average reductio I
of about 25 msec corresponds to an average gain of about 60 msec for each bit. The reduction for the high repetition conditi S, is larger than for the high alternation condition, 39 msec for the high repetition condition corresponds to a 93 msec for every bit. Although the average difference between A2 and A3 d 22: msec for the fist two sessions to 12 msec for the last two sessions, this gradual reduction is not statistica\Iy significant. There seem to be iarge individual differences. y the fourth session, two of the eight Ss were faster under the high a!iternation condition a for five of the eight Ss (including the two whose Ts were faster for A2) the actual difference between high and low repetition equi-information conditions appears to be negligible (an absolute difference of 8 msec or less). 3.2. Mean RT to alternuthm crnd repetitions Table I also presents the mean RTs separately to the repetition and alternation components of rach condition averaged across the last three sessions. Fig. 1 depicts thr, mean RT to repetitions as a function of H, the information in %heoccurrence of a repetition. The means are nlotted
SESSION
I
r”Lr 337+72.3
H
SESSION IV ;lV=296+68.4
I
0
Pig.
1.
1.0 INFORMATION
I
2.0 IN 817’S (II)
H
I
3.0
mean RT to repetitions as a function of IS. Means and equations are plotted separately for sessions I and IV.
NON-REPETITIONS
INFORMAFION
nd IV to illustrate th t the total reductio as a result of sessions was a roximate1-y the Same fc,q bth levels of 49 msec for the low and high information lopes of 72 and 68 msec are not signific s are significarntly different SESSION
I
^yI= 394+ 55.0 H
SESSION
IV
$lV=336+52,9
0
I!0 INFORMATION
Fig. 2.
210
H
3!0
IN BtTS 3Hl
The meau RT to alternations as a fu &on of H. Means and equations are plotted separately for sessions 1 and IV.
for alternations as a function of N for both sessions I and IV. Again, t significantly different but the the two slopes of 56 and 53 are average reduction of 64 msec at each level of In addition, the average reduction o ponents is significantly greater than for the repetition components. This greater average reduction for alternations seems to hold from session to session: 38 for alternations MC! 34 for repetitions from sessions I to I ; 8 and 0 from sessions I and 18 and 12 from sessions III to IV. etitions and alternatio Fig. 3 depicts the average W aged across the last three sessi squares estimates) of 56 and 68 for al peetively, are not statistically significan slopes are quite large, two Ss having slopes which were consisteziliy larger for tbs: alternations across all three sessions. he 95 $%confidence
$6
R. HYMAN AND C. UMILTii
% ALTERNATIONS $~=343+56.3H 0 REPE71TIOW 9 R= 304+ 68.4 N
SITES
T
0
I
LO INFORMATlON
I
2.0 tN GrlTS (H)
1
3.0
Pig. 3. The mean RT to both alternations and repettions alId the quations averaged across sessions II through IV. Also shown are the predicted values, on the basis of the predictions from the repetitions and alternations compuneuts, for conditions Al (2.00 bits), A2 (1.58 bits) Cno repetitions), A3 (1.58 bits, high proportion of repetitions). At 1.58 hits the point with the higher RT represents AZ.
limits for the average difference in slopes are from -8.5 to 33 msec in favor of the repetitions. The: bulk of the difference between RT to alternations and &arepetitions seems to be due to a constant dLplacement of the two functions along the vertical axis. Fig. 3 also illus,.rates how this constant displacement accounts for the differences in the overall mean RT. The greater the absolute difference in intercepts between. the alternation and repetition functions, the greater will appear the differences in slopes of the information function based on overall mean RTs to conditions in hkh information is varied by increasing alternations as compared with overall mean RTs to conditions in which information is varied by increas,ing repetitions. 3.3,
Analysis of errors
Table I also contains the overall proportion of errors for each cond&ion as well as the conditional p&abilities of an error for alternations this experiment, the repetitions. Across the totA of 11,519 trials mar rate was 2 %. For individual Ss, this rate varied from a low of
SIS AND NON-REPETITIONS
he error rate vari
47
significantly with conditions,
ference in error rate for co
either for alternations nor for
e average error rate of 0
4. DISCWSKIN Just which aspects of our findings are due to the amount of time S has between successive occurrence of stimuli, to the particular comn of stimulus-response employed, to the small number o conditions, or to other features of our particular situation is dihlicult to y. But it does seem rcasonablz to claim, whatever else may be different, that our situation provides Ss with more opportunity to process rnations than does orrainformation from both repetitions and imal conditions, however, %s blum’s situation. Even under our more still appear to have greater difficulty in using the information from alternations than from repetitions. The probability of an error for an alternation is twice that for a repetition. This difference in error rates does not change with practi to the occurrence of an alternation is Furthermore, the mean higher than to the occurren a repetition. There is also the hat RT to variations in W is somewhat more sensitive for r s is not statistical y sigkficant. ere seems little doubt that the information On the other hand, hypothesis is much more compatible with our results than with those of Kornblum’s. The relative difference between the alternation and repetition condition is much less in our study; furthermore, the effect of practice is much more pronoumced on the alternations, suggesting that with extended practice, the differences between these conditions will disappear entirely. Indeed, after four sessions, the differences ham?
48
R. HYMAN
AND C. IJMILTii
completely disappeared for at least two of our Ss, and ossibly for as many as five out of the eight. Furthermore, the results suggest that much, if no all, of the initial difference between alternations and repetitions in our experiment can be conceived of as difference in vertical displacement of the RTfunction; practice across the four sessions affects only this vertical displacement, leaving t e slope of RT against N unchanged. ta from a pilot study with two Ss confirms this effect of practice across eight sessions. In ou.!r situation, then, there seems to be no indication that continued practice will reduce the slope of RT on H.
Whether the so~~~4ledinformation hy othesis has been useful up to now or can be. useful in the future is a matter which cannot be settled appeal to ‘critical tests’ or by any objeztijve decision rules. Like any other conceptual tool, the usefulness of this hypoth& will depend greatly upon who applies it, to what it is aIqAied, and $3~ it is applied. One of the first argumentj against the information hypothesis occurred wb,en it was discovered that under som+3conditions the function of RT to rr:jmt the on 1Ytends to be constant. Instead of using this o D (1961) has information hypotbiesis, it has been productive, as illustrated, to search for differences in conditions and psychological process that obtain when the function of RI’ on H is and is not a constant. Now KORWLUM (1968) has brought forth another type of cha The previous challenge, based on the situations in which there is presumed S-R compa.tibility, does not deny that RT is a single-valued functicn ~8 H. but rather points to the possibility that under some conditions this single-valued function becomes a constant. Kornblum uses his findings to argue that RT 5 not even a single-valued function H tile same value of H can produce different mean RTs. In one sense Kornblu~~ is correct. Under many conditions, the same value of W can give rise to different mean RTs We have sett:nexamples of this in HYMAN’Searly study (1953) and KORNBLUVI'S recent one (1968). Kornblum’s findings do present a challenge. Rut we would argue tbat the )nature of the challenge does not concern the usefulness or correctness of the inftirmation hypothesis - a question which is ly best left to history - but rather it concerns the discovery and
WESlS AND NON-REPETITIONS
specification of
9
recesses and conditions that are operative when the tends to be inadequate. ions, one thecmtical and the
time to process only wh, S bus fully extracted all the infcmzation available to hint rbr to tht+foccurrence of each new signal. henever serve a situation in ui-information conditions yield s either S, because ( f impediments in the situa easons, ma:1 not have bee I extracting all the inform to the occurrence of each new signal under one or more of the conditions, or the information hypothesis might be in error because it lumps togetl- er as equivalent conditions that are psychology distinct even under ‘ideal’ conditions. Since one can always argue that conditions were somehow not ideal, this theoretical feature of the information hypothesis seems to preclude critical empirical tests of’ the hypothesis” Nevertheless, there do seem to bl: pragmatic bases, based on e 1 datn,, for arguing for or uthesis. Wkle it seems imagains’ %e utility of the information conditions were ideal, it seems possible to say in any absolute sense t plausible to order situations in terms of their tendency to approximate an ideal situation. When we order two or more experimental situations in terms of their relative tendencies to approximate the ideal, we should feel justified in claiming continued utility for the information hypothesis only if the agreemeni of data to the hypothesis improves with increasing tendency towards the ideal situation. If, in our relatively more ideal circumstances, the mean R equi-information conditions had shown the same rektive discrepancies fl*omthe information hypothesis as they had for .Kornblum”s experiment. tiile continued usefuIness of this conceptual tool would indeed be under question. Since, however, our data strongly suggest that the information hypothesis tends to hold true the more we approximate ideal CO@ &ions, the issue: before us is no1:‘the continued usefulness of this tool, but rather the search for the mechanisms of information processing that enable the hypth& to hold in one condition and not in the other.
50
R. EIWvlAN AND C. UMILTk
4.2. TP’hereptdtions ,hypotlze5fs M[(I~LPJM (1967, 1968) suggests that the repetitio,.ls hypothesis
It serve as an explanatory alternative to the informat on it could very well be the case that in a serial rerrctio tl,ta his, the major consideration is whether or not a stin~ulus has just repeated itself; while in 0 r situation, in which S has s jfficieat reen trials to consider all the alternatives and to .set himself for information in possibilities other than a rep&ition, it could be that the stimuh~s occurrence is the major d(eterminant of We are quite accustomed to multi-process theories today and we neeh not feel any iscomfort in postulating at least two levels at which processing of the input sign& occur - one of which becomes more prominent und certain restrictions. But before wq can fully assess the role of repetit!ons in the search for mechanisms underlying serial and choice RT, some important difficulties must be resolved. The basic argument as presenterS by Kornblum is attra&iely simple. Since RT to a repetition is faster Bhan to an alternation, as we &ease tile proportion of repetitions in a stimulus series the average RT to this series should diminish. And Kornblum’s findings clearly demojlstrate this to be the case. But, by the same logic, we should expect that as we decrease the proportion of repetitions the average RT to a series should increuse. Yet, when Kornblum lowe the probability of a repetition from 0.25 to 0.00, meIn RI’ did not rise as the repetitions hypothesis demands, instead it remained constant over this range. Clearly the: simple argument of the repetitions hypothesis, by its&, .isnot sufficient to account for even Kornblum’s results. Some other unexplained difficulties with the repetitions hypothesis arise when we also consider an earlier experiment of KORNBLUM'S (1967). In that experkment RT to a repetition apparently varied with the prokbility of a reptition but RT to an alternation was independent of the probability of an alternation. This was true only when the number of alternatives was held constant. In contrast, in the second experiment, under very similar collditions, Kornblwm reports that RT varied as a n&ion of the probakrility of occurrence of both l&natives and repetitions. Thus, even wWn Kornbltlm’s particular serial reaction condition, tie role of rep&ions needs to be clarified. aturagy, the argument for the repetitions hypothesis becomes even more tenuous as we eJltend it beyond Kornblum’s very special situation. ornblum claims that ‘with rare exceptions it can be shown that, for a
D iVON-REPET.ITIBNS
51
als, the sequences of signals on which the sed were construct ormation increas simultaneously with the probabi~ty es not list these ‘rare excep AN’S
( 195 3)
eXperiInent.
rvations with respect to sequences rd with my ow an’s results are blum’s conclusions. eight different conditions in the situation in which ing sequential constrai n all but one of thet the probability of a re for the same number of alterhus, seven out of eight seornblum would call high alternation conditions. And yet, only three of these conditions - the S ial cases of ‘no repetition’, gave significantly high RTs. The other four high alternation conditions, along with the one high repetition condition, all behaved ust as they should according to the information sis (if anythi g, Ss were somewhat too f.zst to these conditions, 1: scquen tial conditions s could be explained by the fact tha came late in the experiment). iscrepancies ir! Hyman’s experiment, then, cannot be inter T as a difference between high repetition and low repetitian, but rather as a special difficulty entaille by the non-repetition condition. A consts a sideration of the task dema s under the various conditions s conreason for the special difficulty. The conditions with se that, straints differ from the other conditions of yman’s experiment & trial, the su ective probability distribution on th;e possible on alternatives could change as a function of the receding stimu conditions with no sequential constraints, S faces the &samep distribution on the given alternatives in every trial. constraint requires S to keep track of the precedi trial. In addition to tl& memory I task, S has to generate I& subjective pro&&&y distribution for each new stimulus. the simpler the type of distribution, the easier it wil! this task. si The five sequenti 1 conditions with the 1
R. WYMAN AND C. uMII.Ti
52
periment all had these two features in common: (1) on each trial S was presented with a unimodal subjective probability distribution such while the that one alternative was always relatively highly pro’ remaining n- 1 alternatives had equal and relative y low probabilities of occurrence; and (2) the shifting mode was always easy ‘to trac tiaP (being either a repetition of the preceding stimuPus or re preceding stimulus by a simple spatial rule). The three no conditions, on the other hand, always confronted S with a distribution with n-1 modes dividing the probabili y space equally among themselves and on which the particular set vr-4 modes always shifted after every stimulus. These considerations suggest that, the initial difficulty that Ss in our resent experiment had with the non-repetition condition was not so much a matter of the proportion of repetitions or alternations, but rather the type of changing distribution on each trial and the ease of le to us that a repetition has an important status for ,wo reasons. One reason is that it represents a very easy way to keep track of the most probable response. Another reason is that there may be something inherent in n repetition, independent of S’s expectancies and strategies, that tends to facilitate the response, It also $ausibk that this latter factor may well be the more important con+ &nent in Kornblum’s situation, but before we could draw such a conclusior+,,we would want to see these factors of type of distribution, of kee~ping track of the more probable response, and pure repcIns unconfounded in Kornblum’s situation. 5.
C~N~.LUSI~NS hat
evidence we now have Tuvithrespect to choice reactio the infomation hypothesis, w h specifies equivalent the assumption that S can ii es profit from all1the information aivailable to him prior to each new signal, tends to be a closer and closer approximation to the empirical data as the conditions of respondthe ideal. As long as this tendency re:mains reasonable, en the information hypothesis can be used as a point of departure how S processes information by seeking to define the paramake a differeact between the situations under which the on hypothesis holds and those under which it does noit. As we ‘complicate’ the ideal condition, in the spirit of Donders’ corn-
IN
ATIONWYPQTHESI
AND NON-REPETITIONS - -’
53
ould hopefully discover a hierarchy of diffithat produce deviations from the equivalences esis. Some of these ty_pesof gested =- keeping track of the high probaw several eq 1 modes instead of one an alternation i mation hypothes s is to be abandon mature to do so on
ain of information.
Quart. .I. exp. Psychol. 4,
ulus information 85 a determinant of reaction time. J. exp. tion time for repetitions and non-repetitions: a nlnrmation hypothesis. In: Attention and per, m-w. A. F. Sanders (ed.), Acta Psychol. rial-choice reaction-time: inadequacies of the infornnation ,432---434.
ion time experiments and information theory. ondun. Butterworths. In: C. Chcrr;l (ed.), Mormation theory. 137---146. atical theory of communiSHANNON, C. E. and W. WEAVER, 1949. The mat cation. Urbana: Univ. of Illinois Press. The Rand Cor ration, 1955. A million random digits. Glencoe, Illinois: The Free Press.