Output and retrieval interference in the missing-number task

Transcription

1 Memry &: Cgnitin (/), Output and retrieval interference in the missing-number task JEFFREY A. HADLEY and ALICE F. HEALY University f Clrad, Bulder, Clrad and BENNET B. MURDOCK University f Trnt, Trnt, Ontari, Canada Three experiments are reprted that represent a reexaminatin f the missing-number methd (Buschke, 1963b) f estimating shrt-term memry span. The missing-number task invlved presenting a randm sequence f all but ne f the numbers f a knwn reference set and asking subjects t identify the missing number. Experiment 1 intrduced a mdified missing-number task that included tw missing items and tw chices made by the subject. With a large decline in perfrmancefr the secnd chice relative t thefirst, it is pssiblethatnly the secnd chice was subject t utput r retrieval interference. An alternative explanatin is that subjects utput the number with the weakest memry representatin as their first respnse. By pstcuing subjects t reprt their tw chices in a frward r backward sequence, Experiment 2 prvided evidence against the imprtance f utput interference and supprt either fr the imprtance f retrieval interference r fr the "weakest-first" hypthesis. Hwever, with a paradigm that replaced nly crrectly identified missing numbers, a predictin that subjects wuld select the number with the weakest memry representatin as their first respnse was nt cnfirmed in Experiment 3. Instead, retrieval interference was implicated t explain the first-chice superirity fund in Experiments 1 and 3. The results were interpreted in terms f the TODAM mdel f Murdck (1982, 1987, in press). Researchers generally agree that the amunt f infrmatin that ne can retrieve in a memry span task is satisfactrily estimated by Miller's (1956) seven plus r minus tw "chunks." Fr example, when a "chunk" cnsisted f wrds adjacent in bth presentatin andrecall, Tulving and Patkau (1962) fund that subjects were nt able t utilize mre than seven "adptedchunks" at a time. Mre recently, Ericssn (1985) fund that withut the use f lng-term memry prcesses fr encding and retrieval, digit spans paralleled Miller's finding f abut seven items. Despite a digit span that reached trained levels f 84 fr 1 subject, when "meaningful encdings" (e.g., in terms frunning times, dates, r years) were prevented by increases in presentatin rate, r by the use f letters rather than numbers, his span drpped t the traditinal size f abut seven items. This research was supprted in part by United States Air Frce Human Resurces Labratry Cntract VE57~2-OO1 and United States Anny Research Institute Cntracts MDA K..Q155 and MDA9()3 9O-K-0066 t the Institute f Cgnitive Science at the University f Clrad, Bulder, and by the Natural Sciencesand Engineering Research Cuncil fcanada Grant APA 146 t the University ftrnt. We wish t thank Steve Wallace fr use f his cmputer labratry in these experimcnts and RbertCrwder,RbertGreene, MargaretIntns-Petersn, Stuart Klapp, Michael Humphreys, David Mitchell. and an annymus reviewer fr their cnstructive cmments n earlier versins f this manuscript. Requests fr reprints shuld be sent t Alice F. Healy, Department f Psychlgy, University f Clrad, Campus Bx 345, Bulder, CO Q345. The number f items that can be stred in immediate memry, thugh, remains a mystery. The effect f recalling an item n the recall f subsequent items. which Bradbent (1958) has labeled.. utput interference," is at the center f this dilemma. Nt nly can utput interference be used t explain the superirity fitems recalled first (see, e.g., Dalezman, 1976), it als serves t pint ut the inadequacies f methds that require retrieval f multiple items as a means f examining what is stred in memry. Despite the likelihd that ne cannt recall as much as can be stred, the use f multiple-retrieval methds (i.e. methds that require the retrieval f multiple items) is widespread in testing individual differences. Fr example, Thrndike, Hagen. and Sattler (1986) include bth frward and backward digit span tasks in a recent editin f the Stanfrd-Binet Intelligence Scale. Because the traditinal memry span estimate includes the inhibiting effects f retrieval and utput. it seems that a mre valid measure f memry strage wuld be valuable frm bth a theretical and an applied perspective. The missing-number task develped by Buschke (1963a, 1963b; see Klapp. Marshburn. & Lester, 1983, fr a mre recent use f this technique) was the result f ne imprtant attempt t vercme these prblems f retrieval and utput interference (ther techniques that achieve the same purpse include. e.g., the prbe methd; see Klapp & Netick, 1988). Buschke's technique invlved randmly presenting all but ne f the numbers fa knwn 69 Cpyright 1992 Psychnmic Sciety. Inc.

2 70 HADLEY, HEALY, AND MURDOCK set and asking subjects t identify the missing number. With nly ne respnse per trial, retrieval and utput interference were eliminated and a higher memry span estimate was prpsed. In his first study, Buschke (l963b) cmpared the retrieval-free estimates frm the missingnumber task with estimates frm a digit span task in which subjects recalled, regardless f rder, the presented numbers. He prvided 15 trials in each f six different cnditins that manipulated the range f numbers t be emplyed. He presented t all subjects 4, 6, 8, 10, 12, r 14 numbers and cntrasted the average number f trials crrect, depending n whether a missing number was reprted r whether all numbers had t be recalled. Utilizing a methd described in Wdwrth and Schlsberg (1954), Buschke (1963b) determined a stimulus threshld ver subjects fr each task, the means f which prvided the estimates fr the number f items retained. The resulting apprximatins yielded an average f 5.5 items retained fr the digit span and 8.6 items retained fr the missing-number task. This initial study cnfirmed the pssibility that the missing-number task prvides estimates f the strage characteristics f memry beynd thse limited by the inhibiting effects f retrieval and utput. In a fllw-up study, Buschke (l963a) applied the missing-number task t an investigatin f serial psitin effects. By examining the errrs f cmmissin that ccur when a previusly presented item is reprted as missing, ne can generate a serial errr curve. In this experiment, Buschke randmly presented 12 numbers frm the range f 1 t 13, ne f which was missing. The prbability f an errr acrss serial psitins ranged frm near zer at the 12th psitin t.15 at the 2nd and 4th psitins. Mst imprtant were the declining errr prbabilities that drpped frm the 6th t the 12th serial psitins. Althugh the develpment f the missing-number task was an imprtant accmplishment, this technique has been largely neglected in current memry research. The primary advantage fthe missing-number task was, accrding t Buschke (1963a), the fact that it eliminated the harmful effects f utput and retrieval. Because the inhibiting effect f recalling an item may be due either t the act f utput per se r t prcesses f retrieval prir t utput, we intrduce a distinctin in the present study between utput interference (i.e., respnse effects) and retrieval interference (i.e., prerespnse effects). Recently (see, e.g., Lewandwsky & Murdck, 1989; Mewhrt & Ppham, 1991; Reyna & Brainerd, 1989), the cncept futput interference has been used t accunt fr a range f imprtant memry phenmena. It has thus been shwn that utput and retrieval interference play crucial rles in the recall f presented items. But it is nt knwn hw (if at all) utput andretrieval interference wrk in the identificatin fmissing items. This questin has been ttally unexplred and at first sight might seem unanswerable. Hwever, the missing-number task culd be adapted fr the study f utput and retrieval interference effects by mdifying the standard retrieval-free methd develped by Buschke (1963a, 1963b). Specifically, ne way t study utput and retrieval interference wuld be t expand the missing-number technique t include mre than a single missing number. Fr example, in the case f tw missing numbers, the first respnse wuld be free f any effects f retrieval and utput interference, and any drp in perfrmance with the secnd respnse culd be attributed t interference created by retrieving and utputting the first item. There are cnsiderable data n the missing-ne task, but there are n data at all that we knw f n the missing-tw task. Althugh the missing-tw task may at first seem quite cntrived, it is related t numerus everyday situatins in which individuals try t determine which tw (r mre) items frm a list are missing frm a set. Fr example, a shpper ften tries t determine which items frm the grcery list are missing frm the set included in the shpping cart, and a teacher ften tries t determine which students frm the class are missing frm the set f thse present at an examinatin. Explratin f the missing-tw task shuld reveal interesting and imprtant evidence abut bth the prcesses invlved in identifying missing items and the interfering cnsequences f retrieval and utput. The present experiments were cnducted in rdert prvide such an explratin. In particular, the present study extended the missingnumber technique t the missing-tw task in rder t illuminate hw the identificatin f missing items might cme abut and t examine whether utput and retrieval interference play a rle in the identificatin f missing items as they d in the recall f presented items. EXPERIMENT I The first experiment was a simple extensin f the missing-ne task used by Buschke (1963a) t a case in which there were tw missing items. Methd Subjects. Thirty-six undergraduate students frm an intrductry psychlgy class at the University f Clrad participated in the experiment fr curse credit. They included 15 males and 21 females. Prcedures and Apparatus. Eleven numbers frm I t 13 were sequentially presented n a VT100 CRT screen at a I-sec rate, after which subjects rally reprted their chices fr the tw missing numbers. In additin, after each respnse, a keybard entry fr cmputer strage was made by the experimenter. The presented numbers were arranged in randm rder s that (1) n cnsecutive numbers were in sequence, (2) each number frm I t 13 ccurred fur times at each f the 11 serial psitins, and (3) all numbers served as ne f the missing numbers equally ften. Each sessin began with the subject reading the fllwing instructins: This experimentwill test yur ability t detect whichnambers are missing frm a set f eleven numbersfrm I t 13that will be individually shwn n this screen in a randm rder. Yur jb will be t reprt verbally which tw numbers were nt presented. There is n time limit thugh please reprt yur respnses as sn as yu are able. Once entered yu cannt change yur mind. When the instructins were understd, tw practice trials were perfrmed t familiarize the subject with the task, whereupn the testing began. Fifty-tw trials were given, with a 5-min break after 26 trials. The intertrial interval was 6 sec. A DEC PDP-II cm-

3 OUTPUT AND RETRIEVAL INTERFERENCE 71 Table 1 Percentage f Crrect Respnses fr First and Secnd Chices in Experiments 1 and 3 Chice Experiment First Secnd I puter was used t cntrl the experiment and prvide an utput f the raw data needed fr analysis. Design and analysis. Experiment I has a ttally within-subject design with chice (first and secnd). presentatin psitin (I-II). and actual number (1-13) as the independent variables. Tw sets f analyses were perfrmed. First. the percentages f crrect respnses were examined acrss each chice. Secnd. presentatin psitin and actual number were separately analyzed as a functin f chice fr errr (fcmmissin) frequency. Actual number was als analyzed with three additinal dependent measures: (I) an verall frequency measure (withut regard t whether crrect r incrrect), (2) the percentagef crrect respnses fr each number (given that it was used), and (3) an errr (f missin) frequency. Results The percentage f crrect respnses fr the first and secnd chices averaged ver subjects is presented in Table 1. A ne-factr analysis f variance (ANOV A) with chice (first and secnd) as the independent variable was highly significant [F(1,35) = 137.5, MS e = 56.1, p <.001]. Each subject shwed superir first-ehice perfrmance. The chice x presentatin psitin ANOVA fr errrs (f cmmissin) prduced main effects [F(1,35) = 140.2, MS e = 1.3, P <.001; F(lO,350) = 29.7, MS e = 2.9, P <.001, respectively] and an interactin [F(IO,350) = 2.5, MS e = 2.6, P =.O(m that were each highly significant. Figure I illustrates these results. Newman-Keuls pst hc tests revealed fewer first-chice errrs (fcmmissin) nly at the 5th, 8th, 9th, 10th, and l lth presentatin psitins. The errrs (fcmmissin) fr actual number shwed a strng main effect [F(12,420) = 4.0, MS e =.3, p <.001], as well as a significant interactin with chice F(12,420) = 4.7, MS e =.25,p <.001] (see Figure 2). The expected main effect f chice [F(1,35) = 148.3, MS e =.1, P <.001] was significant. These effects factual number can be best interpreted in terms f verall respnse frequency (regardless f accuracy). With a main effect f actual number [F(12,420) = 4.6, MS e = 2.3, p <.001] and an interactin with chice [F(12,420) = 7.6, MS e = 3.3, p <.001] (see Figure 3), verall frequency shwed a pattern f results similar t that fund with cmmissin errrs. That is, n the first chice, lwer numbers yielded mre errrs and greater verall frequencies, whereas n the secnd chice, higher numbers yielded mre errrs and greater verall frequencies. Cnsequently, given that a number was selected, the percentage f crrect respnses revealed n distinct advantages f any number. Figure 4 illustrates this result, in which the main effect factual number was significant [F(I2,420) = 2.7, MS e = I,1l9.5,p =.002], but a Newman-Keuls pst hc test failed t shw any significant paired cmparisns. In additin, the expected main effect f chice was repeated [F(1,35) = 74.7, MS e = 1,346.4, P <.001], and the chice x actual number interactin was ntsignificant[f(12,420) = l.l,p =.39]. Finally, the distributin fmissin errrs acrss the rdinal sequence is shwn in Figure 5. The main effect f actual number [F(12,420) = 3.7, MS e = 2.9, p <.001] was revealed in a Newman-Keuls pst hc test t be due primarily t the relative paucity ferrrs with the number I cmpared t all ther numbers. ' > "c "::l tt "u: e Ui c: 'iii.. 'E E >- " 3 c: " ::I tt "u: 2 iii :;; I ~ 5 c " ::l g 4 "= ~ 3 ~ c: iii.. 'E E ~ 1stChice ---&- 2nd Chice +--,---r-,-,--, ,--,-.--, , I 3 2 Presentatin _ tst Chice ---&- 2nd Chice +--,--r--,--,--,-,---, , ,--, I I Actual Psitin Figure I. Errr f cmmjssin frequency 8C1'OlI8 presentatin p0 sitin fr ftrst chke and secnd cbice In Experiment I. Actual Number Number Figure 2. Errr f cmmjssin frequency 8C1'OlI8 actual number fr ftrst chice and secnd chice In Experiment I. _ lstchice ---&- 2nd Chice +--,--, ,---r-, r---r-,--, II FIgure 3. OvenU frequency f actual number (crrect and incrrect respnses cmbined) fr ftrst chice and secnd chice In Experiment I.

4 72 HADLEY, HEALY, AND MURDOCK <; e C., 32 ;; Actual Number Figure 4. Percent8ge f crnet respliibes fr aetua1 number, given that it was reprted, fr ftrst chice and secnd chice in Experiment I... e "iii "e 1st Chice nd Chice O+-~r-l--,.---r--r..., ,...,,.., Actual Number Figure 5. Errr f missin frequency acrss actual number in Experiment I. Discussin In Experiment 1, we were able t examine the cmbined effects f utput and retrieval interference with the use f tw missing items and tw chices in the missingnumber task. If there are substantial effects f retrieval and utput interference, the percentage f crrect respnses shuld be greater fr the first than fr the secnd chice. Only the respnse fr the first chice shuld be free f the effects f utput and retrieval interference. In cntrast, the respnse fr the secnd chice shuld be liable t interference related t utputting the respnse fr the first chice. In fact, the percentage f crrect respnses was much higher fr the first chice (54.2) than fr the secnd chice (33.5), thereby dcumenting the large effects f utput and retrieval interference. In additin, large differences in the distributin f cmmissin errrs acrss presentatin psitin existed between first and secnd chices. Pirst-chice errrs were greatest at the early psitins and drpped steadily t near zer at the tw mst recent psitins. Secnd-ehice errrs als shwed a recency effect; they were similar in frequency t first-chice errrs at the early psitins but greater in frequency at the middle and end psitins. Ifthe retrieval prcesses invlved in respnding with the first missing item did nt interfere with the prcesses necessary t respnd with the secnd missing item, then bth chices shuld nt nly have resulted in equivalent percentages Experiment 1 examined the effects f retrieval and utput interference in the missing-numbertask. When asked t select tw missing numbers, subjects in Experiment I revealed inferir perfrmance n the secnd chice. Hwf crrect respnses but als have shwn similar patterns f frgetting acrss presentatin psitin. This utcme nt being fund, clear evidence fr the prblems assciated with retrievaland utput was demnstrated, and supprt was fund fr Buschke's (1963b) riginal prpsal that the higher estimates f memry span fund with the missing-number technique were due t an absence f retrieval and utput interference. Experiment I als prvided sme ther supprt fr these cnclusins with an analysis f actual number. Because f past findings that fewer errrs ccurred nearer the ends than the middle f the rdinal sequence (Buschke & Hinricks, 1968; Buschke & Lenn, 1969), researchers cncluded that presented items must have been perceived and encded in terms f an rdinal sequence (see als Madsen & Drucker, 1966). Experiment 1, thugh, culd nt supprt these cnclusins. Reliable changes in errr frequency did ccur acrss actual number (and differently fr first and secnd chices). But very similar changes als ccurred in the verall frequency f number use (when crrect respnses were cmbined with incrrect respnses). Accrding t this analysis, subjects tended t reprt as the first chice a number frm the beginning f the rdinal sequence and as the secnd chice a number frm the end f the rdinal sequence. Hwever, when reprted, n numbers had a reliable advantage t being crrect. In a similar result, an analysis f missin errrs als failed t agree with past research that shwed increasing errrs tward the middle f the rdinal sequence in this task. Because the numbers reprted as well as the numbers missed had little influence n the prbability f a crrect r an incrrect respnse, respectively, it seems dubtful that an encding strategy that fcused n rdinal sequence was respnsible fr the effects f actual number. Rather, these effects f actual number, which differed dramatically fr the first and secnd chices. seem attributable entirely t retrieval and utput factrs. Fr example, the retrieval prcess may include a search f the rdinal sequence frm lw t high. In summary, a lack f retrieval and utput interference may have been the primary cause f the large and cnsistent perfrmance differences fund frm first t secnd chice. In additin, an analysis f actual number als prvided evidencethat an encding strategy based n rdinal sequence may nt playadminant rle in determining first-chice perfrmance. Instead, the drp in perfrmance with the secnd chice strngly suggested that superir first-chice perfrmance reflected the number fitems ne can reprt when free frm retrieval and utput interference, reestablishing Buschke's (1963a. 1963b) missing-number prcedure as an ptimal methd f estimating the span f immediate memry. EXPERIMENT 2

5 OUTPUT AND RETRIEVAL INTERFERENCE 73 ever, an alternative explanatin fr this pattern f results is pssible. Rather than resulting frm retrieval and utput interference, the perfrmance change frm first t secnd chice may have been the result f subjects' simply using the best chice as the first respnse. In an rdinary freerecall task, the best chice wuld be the ne with the strngest memry representatin (but see Brainerd, Reyna, Hwe, & Kevershan, 1990). Hwever, in the missingnumber task, in which subjects respnd with the numbers nt presented n a trial, the best chice wuld be the ne with the weakest memry representatin. This "weakestfirst" hypthesis culd accunt fr the first-ehice superirity fund in Experiment 1. Experiment 2 was designed t check fr this pssibility. Subjects were pstcued t utput (but nt necessarily t retrieve) their tw chices in either a frward r a backward sequence, which frced them t divide the best respnses (i.e., the items with the weakest representatins) between first and secnd chices. Any remaining first-ehice superirity that might ccur with bth frward and backward reprt rders culd nly be due t difficulties assciated with utput per se. On the ther hand, a disappearance fthe perfrmance differences between first and secnd chices wuld supprt the weakest-first hypthesis and wuld rule ut an explanatin in terms f utput interference. (This finding wuld als be incnsistent with any explanatin invlving a lss f infrmatin as a functin f time.) At the same time, such a result wuld be cnsistent with an explanatin in terms f retrieval interference. Given that the retrieval prcess itself is insensitive t rdinal sequence, the necessity t utput the missing numbers in a prescribed rder wuld result in the first item retrieved reprted equally ften in the first and secnd psitins. Thus, a disappearance f the first-ehice superirity in bth frward and backward reprt rders wuld als be predicted by the retrieval interference explanatin. Therefre, this experiment might allw fr the separatin fthe effects f utput interference frm the effects fretrieval interference. Recall that in Experiment 1 the rder fthe tw chices selected by subjects did nt appear t be randm; rather, the first chice tended t be a lwer number than the secnd chice. Cntrary t the suggestin abve, this finding can be interpreted as cnsistent with a retrieval prcess that is sensitive t rdinal sequence (i.e., with a search fthe rdinal sequence frm lw t high). Given this pssibility, the retrieval interference explanatin wuld nw predict a first-ehice superirity with the frward reprt rder (in which retrieval rder parallels utput rder) but a secnd-ehice superirity with the backward reprt rder (in which retrieval rder is ppsite t utput rder). Furthermre, because the item with the weakest memry representatin wuld presumably be independent f the rdinal sequence (i.e., all numbers frm 1 t 13 ccurred equally ften as missing numbers), such a chice x reprt rder interactin wuld als rule ut the weakest-first hypthesis. In cntrast, ifn difference is fund between the tw reprt rders, evidence wuld be prvided that the subsequent utput prcess, rather than the retrieval prcess, was respnsible fr the subjects' tendency in Experiment 1 t reprt their tw chices frm lw t high. In ther wrds, subjects may retrieve the tw missing numbers in a manner that is independent ftheir relative psitins in the rdinal sequence, but after the tw numbers have been retrieved, they may utput them in numerical rder. Methd Subjects. Thirty-six undergraduate students frm an intrductry psychlgy class at the University f Clrad participated in Experiment 2 fr curse credit. They included 17 males and 19 females. Prcedure and Apparatus. Except fr the psteue fr the required reprt rder, all prcedures and apparatus were identical t thse emplyed in Experiment 1. One secnd afterthelast number in the presentatin, the wrds "FORWARD" r "BACKWARD" were flashed briefly t cue the subject. Design and analysis. Experiment 2 had a ttally within-subject design with chice (first and secnd), presentatin psitin (1-11), actual number (1-13), and rder f reprt (frward and backward) as the independent variables. Three sets f analyses were perfrmed. First, a chice x rder f reprt ANOVA was cnducted, with percentage f crrect respnses as the dependent variable. Secnd, a chice x presentatin psitin x rder f reprt ANOVA was perfrmed, with errr (fcmmissin) frequency as thedependent measure. Last, actual number was analyzed with tw dependent measures that were fund in Experiment 1 t prvide thebest means fcmparing perfrmance acrss rdinal psitins. First, success in reprting a particular number was determined, uncnfunded by hw many times that number had been attempted, and a chice x actual number ANOVA was cnducted with the percentage f crrect respnses (given that they were reprted) as thedependent measure. In additin, examinatin f hw many ccasins each number was verlked (when missing) resulted in an errr (f missin) frequency that prvided a secnd analysis f actual number. Results The percentage fcrrect respnses at each reprt rder fr the first and secnd chices averaged ver subjects is presented in Table 2. The tw-factr ANOVA n chice (first and secnd) and rder f reprt (frward and backward) revealed n maineffects r interactins. All F ratis were less than 1. The chice x presentatin psitin x rder f reprt ANOVA fr errrs (fcmmissin) prduced a main effect f presentatin psitin [F(1O,350) = 20.2, MS e = 1.3, p <.001]. Figure 6 illustrates this effect and the significant interactin between chice and presentatin psitin [F(1O,350) = 2.5, MS e = 1.4, p =.007]. Althugh a Newman-Keuls pst hc test allwed an interpretatin fthe main effect fpresentatin psitin as a steady drp in the errrs (f cmmissin) frm the 6th t 11th psi- Table 2 Percentage f Crrect Resp_ fr First and Secnd Chices at Each Reprt Order in Experiment 2 Reprt Order First Frward 41.9 Backward 42.5 Chice Secnd

6 74 HADLEY, HEALY, AND MURDOCK 20 :0- f.)., c: "a 15.,.>: e Ui I 0 c: 0 iii., 05 E E 0 U DO f.) 56 ~ 48 0 U 40 C 32.,., Q. ~ Presentatin Psitin ----tt--- 1st Chice nd Chice 1st Cn.ce nd Chice Figure 6. Errr 01cmmissin lrequency acrtl88 presentatin p0 sitin lr first chice and secnd cbice in Experiment 2., Actual Number Figure 7. Percentage 01crrectrespmes lr actual number, given that it was reprted, lr first chice and secnd chice in Experiment 2. :0 f.) c., "a ~ 4 U. E 3 Ui :s 2 iii.~ 1 O+--r , r-"-"T-r r , Actual Number Figure 8. Errr 01 missin lrequency acrss actual number in Experiment 2. tins, the significant interactin f chice and presentatin psitin was mre difficult t interpret. That is, althugh the interactin was apparently due t a cmbinatin f: (1) fewer first-chice errrs n the 1st, 10th, and 11th psitins, and (2) fewer secnd-ehice errrs n the 3rd and 8th psitins, nne f the paired cmparisns acrss chice at any f the presentatin psitins reached a.05 level f significance in Newman-Keuls pst hc tests. The main effects fr chice and rder f reprt, as well as all interactins with rder f reprt, were nnsignificant. The analysis f actual number fr percentages f crrect respnses (given that they were reprted) revealed a main effect [F(l2,420) = 12.3, MS e = 679.9, P <.001] and an interactin with chice [F(l2,420) = 6.2, MSe = 6OO.7,p <.001] (see Figure 7). The Newman Keuls pst hc tests shwed that: (1) the main effect f number ccurred as a result f superir perfrmance with the numbers 1 and 13, and (2) the chice X actual number interactin was due t the fact that the numbers 7 and 8 had superir first-ehice perfrmance, whereas the numbers 4 and 13 had superir secnd-ehice perfrmance. The distributin f missin errrs acrss rdinal psitin is shwn in Figure 8. In this case, the main effect f actual number [F(l2,420) = 4.4, MS e = 2.5, P <.001] was attributed. by means f a Newman-Keuls pst hc test, t the fact that the number 1 had fewer errrs than each f the numbers 4,6,7, 10, 11, and 12. Discussin It is clear that the practice f pstcuing subjects t reprt their tw chices in either a frward r a backward sequence was an effective means f distinguishing between an utput interference explanatin fr the superir firstchice perfrmance in Experiment 1, n the ne hand, and either a retrieval interference r a weakest-first explanatin, n the ther. That is, withut causing any main effects r interactins, this manipulatin had a strng effect n the relative perfrmances f first and secnd chices. Fr bth frward and backward reprt rders, the percentage f crrect respnses fr the first chice was equivalent t that fr the secnd chice. In additin, althugh the errr (f cmmissin) frequency acrss presentatin psitin was very different with each chice in Experiment 1, in Experiment 2 these differences between first- and secnd-ehice errrs were greatly diminished. Apparently, when subjects were frced t divide their best answers (as determined by either the weakest-first. r the retrieval interference accunt) between first and secnd chices, the difference between the tw chices was minimized. Hence, a perfrmance tradeff ccurred, and evidence against the utput interference explanatin fr the first-ehice superirity in Experiment 1 was fund. The present results suggest that the first-ehice superirity fund in Experiment 1 was due instead either t retrieval interference r t a weakest-first strategy (in which subjects rder their utput accrding t sme inverse functin f memrial strength). Althugh the subjects in Experiment 1 tended t reprt the tw missing numbers accrding t their rdinal sequence, the frward and backward reprt rders did nt yield perfrmance differences in Experiment 2. This finding is incnsistent with the suggestin frm Experiment 1 that the retrieval prcess includes a search f the rdinal sequence frm lw t high. The tendency t reprt the lwer number first in Experiment 1 must, therefre, have been a cnsequence f utput, rather than retrieval, factrs. That is, subjects may have retrieved the items in an rder that was independent f their psitins in the rdinal sequence, but they chse t utput them frm lw t high.

7 OUTPUT AND RETRIEVAL INTERFERENCE 75 Befre any definitive cnclusins can be made abut the weakest-first strategy, the pssibility f retrieval interference must be cnsidered. Althugh the paradigm used in Experiment 2 cntrlled fr utput rder, it culd nt cntrl fr retrieval rder and therefre failed t eliminate a retrieval interference explanatin fr the firstchice superirity fund in Experiment 1. Fr example, if the number retrieved first was t high r t lw fr a frward r backward reprt rder, respectively, it wuld likely have been withheld by the subject until a mre apprpriate (yet perhaps inferir) first chice culd be retrieved. Therefre, if a particular chice is better because it is retrieved first (as ppsed t being retrieved first because it is better), this task-related phenmenn in which utput rder wuld nt equal retrieval rdermay have been the cause fthe lack fdifference between first and secnd chices in Experiment 2. In ther wrds, althugh evidence was presented against the hypthesis that a first respnse culd be better simply because it was utput first, it remained pssible that a retrieval-based interference phenmenn might prvide an explanatin fr the first-ehice superirity fund in Experiment 1. Unfrtunately, thugh, due t an inability t bserve the prcess f retrieval per se directly, it seemed necessary t test the weakest-first hypthesis further. By returning t a cnstraint-free reprt rder (in which utput rder wuld be likely t cincide with retrieval rder), in Experiment 3 we attempted t prvide a mre refined explanatin fr the first-chice superirity fund in Experiment 1. EXPERIMENT 3 Experiment 3 tested the weakest-first hypthesis. Accrding t that hypthesis, when reprt rder is uncnstrained, subjects select as their first respnse the item with the weakest memry representatin. In a systematic replicatin f Experiment 1, the numbers presented n each trial were varied s that a manipulatin f memry strength r familiarity was pssible. Only the missing items that were crrectly identified were replaced, s that memry strength culd be judged by the number f cnsecutive trials n which an item had remained missing. In ther wrds, when a number is missing n the preceding trial, its memry representatin shuld be weaker than when it is presented n the preceding trial. Hence, cntrary t the situatin with the standard recall task, repetitin fa missing number shuld decrease, rather than increase, its memry strength. Supprt fr a weakest-first hypthesis requires three separate findings. First, a reestablishment f the perfrmance differences between first and secnd chices is necessary. Secnd, repetitin f missing numbers must be shwn t benefit perfrmance n the missing-number task. And third, any beneficial effects f repetitin must be weighted in favr f first-ehice perfrmance. Methd Subjects. Thirty-six undergraduate students frm an intrductry psychlgy class at the University f Clrad participated in Experiment 3 fr curse credit. They included 18 males and 18 females. Prcedure and Apparatus. As in Experiments 1 and numbers frm 1 t 13 were individually presented n a YTI CRT screen at a l-sec rate, after which subjects rally reprted their best chices fr the tw missing numbers. Althugh all task variables and instructins t the subject were identical t thse used in Experiment 1, the prcedures fr determining the missing numbers in each trial were unique t the present experiment. A prcess was carried ut in which unreprted missing numbers remained missing in subsequent trials; replacement f any missing number was nt made until it was reprted by the subject. Fr example, if 3 and 10 were missing and 8 and 10 were reprted. 3 and a randmly selected number (ther than 10) wuld be missing n the next trial. In additin, althugh all subjects perfrmed at least 52 trials, sme subjects required additinal trials t ensure that each number frm 1 t 13 was used as a replacement three times. As a result, althugh the ttal number f trials perfrmed ranged frm 52 t 63 (M = 53.1, SD = 3.0), the number ftrials that made pssible a meaningful analysis f actual number ranged frm 28 t 63 (M = 43.8, SD = 8.9). All ther dependent measures were based n the 52 trial scre used in previus experiments. Design and analysis. Experiment 3 hada ttally within-subject design with chice (first and secnd), presentatin psitin (1-11), actual number (1-13), and missing age (1-17) as independent variables. With the exceptin fthe changes instituted in Experiment 2 fr the analysis f actual number, all statistical adalyses used in Experiment 1 were perfrmed in Experiment 3. In additin, with missing-number "age" defined by hw many cnsecutive trials an item had been missing (missing numbers began with an age f 1 and gt "lder" with each trial n which they were nt chsen), several ther analyses described in the results sectin were included t determine theeffect f age n missing-numberperfrmance. Last, three analyses were cnducted t examine whether the lder (and weakest) item was mre likely t be selected n the first chice. By assigning an age f zer t presented items (i.e., cmmissin errrs), a ne-factr ANOYA with chice as the independent variable and respnse age as the dependent variable was pssible. Secnd, a ne-factr ANOYA was cmpleted with respnse age als as the dependent measure, but nly n trials n which bth chices were crrect. And third, nly trials with ne crrect respnse were cnsidered, s that an analysis was pssible that cmpared the age f the chsen number with the age f the verlked number in a tw-factr ANOYA that crssed chice (when crrect n the first chice and when crrect n the secnd chice) with missing number (reprted and nnreprted). Results The percentage f crrect respnses fr the first and secnd chices averaged ver subjects is presented in Table 1. A ne-factr ANOVA n chice yielded a highly significant effect, with superir first-ehice perfrmance n percentage fcrrect respnses [F(I,35) = 103.6, MS e = 59.3, p <.001]. The chice X presentatin psitin ANOVA fr errrs (fcmmissin) prduced main effects [F(1,35) = 107.2, MS e = 1.4, p <.001, and F(10,350) = 26.8, MS e = 2.6, p <.001, respectively] andan interactin [F(10,35O) = 3.1, MS e = 2.7, p =.001] that were each highly significant. Figure 9 illustrates these effects. A Newman Keuls pst hc test shwed: (1) a main effect f presentatin psitin, in which errrs remainedhigh andequivalent frm the 1st thrugh 5th psitins befre drpping steadily t near zer at the mst recent presentatin psitin, and (2) a chice X presentatin psitin interactin,

8 76 HADLEY, HEALY, AND MURDOCK ij c: ' "g 3 u: (; :: 2 w c ";;; '" I "E E U O+----,----.-,--~ r---r-,. r., Presentatin Psitin Figure 9. Errr f cmmissin frequency acrss presentatin p0 sitin fr first cbice and secnd chice in Experiment 3. U 60 e (; U 1: '" c Qj Q. > c '" u: '" C" - i st Cbice nd Cb.ce Figure 10. Percentage f crrect respnses fr actual number, given that it wasreprted, fr first cbice and secnd cbice in Experiment 3. c: ";;; "E '" +-...,..---r r r r--r.r-,--, Actual Number ~ isr Chice +-...,..-_._ r r---.--r--r.r--"' Actual Number 2nd Chice FIgure 11. Errr f missin frequency acrssactual number in Experiment 3. which was due t fewer first-ehice errrs at nly the 7th thrugh 10th psitins. The analysis f actual number fr percentage f crrect respnses revealed few distinct advantages f any number (given that it was chsen). Figure 10 illustrates this result, in which a main effect f actual number [F(l2,420) = 4.2, MSe = 622.9, p <.001] was interpreted by a Newman-Keuls pst hc test as a superirity fthe final number 13 ver the ther numbers. The chice x actual number interactin was nt significant[f(12,420) = 1.3, p =.20], althugh the main effect f chice was significant[f(1,35) = 98.1,MS e = 1,139.1,p <.001]. The distributin f missin errrs acrss the rdinal sequence is shwn in Figure 11. The main effect f actual number [F(I2,420) = 2.7, MSe = 12.4, P =.002] was shwn by a Newman-Keuls pst hc test t be due t a lack f errrs with the number 1 in cmparisn with all ther numbers. As a result f the replacement prcedures, the mean age difference between the tw missing alternatives n each trial was 1.9 and the standard deviatin was 1.0. Out f a ttal f 3,744 missing numbers used, 1,769 numbers were intrduced with an age f ne, 1,688 missing numbers were eventually reprted, and 81 were left unreprted at the cmpletin f the experimental sessin. Patterned after an analysis used by Murdck and Babick (1961), an expected frequency distributin acrss age, which wuld ccur if repetitin had n effect n perfrmance, was cmpared with an bserved frequency distributin in a chi-square gdness-f-fit test. That is, given that perfrmance was independent f all previus trials, the prbability f reprting a missing item (with p estimated frm the bserved mean age f a missing number) wuld equal p at the age f ne, p(1-p) at the age f tw, p(1_p)2 at the age f three, and thus, mre generally (with n as missing age), the gemetric distributin described by p (1 - P)"- 1. These expected prbabilities were multiplied by the ttal number f missing items reprted by all subjects, and the resulting gemetric distributin was tested against the btained distributin. Mre specifically, n the basis f the mean age f a missing number, p was estimated at.483, and this prprtin was used t predict hw the 1,688 crrect respnses wuld be distributed acrss missing age (if age had n effect n perfrmance). Fr example, the expected frequency f crrect respnses at the age f three wuld equal the ttal number f crrect respnses (1,688) multiplied by its expected prbabilityf a crrect respnse [.483 (1-.483)2 =.129] and thus wuld equal apprximately 218 crrect respnses. The btained and expected frequency distributins acrss missing age are presented in Table 3. Althugh the resulting chi-square gdness-f-fit was significant [x 1 (8, N = 36) = 16.25, P <.05], the differences between btained and expected frequency distributins did nt illustrate a beneficial effect f repetitin. Cntrary t Table 3 Observed and Expected Frequency Distributins f Crrect Respnses Acrss Missing Age Age Observed Expected ~ ~~ ,688 1,688

9 OUTPUT AND RETRIEVAL INTERFERENCE 77 a case in which crrect respnses ccur earlier than expected, the significant chi-square was due t several numbers that remained missing lnger than expected. Hwever, because this chi-square did nt emply independent bservatins (there were entries frm each subject at each age categry), the differences between expected and btained frequencies were als examined acrss subjects. A (btained minus expected) signed difference measure fr each subject was calculated at each age categry, and a series f independent ( tests were cnducted. Table 4 presents the r-test results at each missing age in which nly the age categries f 9, 11, and displayed btained minus expected mean differences that were significantly different frm zer. Whereas the significant chisquare seemed t suggest a serius discrepancy, an examinatin f these t tests revealed that the majrityfcrrect respnses were distributed acrss missing age in a very similar manner t what wuld be expected if repetitin had n effect n perfrmance. An additinal analysis that cmpared btained and expected frequency distributins was als taken frm Murdck and Babick's (1961) study. Because the average number ftrials necessary t make a crrect respnse f a missing number-assuming a gemetric distributinis equal t the reciprcal f the verall prbability f a crrect respnse (e.g., with a prbability f a crrect respnse f25 %, subjects wuld be expected t have an average f ne crrect respnse every fur attempts r a mean crrect age equal t 1/.25), a signed difference measure between btained and expected mean crrect ages was als examined in a ( test. A significant t test that displayed a mean difference measure significantly less than zer wuld supprt a beneficial effect f age n missingnumber perfrmance. Instead, hwever, althugh a tendency did exist in this directin (btained and expected mean crrect ages were 2.2 and 2.3, respectively), the ( test was nt significant [(35) = -1.1, p =.17]. The examinatin f missing age acrss chice yielded ne significant finding. Althugh respnse age did result Table 4 Observed Minus Expected Mean Differences in Crrect Frequency With Standard Errrs and t-test Results Presented at Each Missing Age Age *p <.05. M tp <.001. SE (35) t * lOt Table S Mean Age f Reprted and Nnreprted MJssina Numbers When Crrect Only n Either First r S«nd Cbk:e In Experlment3 Crrect Chice First Secnd Reprted Missing Number Nnreprted 1.l in a main effect f chice [F(1,35) = 30.8, MS e = 0.1, P <.001] in which first chice was lder than secnd chice (first and secnd chice mean respnse ages were 1.1 and.8, respectively), this utcme was prbably a simple cnsequence fthe fact that there were mre crrect respnses n the first chice, and it was nt necessarily related t a tendency by subjects t select the ldest item n the first respnse. As a result, when respnse age was examined nly fr trials n which bth chices were crrect, n maineffect fchice was fund [F{1,35) < 1], and the first chice tended t be yunger than the secnd chice (first and secnd chice mean respnse ages were 1.0 and 1.2, respectively). Similarly, n trials with nly ne crrect respnse, the examinatin f missing age in a chice (when crrectn the first chice and when crrect n the secnd chice) X missing number (reprted and nnreprted) ANOVA revealed n main effects [F(1,35) < 1 and F(1,35) = 2.8, p =.10, respectively] and n interactin [F(1,35) = 1.4, p =.24]. As shwn in Table 5, tw imprtant trends did emerge. First, the nnreprted missing number tended t be lder than the reprted missing number. And secnd, this finding tended t ccur primarily when subjects were crrect n the first chice rather than the secnd chice. Discussin The primary result frm Experiment 3 is that the replacement prcedure in which subjects were given as many trials as necessary t reprt each missing number failed t benefit perfrmance n themissing-number task. In fact, the cmparisn f the btained frequency distributin acrss missing age with the expected frequency distributin (assuming that repetitins did nt affect perfrmance) resulted in a significant chi-square gdness-f-fit in which several missing numbers were reprted laterthan expected. Hence, the repetitin f missing numbers actually appeared detrimental t perfrmance n the missingnumber task. At the same time, thugh, additinal analyses indicated that the majrity fcrrect respnses were distributed acrss missing age similarly t what wuld be expected if repetitin hadn effect n perfrmance. That is, ( tests perfrmed acrss subjects at each missing age resulted in significant mean differences between btained and expected frequencies at nly 3 f the 13 age categries. Mre imprtantly, up t and including the age f eight (where ver 99% fall crrect respnses ccurred), n significant t tests were fund. As a result, when the average number f trials necessary t reprt a missing item was cmparedwith an expectednumberfr each sub-

10 78 HADLEY, HEALY, AND MURDOCK ject, the mean difference was nt significantly different frm zer. Because perfrmance n any given trial was, then, essentially independent f the number f trials n which an item had remained missing, ne can cnclude that: (1) a best chice based n missing number age was nt used, and therefre (2) a weakest-first hypthesis in which subjects were biased t select the ldest number (r number with the weakest memry representatin) as their first respnse cannt accunt fr the first-ehice superirity fund in the present experiment. Additinal evidence against a weakest-first hypthesis was als generated by directly bserving the age f items selected fr first and secnd chices. Fr example, the strngest evidence was uncvered by nting that when nly ne respnse was crrect, the mean age fthe verlked number did nt significantly differ frm (and tended t be lder than) the mean age f the reprted number. Thus, it seems clear that missing-number success had little t d with the age r memry strength f missing numbers. In fact, because respnse age was als equivalent when bth chices were crrect (and tended t be yunger fr the first chice), whether the lder r yunger missing number was chsen first must be due t ther factrs. Althugh these results were cunter t the imprved shrt-term memry recall f repeated items that has been fund in many studies, even when the items were repeated acrss separate trials and subjects believed that prir lists were irrelevant t their perfrmance n a given list (e.g., Cunningham, Healy, & Williams, 1984; Hebb, 1961; Kintsch, 1965), studies with methds similar t thse used here als did nt yield a beneficial effect f repetitin. The study mst similar t urs was cnducted by Alan Bstrm and Grdn Bwer (G. H. Bwer, persnal cmmunicatin, May 12, 1988; see als Kimble, 1967, pp ). That study included a missing-ne experiment in which the same digit was kept missing until it was crrectly identified. Bstrm and Bwer examined whether the prbability f a crrect respnse was statinary and cnstant, and thus independent f the number f prir presentatins f a digit string t which the subject had respnded incrrectly. They fund reasnably cnstant, statinary crrect-respnse prbabilities fllwing 0, 1, 2, r 3 successive errrs n a digit string in which the rder fdigits varied but the missing digit was the same. Bstrm and Bwer cncluded that there was n accumulative incremental learning f the missing digits. In a well-knwn attempt t understand hw repetitin affects assciative learning, Rck (1957) similarly cncluded that the frmatin fassciatins culd nt be explained by a prcess f gradual strengthening as a functin f repetitin. In a task that required subjects t learn a list f 12 letter-number pairs (in Experiment 1), r 12 pairs f three-letter nnsense syllables (in Experiment 2), an experimental grup in which nly successfully cmpleted pairs were repeated n the next trial was cmpared with a cntrl grup. And, by discvering that the mean number f trials necessary t btain ne errrless trial did nt differ acrss grups, Rck reasned that the cntrl subjects must nt have benefited frm the repetitin fpairs in the initial frmatin fthe necessary assciatins. Despite an ften cited criticism that Rck's cnclusins were cnfunded by the pssibility that replacement f nly missed (and presumably mre difficult) assciatins prvided subjects an pprtunity t select easier tbe-learned items (see, e.g., Underwd, Rehula, & Keppel, 1962), several subsequent studies have nevertheless cntrlled fr this ptential cnfunding and in the prcess have cnfirmed Rck's cnclusins (Clark, Lancefrd, & Dallenbach, 1960; Estes, Hpkins, & Crthers, 1960; Rck & Heimer, 1959). Fr example, in a study that supprted Rck's cnclusin with a free-recall task, Murdck and Babick (1961) used a similar paradigm that avided cnfunding due t item difficulty. Of 25 wrds presented fr recall, ne critical wrd was repeated n as many trials as were necessary fr its recall, at which time a new critical wrd was intrduced in its place. Tw main findings demnstrated an inability f subjects t benefit frm repetitin. First, the prbabilities f recalling critical and nncritical wrds were nt significantly different. Secnd, a chi-square gdness-f-fit test that cmpared an btained distributin f crrect respnses at each repetitin with an expected gemetric distributin (assuming repetitin had n effect) was nt significant. Althugh the results frm Bstrm and Bwer, Rck (1957), and Murdck and Babick (1961) paralleled thse fthe present study, mre recently Murdck and Lamn (1988) have presented evidence that made a different set f cnclusins pssible. In a recgnitin learning paradigm in which recgnized wrds n ne trial were replaced n the next trial, the repetitin f unrecgnized wrds resulted in greater recgnitin (relative t recgnitin freplacement wrds) than did a cntrl cnditin in which n replacementtk place. Althughthese results cnflict with the research reviewed abve, this difference seems explainable in terms f task differences. Specifically, it seems pssible that the critical disparity existed in the predictin that was tested in each case. Whereas Murdck and Lamn upheld a predictin that repetitin wuld benefit perfrmance in a recgnitin task, in which the strngest r mst familiar items wuld be the crrect respnses, the present study failed t demnstrate that the ppsite predictin culd be sustained in a missingnumber task, in which the weakest r least familiar items wuld be the crrect respnses. Given the evidence cunter t a weakest-first hypthesis, what, then, caused the superir first-chice perfrmance? Because the results f the present experiment were nearly identical t thse f Experiment 1 (see Table 1), ne answer t this questin can be fund by returning t the cnclusins made in the first experiment. Nte that (1) the percentage fcrrect respnses drpped dramatically frm the first t the secnd chice, and (2) large differences between the distributins f cmmissin errrs acrss presentatin psitin existed frm the first t the secnd chice. These bservatins prvide evidence

11 OUTPUT AND RETRIEVAL INTERFERENCE 79 fr the prblems assciated with retrieval and supprt Buschke's (1963b) prpsal that the higher missingnumber estimates were due t an absence fthe detrimental effects fretrieval. Althugh it was shwn in Experiment 2 that the surce f these prblems assciated with retrieval was nt utput per se, neither Experiment 1 nr Experiment 2 culd rule ut retrieval prcesses prir t utput as a pssible surce finterference. Therefre, by prpsing a distinctin between utput interference and retrieval interference, ne culd explain a first-chice superirity in terms f retrieval prcesses. GENERAL DISCUSSION Summary The missing-number task was intrduced by Buschke (1963b) as a retrieval-free means festimating the capacity fshrt-term memry. With nly ne utput fthe missing number, Buschke claimed that an imprved estimate free frm the inhibiting effects f retrieval was pssible. The three experiments reprtedhere expanded upn Buschke's wrk by including tw missing numbers and tw chices n each trial. Large perfrmance differences between first and secnd chices in Experiment 1 were cnsistent with interference due t utput and retrieval. Experiment 2 intrduced the hypthesisthat subjects instead hadthe ability t access a single best chice that was based n an inverse functin f memry strength. When subjects were pstcued fr either a frward r a backward reprt rder, the predicted lss f first-chice superirity was fund. This finding supprts either the weakest-first hypthesis r an explanatin in terms f retrieval interference. The utput demands f Experiment 2 may have resulted in either the item with the weakest memry representatin (in accrd with the weakest-first explanatin) r the item that is retrieved first (in accrd with an explanatin in terms f retrieval interference) being reprted equally ften in the tw respnse psitins. The third and last experiment, then, resulted in the mst surprising fmdings. In an attempt t find new supprt fr a weakest-first hypthesis, we examined a predictin that subjects wuld select the item with the weakest memry representatin as the first chice. In a paradigm that manipulated memry strength by replacing nly crrectly identified missing numbers, a replicatin fthe first-chice superirity frm Experiment I culd nt be explained by a bias t select the missing numbers that had been missing the lngest. Mre imprtantly, because missing-number success was essentially independent f the number f trials n which an item had remained missing, evidence fr a weakestfirst hypthesis was clearly absent. And because utput interference was ruled ut as a cntributing factr in Experiment 2, nly the retrieval interference hypthesis survived all three experiments. Theretical Analysis Applicatin and tests fthe missing-number technique wuld be facilitated if we had a better understanding f the prcesses invlved. Hw is the missing-number task perfrmed? The answer requires a brader theretical framewrk r mdel. Currently, several cmpeting mdels are brad and general enugh t transcend specific experimental paradigms: the SAM mdel f Raaijrnakers and Shiffrin (Gillund & Shiffrin, 1984; Raaijmakers & Shiffrin, 1981; Shiffrin & Raaijrnakers, in press), the MINERVA mdel f Hintzrnan (1986, 1988), the TODAM mdel f Murdck (1982, 1987, in press), the CHARM mdel f Eich (1982, 1985), the matrix mdels f Andersn (1970), Pike (1984), and Humphreys, Bain, and Pike (1989), and varius cnnectinist mdels (Hintn & Andersn, 1981; McClelland & Rumelhart, 1981; Rumelhart & McClelland, 1982). It turns ut that there is a natural and simple accunt f the missing-number task in TODAM (Murdck, in press), and we will fcus n that. In any distributedmemry mdel, items are stred by superpsitin. In TODAM, fr instance, items are added t a cmmn memry vectr. Furthermre, a mdel such as TODAM needs a wrking memry (WM) t carry ut the assciative and retrieval peratins (e.g., cnvlutin andcrrelatin). Numbers frm a highly verlearned set, andthese are presumably stred in sme srt fa lexicn r semantic memry. Here is ne way in which the missing-number task culd be perfrmed. The instructins specify the reference set, s the requisite numbers (here, 1-13) are summed and a representatin is entered int ne fthe registers fwm. Then, as each list is presented, the numbers are summed and the result is placed in a secnd register f WM. At retrieval, the difference f these tw registers is entered int a third register, and in the present case, this difference cnstitutesa nisy versin fthe sum fthe tw missing numbers. The nise is an inherent prperty f any distributed-memry mdel; it can be minimized (e.g., by increasing the numberf elements in the item vectrs that represent the stimuli), but it cannt be eliminated. The nisy versin must be deblurred (i.e., interpreted) and mapped int tw separate items (the tw missing numbers), and a cnnectinist netwrk such as a Hpfield net (Hpfield, 1982) r the "brain-state-in-a-bx" (Andersn, Silverstein, Ritz, & Jnes, 1977) wuld be required t deblur a linear cmbinatin f tw respnses. This wuld nt be part fthe distributed-memry mdel per se, but a separate mdule fr the respnse stage (e.g., the R system in TODAM). Hw wuld such a view explain the results? In free chice (Experiments 1 and 3), by any reasnable deblurring scheme the number deblurred first wuld be mre accurate, s first chice shuld have fewer errrs than secnd chice. The disadvantage f being deblurred secnd can be viewed as the cause f what we have been calling retrieval interference. That is, the prcess used t deblur, r recver, the first missing number frm the third WM register may destry sme f the infrmatin needed t deblur the remaining missing number, thereby yielding missin errrs even when there is n frgetting fthe presented numbers. In frced chice (Experiment 2), mst f the time bth numbers wuld have t

12 80 HADLEY, HEALY, AND MURDOCK be deblurred befre either culd be reprted, but the first culd be stred in WM until the prcess is cmpleted. N utput interference wuld be expected because the task demands d nt exceed the capacity generally ascribed t WM (fur t five registers). The recency effect is mre prminent fr the first-ehice data than fr the secnd-ehice data because the later are nisier (due t the higher errr rate). The recency effect per se is a natural cnsequence f hw infrmatin is stred in (wrking) memry. TODAM uses the strage equatin frm the matched-filter mdel (Andersn, 1973); namely, Mj = exmj-1 + fj, where ex is the frgetting parameter, which prduces pure recency. (M is the memry vectr, here a register in WM, and fj wuld be the jth number in the sequence.) TODAM can thus accunt fr cmmissin errrs that are fund in bth the missing-ne and missing-tw tasks. Ifthere is sme frgetting f the presented items, nt all f them will be included in the secnd WM register. As an example, if (l) the reference set cnsists f the 13 numbers frm 1 t 13, (2) the set f numbers presented t the subjects in a missing-tw task cnsists fthe 11 numbers 3, 11, 12, 1,4,5,6, 13, 7,9, and 10 (i.e., the numbers 2 and 8 are missing), and (3) the number 9 is frgtten, then the secnd WM register wuld include a sum f the numbers 3, 11, 12, 1, 4, 5, 6, 13, 7, and 10. As a result, the third WM register wuld include a nisy versin f the sum f the numbers 2,8, and 9 (i.e., the tw missing numbers alng with ne f the presented numbers, which had been frgtten). A cmmissin errr wuld ccur if9, rather than2 r 8, were deblurred frm the third WM register. As mentined earlier, the prcesses in the respnse mdule (r R system) used t deblur the third WM register need t be delineated, and investigatins fthe missing-tw task shuld be helpful in prviding relevant evidence abut these prcesses. Fr example, the findings f Experiment 3 imply that memry strength is nt a factr relevant t the deblurring prcess. Furthermre, it may be illuminating in future research t manipulate the similarity f the items in the reference set alng varius dimensins, including the phnlgical and the visual. Bth the verall frequency f cmmissin errrs and the decline in perfrmance fr the secnd relative t the first chice shuld decrease if the deblurring prcess is facilitated by reducing the similarity f the items. Other than a respnse bias (nt explained by any fthe mdels), there is n effect f the actual number 'in the missing-tw task, and n reasn why there shuld be. There is n effect f repetitin in Experiment 3, because the prcess is ahistrical; that is, n each trial a new entry is stred in WM, and n cumulative recrd is kept. This explanatin prvides a qualitative accunt f the findings fthe present experiments but nt a quantitative accunt. Fr a quantitative accunt, ne wuld have t implement this descriptin in a particular distributed memry mdel with a particular respnse mdule and either estimate parameters r carry ut the necessary simulatins. Hwever, we shuld emphasize that nne f this is ad hc; all the requisite prcesses have been suggested (and implemented) befre. All that we are ding here is t cmbine them in a particular way t shw hw a missing-number task with tw missing numbers culd be perfrmed. It is nt strictly necessary t have a distributed-memry mdel. The MINERVA mdel f Hintzman (1988) des nt use superpsitin; but it is a glbal matching mdel (Humphreys, Pike, Bain, & Tehan, 1989), and it culd presumably d the same thing because the infrmatin is summed at the time f retrieval. It wuld be mre prblematic in the CHARM mdel f Eich (1985), because she uses autcnvlutin fr item vectrs; deblurring in the absence f partial cues wuld thus be mre difficult. The SAM mdel f Shiffrin and Raaijrnakers (in press) is a cmputatinal mdel, nt a prcess mdel, s further elabratin wuld be required t apply it t this particular task. Finally, the matrix mdels f Andersn (1970) and Humphreys, Bain, and Pike (1989) are designed mre fr the strage fassciative than fr the strage f item infrmatin, but because the latter nw includes item infrmatin as well, it t culd prbably be applied t the missing-number task. Accrding t ur explanatin, what we have called the "weakest" item wuld in fact be the strngest item when the presented set is subtracted frm the reference set. This is intuitively smewhat mre satisfying, because it is easier t imagine hw ne culd identify the strngest item than it is t imagine hw ne culd identify the weakest item. Finally, it shuld be pinted ut that this accunt shws hw an augmented versin f Buschke's (l963b) missingscan task culd be perfrmed withut any scan at all. Serial prcessing f tw sets f different sizes t identify the items missing frm the intersectin is awkward and clumsy at best. We prefer instead an accunt that is based n a distributed memry with a respnse mdule, and it seems t be cnsistent with the majr results frm the present experiments. Cnclusins The ptential imprtance f research with the missingtw task shuld nt be underestimated, fr several reasns. First, an understanding f the prcesses invlved in this task shuld prvide insight int the prcesses invlved in related tasks perfrmed utside the labratry; fr example, when a teacher administers an examinatin t students in a classrm (analgus t the presented set fitems), he r she determines which students are absent (the missing items) frm the class (the reference set). Secnd, the missing-tw task differs frm ther related labratry tasks, such as part-list cuing and single-prbe prcedures, because it uniquely islates the effects futputting ne item n the retrieval and utput f anther item. Fr example, the single-prbe prcedure des nt

13 OUTPUT AND RETRIEVAL INTERFERENCE 81 capture the interactins amng the recalled items and items still unrecalled r the interactins between unrecalled items. Third, this technique might prvide interesting insights int feeling-f-knwing judgments, because infrmatin is prvided abut which items are nt knwn, rather than abut which items are knwn, t have ccurred in a presented set. Finally, applicatin f the missing-tw task may be critical t the study f memry develpment. One f the mst stable findings in the develpmental literature is the imprvement f memry span. But t what degree this trend actually represents develpmental decreases in the effects f retrieval interference (rather than increases in strage capacity) is nt apparent (see Brainerd & Reyna, 1989, fr a related suggestin). Because it allws fr the examinatinf the effects f retrieving ne item n the retrieval f a subsequent item, the missing-tw task is a ptentially imprtant tl fr memry research. 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