PSYCHOLOGICAL SCIENCE

Research Report

THE LOSS OF POSITIONAL CERTAINTY INLONG-TERM MEMORY

James S. NairnePurdue University

Abstract—Long-term memory for se-quential position was examined follow-ing retention intervals that ranged from30 sec to 24 h. The Estes perturbationmodel (1972) is shown to provide a rea-sonable qualitative fit of the dynamics offorgetting, even though the model wasdesigned to account for the phenomenaof immediate memory. Similaritiesamong the forgetting processes ofshort-and long-term memory are considered.

In studies of immediate memory fororder, the ability to position an item cor-rectly in a short list declines rapidly withthe passage of time. After only a few sec-onds of distraction, subjects' responsedistributions resemble generalizationgradients anchored around the true serialpositions. Response likelihood peaks atthe correct position and declines gradu-ally as distance from the true value in-creases (Healy, 1974; Jahnke, Davis, &Bower, 1989; Lee & Estes, 1977, 1981;Shiffrin & Cook, 1978). Estes (1972) hascharacterized these functions, or uncer-tainty gradients, with equations of thefollowing form. The probability that anitem will be remembered as occupying aparticular interior position / at time n +1 is:

(e/2)X,- _(1)

where 6 is the probability that the sub-ject's position memory will undergo aperturbation and adopt a neighboring po-sition value. The net result is that sub-jects are likely initially to place items innearby positions when incorrect, butover time the position functions flattenand distant placements become morelikely. For items occupying the end-

Address correspondence to James S.Nairne, Department of Psychology, PurdueUniversity, 1364 Psychology Building, Room3152, West Lafayette, IN 47907-1364, E-mail:NAIRNElffiBRAZIL.PSYCH.PURDUE.EDU.

points of the position dimension (firstand last in the list), the equations areslightly different: for example.

Uncertainty about the endpoint valuesincreases more slowly because responseposition cannot perturb beyond the di-mension boundaries. In this case, betterperformance is found for the primacyand recency items and the serial positioncurve is generally bow-shaped.

In the initial application to immediatememory, perturbations in the mnemonicrepresentations of position were arguedto arise from the rehearsal-based recod-ings that are likely to occur throughoutthe retention interval (Cunningham,Healy, & Williams, 1984; Estes, 1972;Lee & Estes, 1977, 1981). However, re-cent work from this laboratory (Nairne,1990, 1991) has shown that the perturba-tion equations can apply to the loss ofposition information in general, even un-der conditions in which rehearsal-basedrecodings are unlikely to occur. Sub-jects in these experiments were asked tomake pleasantness ratings about fivewords in each of five lists. After a 10-mindistraction period, a surprise reconstruc-tion task was administered that requiredsubjects to place the rated items in theiroriginal positions of occurrence. The re-sulting serial position curves and posi-tional uncertainty gradients were fitquite well by the perturbation model,without any changes in its basic assump-tions, even though the retention wasclearly long-term.

The current report continues this ap-plication by examining the loss of posi-tional certainty across a variety of reten-tion intervals, ranging from 30 sec to 24h. In addition to providing basic data onthe forgetting of position informationover a time-course of hours, the intentwas again to make at least qualitativecomparisons with the predictions of theperturbation model. The forgetting func-

tion should show a characteristic form,and the uncertainty curves should re-semble generalization gradients that flat-ten with the passage of time.

METHOD

Subjects

The subjects were 144 undergradu-ates who participated for credit in an in-troductory psychology course. The ex-perimental sessions were conducted insmall groups.

Materials and Design

The experiment employed 25 words,arranged sequentially in five lists of fivewords. The stimulus items were me-dium- and high-frequency nouns, four tosix letters in length, taken from thePaivio, Yuille, and Madigan (1968)norms. Assignment of the words to listsand positions within lists was determinedrandomly by sampling without replace-ment from the overall pool of 25 words.All subjects received the same wordspresented in the same presentation or-ders. Retention interval was manipulatedbetween subjects; each retention groupcontained the same number of partici-pants (A = 24).

Procedure

Subjects were asked to make pleas-antness ratings on a scale ranging fromI (unpleasant) to 3 (pleasant) for eachof the 25 words as it was presented.The words were presented aloud on atape recorder and 2.5 sec separated theonset of each item. Each list of fivewords began with the word "ready" andended with a 5-sec blank interval. Sub-jects were not informed about the subse-quent retention test, nor were they givenany information about why the wordswere grouped in lists. They were simplyled to believe that they were participat-

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ing in a speeded ruting task. Subjectswioli: their ratings on a response sheetcontaining five rows of five bkmks; onerow was designated lor each list.

Following the rating task, subjects infive of the retention conditions were ex-cused and told to return at a designatedtime for further word ratings. The fiveretention groups were excused for 2, 4,6. 8, or 24 h. respectively. Subjects in thesixth retention condition were asked tocount backwards from 100, by writing onthe back of their rating sheet, for 30 sec.At the point of test, subjects in all con-ditions were handed a new responsesheet that once again contained five rowsof five blanks. Above each row of blankson the test sheet, however, the five ratedwords from a list were typed, but in anew random order. Everyone was toldthat each grouping of five words con-tained items that had been presented to-gether in a list; the task was to recon-struct the original order of presentationfor each list. As I have argued elsewhere(Nairne, 1990, 1991), reconstructiontasks of this type can be viewed as puretests of position, or possibly order, mem-ory because the critical items are madeavailable at the time of test.

RESULTS AND DISCUSSION

The predictions of the perturbationmodel were based on iterative applica-tions of Equations 1 and 2. Althoughthere are more sophisticated versions ofthis model (Healy, Fendrich, Cunning-ham, & Till, 1987; Lee & Estes, 1981).the earlier long-term data were fit quitwell by the simple version (Nairne,1991), so it seemed appropriate to con-tinue its use here. The perturbation rate,e, was set at 0.12 (based on inspection ofthe data), and the equations were appliedfive times to fit the 30-sec group and,thereafter, five times for every 2 h of re-tention interval. Thus, the equationswere applied 10, 15, 20, 25, and 65 timesfor the 2-, 4-, 6-, 8-, and 24-h delay con-ditions.

The Forgetting Curve

The data of primary interest, recon-struction performance as a function ofretention interval, are shown in Figure 1.The filled circles display subject perfor-

mance and represent the proportionscorrect averaged across the five serialpositions. The open circles show the pre-dictions of the perturbation model andalso were calculated by averaging perfor-mance across the five serial positions.The forgetting curve shows a character-istic, negatively accelerated form:Greater amounts of loss are seen early inthe function and performance reached alevel close to asymptote at about 8 h ofdelay. Of main interest, the function is fitquite well by the model except for the24-h condition, where subjects per-formed significantly better than pre-dicted.

The Uncertainty Gradients

A more detailed display of how per-formance varied as a function of serialposition is shown in Figure 2. The threerows of panels—depicting only the 30-sec, 4-h, and 24-h retention conditionsfor ease of comparison—show how posi-tion responses were distributed acrossserial position for each of the five pre-sented positions; for example, the firstpanel in the first row shows how oftensubjects in the shortest delay conditionplaced the first item in a hst in each ofthe five possible response positions. Theopen circles in each panel display thepredictions of the perturbation model,based on the same parameter valuesused in Figure I. Consistent with earlierwork (Nairne, 1991), the serial positioncurves were bow-shaped, and the re-sponse distributions resembled general-ization gradients anchored around thetrue presented positions. Subjects were

0 2 4 6 a 10 12 H IS ia 20 ; 2 24

Retention Interval (Hours)

Fig. 1. Overall proportion correct recon-struction performance, as a function ofretention interval, for subjects andmodel.

more likely to position an item correctlyif that item occurred first or last in a list(e.g., the first and last panel in a row);when an error occurred, subjects werelikely to place the item incorrectly in anearby position. Moreover, as predicted,with the passage of time the gradientsflattened and distant error placementsbecame more likely.

Qualitatively, it is clear that the per-turbation model captures the essentialtrends in the data quite well. Knowledgeabout temporal serial position is not all-or-none, but is better characterized as adistribution of positional uncertainty thatchanges systematically with delay. Inthis respect the present data mirror thepatterns of immediate memory, and sug-gest that similar mnemonic processesmay be operating in both the short- andlong-term cases. More problematic forthe perturbation model are the subjectdata at the longest retention interval (24h). The simple version of the model, rep-resented by Equations 1 and 2, predictsthat performance should approachchance at long delays. Clearly, subjectsin the present experiment were perform-ing better than expected after 24 h, andseem unlikely to approach chance per-formance in any reasonable time frame.

It is interesting to note that the per-turbation model also underpredicts per-formance at long distractor intervals inimmediate memory. Healy et al. (1987)found significantly better subject perfor-mance than expected at long distractorintervals (e.g., 60 sec), and proposedanother parameter to reflect more"permanent" retention of position. Al-though the psychological significance ofsuch a parameter is unclear in thepresent instance, it seems likely that amodified version of the model, along thelines proposed by Healy et al. (1987),would provide a better fit. A close exam-ination of the uncertainty gradients indi-cates that performance after 24 h was es-pecially good in the primacy portions ofthe list (relative to the model predic-tions), and this finding may ultimatelyprove to be of some importance.

The "Dating" Curves

Another way to represent the data ofFigure 2 is to plot the expected values ofthe position distributions for the subjects

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James S. Nairne

30 Seconds

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

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Fig. 2. The positional uncertainty gradients for each of the five serial positions after30 sec, 4h, and 24 h of delay. Each row of panels shows, consecutively, positions onethrough five. The closed circles represent the actual data; the open circles are thepredictions of the model.

and model. These data, for the samethree retention intervals, are shown inFigure 3, The left panel shows the sub-ject data; the right panel shows the per-turbation model predictions. In eachcase, the points can be compared to ide-alized performance where position re-

sponses match the actual presentationpositions. Analyzing performance in thisway is instructive because forward andbackward "telescoping" effects, whichare common in the assignment of datesto naturalistic events (Huttenlocher,Hedges, & Bradburn, 1990; Rubin &

2-

Data

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no

Modei

1 2 3 4

Serial Position1 2 3 4

Serial Position

Fig. 3. The expected values of the position response distributions for each serialposition. The solid lines in the left and right panels show idealized performance.

Baddeley, 1989), are displayed clearly.When assigning a date (position) to anitem that occurred early in a sequence,subjects (and model) tend to place theitem at a later position than its actual oc-currence; in other words, it is brought toa more recent point in time, mimickingthe way that a distant object is broughtcloser into view by a telescope. Thesame process operates in the opposite di-rection for items that occurred late in asequence. Subjects tend to place theseitems, on average, at earlier positions inthe list than those where they actuallyoccurred. Although robust, neither ofthese tendencies is particularly mysteri-ous; they arise as a consequence of thelist boundaries that prevent items fromdrifting to positions outside the list pre-sentation window.

DISCUSSION ANDCONCLUSIONS

The present experiment provides newdata on the forgetting of order, or posi-tion information, over a time course ofhours. The forgetting curve showed acharacteristic form, and the serial posi-tion curves and uncertainty gradients fol-lowed the qualitative patterns commonlyfound in studies of immediate retention.An immediate memory model, the per-turbation model of Estes (1972), pre-dicted the empirical trends quite welloverall, except for the longest retentioninterval. Because the dynamic propertiesof forgetting were explained adequatelyby the model, it appears that the previ-ous fits by Nairne (1991), who sampledonly one retention interval, cannot be at-tributed simply to an accessing of thefixed remnants of initial short-term mem-ory processing.

Still, although the descriptive aspectsof short- and long-term forgetting appearsimilar, it remains to be seen whether theperturbation model can adequately ex-plain both cases within a single applica-tion. For example, is there a single rulefor the application of 9 that will fit for-getting functions over seconds, minutes,and hours? To answer this question con-vincingly, data will need to be collectedthat allow for comparable comparisonsof order retention across the differenttime scales. At present, the proceduresused in delayed and immediate retention

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arc different, making direct comparisonsditlicult. In immediate memory experi-ments ol the type studied by Healy cl al.(1987) and Eslcs (1972), subjects ex-pected the order test and each list waslollowcd by an interfering distractortask. The current procedure used inci-dental learning and. with the exceptionof the 30-sec retention group, no imme-diate distractor task. It is reasonable toassume that a variety of factors, includ-ing intention and potential interference,might atTect the likelihood that the per-turbation process will occur.

Finally, these results provide supportfor some recent models dealing with thenaturalistic retention of occurrence in-formation (Huttenlocher et al., 1990; Ru-bin & Baddeley, 1989). In these cases,the pertinent data have been collectedfrom the dating of prior events (e.g., col-loquium topics, movies seen), with re-tention usually being assessed afterweeks or months. Despite the fact thatvery little control could be exercisedover the items, the sequences of occur-rence, or the exact retention intervals,these researchers have typically foundthat uncertainty about the date of occur-

rence (as measured by the absolute er-ror) increases regularly with elapsedtime, Vhe currenl data confirm thesetrends under the controlled conditions ofthe laboratory, and provide systematicanalyses of response distributions as afunction of sequential position.

Acknowledgments—I would like to thankCynthia Aguilar and Leo Woessner forheip in collecting the data.

REFERENCES

Cunningham, T,F,. Healy. A,F., & Wiiliams, D.M,(1984), Effects of repetition on short-term re-tention of order information. Journal of Exper-imental Psychology: Learning. Memory, andCognition.'10. 575-597,

Estes. W.K,, (1972), An associative basis for codingand organization in memory. In A,W, Meiton& E, Martin (Eds,), Coding processes in hu-man memory (pp. 161-190), Washington, DC:Winston.

Healy, A,F, (1974), Separating item from order in-formation in short-term memory. Journal ofVerbal Learning & Verbal Behavior. 13. 644—655,

Healy, A,F,, Fendrich, D,W,, Cunningham, T,F., &Tili. R,E, (1987), Effects of cuing on short-term retention of order information. Journal ofExperimental Psychology: Learning. Memory,and Cognition. 13. 413-425,

Hutteniocher. J., Hedges, L., & Bradburn. N.(1990). Reports of elapsed time: Bounding androunding processes in estimation. Journal ofExperimental Psychology: Learning. Memory,and Cognition. 16. i96~2l3.

Jahnke. J . C . Davis. S.T,. & Bower. R,E. 0989).Position and order information in recognitionmemory. Journal of Experimental Psychology:Learning. Memory, and Cognition, 15. 859-867.

Lee, C,L..& Estes, W,K. (1977). Order and positionin primary memory for letter strings. Journalof Verbal Learning &. Verbal Behavior. 16.395-118,

Lee. C L , , & Estes. W.K. (1981), Item and orderinformation in short-term memory: Evidencefor multilevel perturbation processes. Journalof Experimental Psychology. Human Learningand Memory. 7. 149-169.

Nairne. J.S, (1990). Similarity and long-term mem-ory for order. Journal of Memory and Lan-guage. 29. 733-746.

Nairne. J,S, (1991), Positional uncertainty in long-term memory. Memory & Cognition 19. 332-340,

Paivio. A.. Yuille. J C . & Madigan. S.A. (1968).Concreteness. imagery, and meaningfulnessvalues for 925 nouns. Journal of ExperimentalPsychology Monograph. 76 (1, Pt. 2),

Rubin, D C . & Baddeley. A.D. (1989). Telescopingis not time compression: A model of the datingof autobiographical events. Memory &. Cogni-tion. 17. 653-661.

Shiffrin, R.M.. & Cook. J.R. (1978), A model forshort-term item and order retention. Journal ofVerbal Learning and Verbal Behavior. 17.189-218,

(RECEIVED 4/17/91; REVISION ACCEPTED

7/8/91)

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