RECALL OF PAIRED-ASSOCIATES AS A FUNCTION ! , 1

I OF OVERT AND COVERT REHEARSAL PROCEDURES I

BY

JOHN W . BRELSFORD, JR. and RICHARD C, ATKINSON

TECHNICAL REPORT NO. 114

July 21, 1967

PSYCHOLOGY SERIES

INSTITUTE FOR MATHEMATICAL STUDIES IN THE SOCIAL SCIENCES

STANFORD UNIVERSITY

STANFORD, CALIFORNIA

https://ntrs.nasa.gov/search.jsp?R=19670024957 2018-09-08T00:22:51+00:00Z

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lEm1cALREmTs PSYCHOLOGY SERIES

INSTITUTE FOR MATHEMATICAL STUDIES IN THE SOCIAL SCIENCES

t h l i Is rlro ,horn In pnntlmor.) (flaw d publlutlon sham In p n m h a n r I f plbllahd 11th Is d l h t fmm tltlc of Technlul R W ,

D. Davldson, S. Slrpcl, and P. Suppn. S a m exprlnnta nd dated theay on the muswmmt of utlllty ud rubjectln p& l l l tY . A U W l 15,

P. Supper. Note on computing al l optlnul rolutlona of a d w l llmu pwacnnlng poblem. Nwrrkr 15, 1955. 0. Oawidson and P. Supps. Experimental masucmnt of ul l l l ly by uac of a llmr p q m n l n g ndl . Apl l 2, 1956. ExPWlmncII Mlt d J

E. W. Adam and R. Fagot. A mcdol of rlsklesr cholcc. Augurt 7, 1956. ( f l eh~v la r~ l Sclonw, 1 9 5 9 , s 1-10) R. C. Atklnson. A comparlson of tbee models for a Humckys-type condltlonlng sltwtlon. Nwrlr)m 20, 1956. 0. Scott and P. Supper. Foundational aspect1 of theorln of masvcmnt . Ap l l 1, 1957. 0. Symbollc Lwlc , 1958, g, 113-128) M. Cnlach. Interval measurement of rublectlve nugnltuder with subllmlnal d l f fmncn . Aprll 17, 1957. R. C. Atkimon ~d P. Suppes. An rmlysls of two-pnon wme sllwtlom In tcmn of atatlatlwI Irmlng theory. Aplt 25, 1957. g. 3.

R. C. Atklnron and P. Suppes. An UyIysIr of a bo-#nm InUfacllon sitwtlon In turn d J urlrov psrrr. May 29, 1957. (In R. R. Bush

J. P o w and R. C. AtklMon. Dlawlmlmtion I r rn lng In J v h l condltlmlng sltwtlon. July 15, 1957. g. r p . hyckd. , 1958,

P. Supps and K. Wdsh. A non- t inu model f o r t h expr1mnt.i m a r v c m n t of utility. August 21, 1956. (8chJVIarJl Sclmw, 1959.4,

E. Adam ud S. Merrlck. An uionutlzation of Thmtone'r succoaslve Intervals and palnd compulrona scrllng modela. Sept.nkr 9, 1957.

R. F~got . An ordnrd metric model of lndlvldual cholw b r h ~ v l a . Septemb.r 12, 1957. U model far ordcnd metrlc lCJlln9 by CoCnPrl lon of

H. Rwden, P. Suppes, md K. WJtsh. A model far the exprlmental mearvrmnt of thr utillty of gambling. Srpt.nkr 25, 1957. (Ilrhvlml

P. Swims. Two fornul &Is far lnml plmlples. Nonmbrr 1, 1957. W. K. Earn and P. Suppr. F o ~ n d ~ t i ~ ~ of statlstlul lemlng theory, 1. Thr llrwrr model fm almplc Icmlng. No~rnkr 20, 1957. (Foundr-

1955. (Experimental test of the b u l c model, Chapter 2 In Ltecirlon-mklnp: & Expalnmtll A-h. Stanford Unlv. Resa, 1957)

linear pogammlng model, Chaptn 3 In Dcclaion-hlnp: E x p r l m n ~ l Approlch. S M c d ul lv . Pmr, 1957)

p,yckol., 1958.55, 369-378)

ud W. K. E a t n (EL.), Studlea In Mlthcnutlcal Lcmlng Themy. Stanford Unlv. h a , 1959. Pp. 65-75)

21-26)

204-2111

(An axlomtlc formulation and gcncrrllzation of succcsslve Intervals rcallng, Psychompika, 1958, g, 355-3681

Intervals. Paychomlrlka, 1 9 5 9 , z . 157-168)

- Sclence, 1959,& 11-18)

tlom of liner madela. In R. R. Bush and W. K. Estea Ed,.), Studlrr In MJthenullcrl L r m l n g Theory. Stanford Unlv. h a , 1959. Pp. 137-179)

D. Oavldron and J. k s h a k . Expwlmetrl tests of a stochastlc dcclslon thew. July 25, 1958. (In C. W. Chwchmn a d P. R J t m h (Ed¶.),

J. ~ m p c r t i and P. Suppcr. ChJhl of inflnite a r k n d their application to lemlng thrw. October 15, 1958. (P~cIf lc J c ~ d of M a t l m ~ t l c ~ ,

P. sums. A llnar l t m l n 9 model fa J contlnuum of mponaes. Dctobcr 18, 1958. On R. R. Bush ~ n d W. K. Earn (EL.), Sludlcr In

P. Supm. Mcrauemnt, cplr lcd meanlngfulnnr d thm-valwd lw lc . Dowmbrr 29, 1958. (In C. W i t Chwchnrn ud P. Ratoorh

P. o u p p s and R. C. Alklmon. Mukw Icmlng modela for multlperson tltutlm, 1. T h theory. F&wy 20, 1959. (Ch~plr 1 In

J. Linpcrtl Jnd p. Supper. s0m JSYmptotlC poprllcr d Luw'r boh leunlnp mcdol. Aprll 24, 1959. (PsychonWIkJ, 1960, E, 233-241) P. Suppas. Behavlorlstlc foudatlmr of utlllty. July 27, 1959. Ecmometrlu, 1961, 9, 186-202) p. SUPW and F. Knsne. Appl lu t lm of stlmulua smpllng theory to rltwtionr lnvolvlng rocld ~I~IUI. Sy.nbrr 10, 1959. (ha.

p. S U W . stimulus rlmPllng thew far a contlnuum of msponan. Scplembn 11, 1959. Qn K. Wow, 5. Kr l l n , ud P. S m (Lb.),

W. K. Eat., ud P. Suppas. Famd~tlons of rtatlatlul lemlng theory, II. n* stlmulus rmpllng modrl. Octobrr 22, 1959. P. Suppr, and R. C. Atklmon. M~rkov lemlng modolr for multlpmon rltwtlonr, II. Methodl ofrulyrlr. Docmbu 28, 1959. (ckp, 2

R. C. Atklmon. Thr Ute of &Is I n r x p r l d pychologr. May 24,1960. Oynthne, 1960, & 162-1711 R. C. Atklnron. A kmallutlm of atlmulus rmpl lng theory. Jum 14, 1960. (Psychomtrlka, 1 9 6 1 , 2 , 281-290) p. Suppr and J. M. Culsmlth. Expcrlmntal Jnrlyrlr of J duopoly rltwtlon hom the rMpolnt of nuthenrtlul l r m l n g theory. Junr 17, 1960.

G. b w . Rqmtlea ofthe one-elemnt moddar ap~l lod to prind-urocirtr Icmlng. J w 29, 1960. (Appllutlon of J modrl to paid-

kkouemenk Dcflnltlon a d Thearles. N s Yark: Wlley, 1959. Pp. 233-269)

1959, j.739-754)

- ---

Wknullul L c v n l w theory. Stanford Unlv. hi, 1959. Pp. 400-414)

(Eds.), Waaunment: Deflnltlon and Thorles. N s York: Wllry, 1959. Pp. 129-143)

Wov Lcmlng Modrlr for Multlpnon Interaction. Stanford Unlv. Press, 1960) -

k v . , 1961,=, 46-59)

Mathenvticil kthoda In thr SWIJI Scknws. Swford Univ. R r r , 1960. Pp. 348365)

In M ~ h v LHmlng Modrls far Multlpmon Intrrrtlons. Stanford Unlv. P m r , 1960)

Ontmutlbnal Ecmomlc Revls, 1962,2, 1-19)

u s o c l ~ h Iemlng, Paychomtrlka. 1 9 6 1 , 2 , 255-280) J. H. Blau. The comblnlnp of CIJSS~S condltlon in lrrrnlng theory. August 23, 1960. (See Tramfornullon of pobabll l t ln, R d l n p r dl&

A M . Math. Soc., 1961, 1,2, 511-5181 --- p. SUM. A compr)lrcm of the manlnv ~d uaes of modrlr In nuthenutlcs and the inplr lcal r c l m c n . August 25, 1960. (Synthnr, 1960,

p. Supper Jd J. Zlnms. Stochatlc lernlng thearla for J mpomc contlnuum wlth nondgtwmlm!a nlpfmcrmnt. Octobrr 25; 1960.

p. S U P p r Jnd R. Clnsberg. Appllcatldn of a rtlmulur smpllng model to.chlldmn's concept forni.tlon of b l N V numbers, wlth Jnd wllhout an

12, 287-301)

(PlyChOmlrlkJ, 1961,%, 373-390)

Overt CWeCtlon nsponre. h c c r b n 14, 1960. (Appllutlon of a rtlmulus sampling model to chlldnn'r concept formrtlon wlth mnd wlthout an overt cmcctlon response, JOWJI exp. Psychol, 1962, 2, 330-336)

(Continued on Inside back cover)

RECALL OF PAIRFD-ASSOCIATES AS A FUNCTION

OF OVERT AND COVERT REIBARSAL PROCEDURES

by

John W. Brels ford , Jr. and Richard C . Atkinson

?IECHNICAL REPORT NO. 114

' J u l y 21, 1967

PSYCHOLOGY SERIIZS

Reproduction i n Whole o r i n P a r t i s Permi t ted f o r

any Purpose of t h e United S t a t e s Government

INSTITbm FOR MATHEMATICAL STUDIES I N THE SOCIAL SCIENCES

STANFORD UNIVERSITY

STANFORD, CALIFORNIA

Abstract

The effect on memory of the mode of studying paired-associates

was investigated using a continuous-presentation technique.

rehearsal was found to be superior to covert study for all S s . Further-

more, the form of the forgetting curve was qualitatively different

for the two study procedures. The overt-rehearsal curve dropped

slowly at first and then very rapidly defining an S-shaped function,

whereas the curve for the covert-study condition decayed exponentially.

A mathematical model employing a short-term rehearsal buffer and a

long-term memory state accurately predicted the data obtained under

the two study conditions.

Overt

-

Recall of Paired-Associates as a Function

of Overt and Covert Rehearsal Procedures 1/

John W. Brelsford, Jr .y and Richard C . Atkinson Stanford University

I

In several recent experiments (Atkinson, Brelsford, and Shiffrin,

1967; Brelsford, Keller, Shiffrin, and Atkinson, 1966) short-term mem-

ory for paired-associates has been examined using a continuous-

presentation technique that provides for the efficient gathering of

large amounts of data under fairly homogeneous conditions. In these

experiments - Ss studied the paired-associate items in a covert manner

only, i.e., no overt verbalization of the stimulus-response pairs

occurred. It is of interest to determine whether performance in these

experiments is a function of the particular mode of study. The present

paper involves a within-subjects comparison of two types of study pro-

cedures, both using the continuous-presentation technique. On certain

blocks of trials - Ss studied covertly as in the earlier experiments, while on other trial blocks - Ss rehearsed overtly, vocalizing the

stimulus-response pairs as they were presented for study.

EXPERIMENT I

Method

Subjects. The - Ss were eight students from Stanford University who received $2 for each hour they participated in the experiment.

Each - S participated in eight l-hr- experimental sessions.

1

Apparatus. The experiment was conducted i n the Computer-Based

Learning Laboratory a t Stanford University.

t i o n of s t i m u l i , and response recording were ca r r i ed out by computer

programs running i n a modified PDP-1 computer under the con t ro l of a

time-sharing system. S t imul i were e l e c t r o n i c a l l y generated and d i s -

played on a cathode r ay tube (CRT) .

typewriter keyboard located immediately below the lower edge of the CRT.

S t imul i and Responses. The s t imu l i were s i x two-digit numbers

A l l programing, genera-

Responses were made on an e l e c t r i c

randomly se lec ted a t the beginning of each experimental sess ion from

the s e t of a l l two-digit numbers between 01 and 99. Once a s e t of

s t i m u l i was se l ec t ed f o r a given subjec t and sess ion , i t was used

throughout t h a t sess ion .

be t were used a s responses.

I n every sess ion the 26 l e t t e r s of the alpha-

Procedure. Each experimental sess ion l a s t e d fo r 200 t r i a l s and

was composed of four a l t e r n a t i n g 5 0 - t r i a l blocks of over t r ehea r sa l

t r i a l s ( c a l l e d 0 - t r i a l s ) and covert study t r i a l s ( ca l l ed C - t r i a l s ) . The i n i t i a l 5 0 - t r i a l block f o r each sess ion was randomly se lec ted

t o be e i t h e r an 0- or a C-block. A sess ion began with a s e r i e s of s i x

consecutive study t r i a l s ; one study t r i a l for each stimulus t o be used

during the se s s ion . The form of these i n i t i a l study t r ia l s depended

upon whether an 0- or a C-block had been se lec ted t o begin the sess ion .

I f t he sess ion was t o begin with a C-block, the word study appeared on

t h e upper f ace of the CRT on each i n i t i a l study t r i a l .

word study the re appeared one of t he s i x s t imu l i t o be used i n the

sess ion , along with a randomly se lec ted response. The S s had been

i n i t i a l l y in s t ruc t ed t o t ry t o remember, but not ove r t ly rehearse ,

Beneath the

-

2

the assoc ia t ion between the stimulus-response p a i r s t h a t appeared wi th

the word study., If the sess ion was t o begin with an 0-block, the word

rehearse appeared above t h e word study on each i n i t i a l study t r i a l .

Except f o r the word rehearse, 0 - t r i a l s were i d e n t i c a l t o t.he C - t r i a l s .

For these 0 - t r i a l s S had been ins t ruc ted t o say aloud the stimulus- - response p a i r twice while it was on t.he CRT f o r study; mrthermore, he

had been in s t ruc t ed t o pace himself so t h a t h i s verba l r ehea r sa l tended

t o f i l l t he time period of the stJudy t r i a l . Each of the s i x i n i t i a l

study t r i a l s l a s t e d f o r 3 sec. , with a 3-sec. i n t e r t r i a l i n t e r v a l ( I T I ) .

As soon as there had been one i n i t i a l study t r i a l for each of the s i x

s t i m u l i t o be used i n the session, the sess ion proper began,

Each of the 200 t r ia l s i n an experiments1 sess ion involved a

f ixed s e r i e s of events run of f in the following order :

t e s t appeared on the upper face of the CRT. &neath the word t e s t

a randomly se l ec t ed member o f t he 6-item stimulus s e t appeared.

- Ss had been i n s t r u c t e d t h a t , when the word - t e s t and a stimulus appeared

on the CRT, they were t o respond by pressing t h e appropriate key with

the l a s t response they had associated with t h a t stimulus, The t e s t

po r t ion of each t r i a l l a s t e d f o r 3 sec ,

f o r 2 sec. 3) The study por t ion of the t r i a l occurred. 4 ) A 3-sec.

I T 1 occurred ending the t r i a l .

1) The word

- The

2 ) The CRT was blacked out

J u s t as i n the i n i t i a l s t u d y t r i a l s , t he study periods were of

two types.

upper face of t he CRT f o r 3 see. Below the word study a stimulus-response

During blocks of C- t r i a l s , the word s tudy appeared on the

3

i

i .

pair appeared.

portion of the trial.

selected for the response set, with the stipulation that the response

be different from the immediately preceding response assigned to that

stimulus. The 0-blocks were identical to C-blocks except that on

0-trials the word rehearse appeared above the word study. The Ss

followed the rehearsal instructions as described earlier. There was

no break in the sequence of trials when switching from one study pro-

cedure to the other; thus items studied on the last few trials of an

0-block tended to be tested during the C-block and visa versa.

The stimulus was the same one used in the preceding test

The new response for that stimulus was randomly

-

The verbal responses of Ss on 0-trials were monitored by an elec- -

tronic intercommunication system. Because of warm-up and adaptation

effects, data from the first experimental session for each - S are not

presented. Data from the first 15 trials of each C- and 0-block were

also discarded since we are not interested in results for stimulus-

response pairs that were studied under one experimental condition and

tested on the other.

Results

In order to evaluate the over-all differences between overt and

covert procedures, the proportion of correct responses for each of the

experimental conditions was computed. Taking the average of these pro-

portions over - Ss, the mean probability of correct response is .74 for

the overt rehearsal condition and .58 for the covert study condition.

The difference between the two conditions is highly significant,

- t(7) = 4.05, E < .01.

4

I .

I - The number of t r ia ls intervening between study and t e s t on a given

stimulus-response p a i r w i l l be re fer red t o as the “ lag“ f o r t h a t pa i r .

Thus, i f the t e s t f o r a given p a i r occurs immediately following the study

period f o r t h a t p a i r , t he l a g i s 0.

both a t e s t and study on another stimulus i tem) , the l a g i s 1, and so on.

Since a l l of the stimulus-response p a i r s s tud ied during 0-blocks can be

considered as one experimental condition and those s tudied during

C-blocks as a separate condition, it i s poss ib le t o examine the propor-

t i o n of co r rec t responses f o r various lags under each experimental

condition

If one t r i a l intervenes (involving

Figure 1 presents the r e l a t i o n between study mode and the proba-

b i l i t y of a cor rec t response as a func t ion of lag . I n t h i s f i gu re each

po in t i s the mean proportion o f correct responses f o r the e igh t Ss. It

can be seen t h a t t h e two l a g curves a re q u a l i t a t i v e l y qu i t e d i f f e r e n t .

The over t r ehea r sa l curve drops slowly a t f i rs t and then very rap id ly ,

def in ing an S-shaped l ag f’unction, whereas the covert study curve drops

abrupt ly between l a g 0 and 1 and then decays exponentially. The curves

a re not displayed beyond l a g 13 since the re are too few observations.

EXPERIMENT I1

Met hod

Because of the r a t h e r dramatic d i f fe rences obtained i n Exp. I,

we decided t o r e p l i c a t e the study using a s l i g h t l y d i f f e r e n t procedure.

Exp. I1 was i d e n t i c a l t o Expo I i n a l l respec ts except f o r t he way the

s i x s t imu l i were chosen. A t t he s t a r t of the f i rs t experimental

s e s s ion a s e t of s i x consecutive two-digit numbers w a s randomly

5

. .

I - > c a a

0.

0

N

6

se lec ted f o r each S. These same numbers were then used as s t imu l i f o r

t h a t - S throughout the experiment.

s e l ec t ion procedure was introduced i n Exp. I1 t o maximize the - S ' s

f a m i l i a r i t y with the stimulus s e t . Di f fe ren t subjec ts were used i n

experiments I and 11.

Results

- This modification of the st imulus

As i n Exp. I, the proportion of cor rec t responses f o r each experi-

mental condition was computed.

of cor rec t responses i s -82 for the over t rehearsa l condition and .63

f o r the covert study condition. A s i n Exp. I, t h i s difference i s

Averaging over - Ss, the mean proport ion

highly s i g n i f i c a n t , - t ( 7 ) = 4.72, 13. < .01. It a l so should be noted t h a t

the proportion of cor rec t responses d i d not appear t o depend upon the

p a r t i c u l a r st imulus; i .e., i t was about the same f o r a l l s t imu l i i n -

dependent of t h e i r r e l a t i v e posi t ion i n the s e t of s i x consecutive

numbers . Figure 2 presents the l a g curves f o r Exp. 11. It can be seen t h a t

- they a re very similar t o those of Exp. I, except t h a t the proportion

of cor rec t responses a t a given lag i s t y p i c a l l y g rea t e r i n the second

expe r iment .

DISCUSS I O N

I n these experiments i t i s c l e a r t h a t the r e c a l l of a paired-

assoc ia te i tem depends upon the manner i n which it was rehearsed a t

t he time of study. It i s not surpr i s ing t h a t items ove r t ly rehearsed

a r e reca l led more o f t en than those t h a t a re covert ly studied. I f

nothing more, over t rehearsa l insures t h a t - S examines each stimulus-

response p a i r presented f o r study and rehearses it a t l e a s t twice

7

In the covert study situation there is the possibility that some items

when presented for study may not be rehearsed and may possibly even be

ignored. Of course, overt rehearsal could be detrimental to the extent

that verbalization of a particular stimulus-response pair might disrupt

a more general subvocal rehearsal scheme involving several items simul-

taneously. In the present case it appears that the advantages of overt

rehearsal outweigh any disadvantages of covert study, because, for every

- S, the overt rehearsal procedure proved superior. What is of more interest than the general finding that overt re-

hearsal is superior to covert study, is the specific interaction between

the study procedure and the lag between study and test. It is of inter-

est to determine whether this particular interaction can be predicted

within the context of any extant theory of memory. In recent theoreti-

cal formulations of short- and long-term memory, Atkinson and Shiffrin

(1965, 1967) and Atkinson, Brelsford, and Shiffrin (1967) Ljroposed a

model that is applicable to the present experiments.

The model assumes that data from studies of the type described here

may be characterized by a two-stage process involving a short-term mem-

ory state called the "rehearsal buffer" and a long-term storage state.

Since the experimental variables of interest involve only the rehearsal

buffer, all we need say about long-term store is that it is characterized

by the parameters 8 and Z, both of which are assumed to be the same

for our two experimental conditions.

The rehearsal buffer is represented as a constant-size, push-down

list that holds r stimulus-response items simultaneoiisly. Items are

kept alive in this list via rehearsal. Since there are only r items

9

in the buffer at any one the, we must specify the rules by which items

enter and leave the buffer. At the time a given stimulus-response item

is presented for study, its stimulus member may or may not already be in

the rehearsal buffer. If the stimulus is in the buffer, the new item

being studied will enter the buffer and replace the corresponding

stimulus-response item. If the item being studied is one whose stimulus

member is not currently in the buffer, then the new stimulus-response

item enters the buffer with probability a, and some item currently in

the buffer is knocked out. The value of the parameter 01 reflects the

probability of entering a new item into the buffer. For example, 01

may depend on the ease with which new items can be integrated into

on-going rehearsal schemes. If a particular set of items is easy to

rehearse, the subject may not want to break up the combination to insert

a new item. For the present experiments it is assumed that the overt-

rehearsal procedure will lead to an increase in the value of

compared to the covert procedure.

01 when

The model outlined here is the same one used by Atkinson, Brelsford,

and Shiffrin (1967) to provide an extremely accurate account of data from

a series of studies employing the covert-study procedure of the present

experiment.

data because of the pronounced S-shaped form of the lag curve.

increasing the value of CI will predict better performance in the

overt condition, the lag curve will have the form of an exponentially

decreasing function, which is clearly not found in the data. In order

to account for the S-shaped curve, we need to assume that in the overt

condition S tends to eliminate the oldest items from the buffer first.

10

However, this version of the model will not fit the overt

Although

-

I n the model f o r the covert case, a new item enter ing the buf fer is

sa id t o knock out a t random any item cur ren t ly i n the buf fer . It w i l l

be assumed f o r the overt case tha t an en ter ing item tends t o replace the

o ldes t i tem i n the bu f fe r , The probabi l i ty of eliminatin@; an i tem from

the buffer i s spec i f ied as follows: i f there a r e r items i n the buf fer

and they a r e numbered so t h a t item 1 i s the o ldes t and item r i s the

newest, then the probabi l i ty tha t an en ter ing i tem w i l l knock the j

item from the buffer i s

t h

[6(1 - 6)'-']/[1-(1 - 6)r] . This equation i s

derived from the following scheme: The o ldes t i tem i s knocked out wi th

p robab i l i t y 6 . I f i t i s not eliminated, then the next o ldes t i s

knocked out with probabi l i ty 6. The process continues c y c l i c a l l y

u n t i l an item i s f i n a l l y selected t o be knocked out . When 6 approaches

zero, the knockout p r o b a b i l i t i e s are random. When 6 i s g rea t e r than

zero there w i l l be a tendency for the o ldes t items t o be eliminated from

the buf fer f i r s t ; i n f a c t , i f 6 equals one, the o ldes t i tem w i l l

always be knocked out .

higher the value of 6

A s shown i n Atkinson and S h i f f r i n (1967), the

the grea te r the S-shaped e f f e c t predicted f o r

the l ag curve.

The model f o r the curves i n F igs . 1 and 2 i s therefore s t ruc tured

a s follows: The parameters r , 8 , and T w i l l be assumed t o be the

same f o r the covert and overt study conditions; the parameters Q! and

6 w i l l be assumed t o be affected by the experimental manipulation. To

be prec ise , i n the covert case a w i l l be estimated f r e e l y and 6 s e t

equal t o zero. I n the overt case a: w i l l be s e t equal t o one (which

means tha t every i tem en te r s the b u f f e r ) , and

f r e e l y .

8 w i l l be estimated

The parameter e s t i m a t e s y t h a t provide the bes t f i t t o the da ta

11

of Exp. I were r = 3, 8 = .97, and T = .go; for the covert condition

the estimate of a was .58 (with 6 -+ 0), and for the overt condition

the estimate of 6 was .63 (with a = 1.0) a The predictions for these

parameter values are shown in Fig. 1 as smooth curves. A corresponding

set of predictions was made for the data of Exp. I1 yielding r = 3 >

8 = 1.23, and T = .92; for the covert condition the estimate of

a was .63 (with 6 + 0) and for the overt condition the estimate of

6 was .51 (with a = 1.0) a The predictions generated by these parameter

values are presented in Fig. 2 as smooth curves. It can be seen that

in both experiments the model is doing a reasonably good job of account-

ing for these data.

We now wish to examine a few additional aspects of the data from

Exp. I. First we consider the "all-same" and "all-different" lag

curves. Figure 3 gives the "all-same" lag curves for the overt and

covert conditions. This curve gives the probability of a correct

response for an item when all of the intervening items (between its

study and test) have the same stimulus. Figure 3 also presents the

"all-different" lag curves.

a correct response to a given item when the other items intervening

between its study and test all involve different stimuli.

tions generated by the previous parameter values are given by the smooth

curves; they appear to be quite accurate.

This curve is the probability of making

The predic-

We now look for an effect that will be sharply dependent upon the

value of a and hence differ for the overt and covert conditions.

Such an effect is given in Fig. 4.

a correct response to the last stimulus-response pair studied in a series

Graphed there is the probability of

12

I- z w w Ir, Ir, D J J

a

- I

a

id

: !i 0

R

R 8

iJ 0

0

cd

Q

M

of consecutive t r i a l s involving the same stimulus; the p robab i l i t y

cor rec t i s lumped over a l l possible l ags a t which t h a t stimulus-response

p a i r i s subsequently t e s t ed . This p robab i l i t y i s graphed as a func t ion

of the length of the consecutive run of t r i a l s with the same stimulus.

For example, if the study of i t e m 42-B i s preceded by th ree consecutive

t r i a l s using stimulus 42 (but d i f f e r e n t responses), then what i s being

p lo t t ed on the ordinate i s the p robab i l i t y of giving response B t o 42

when it i s eventua l ly t e s t e d and on t h e absc issa "three preceding items

with the same stimulus." If a i s l e s s than one, then the l eng th of

the preceding sequence of items with the same stimulus w i l l be an impor-

t a n t var iab le . Since any item i n the sequence which e n t e r s t he buf fer

w i l l cause every succeeding item i n t he sequence t o e n t e r t he buf fer , t he

p robab i l i t y t h a t t h e item i n question e n t e r s the bu f fe r w i l l approach

one as the length of the preceding sequence of items a l l using the same

stimulus increases . For a! equal t o one (ove r t condi t ion) , every item

e n t e r s t he bu f fe r and therefore no change would be expected.

i n Fig. 4, the da t a and theory are i n good agreement. The s l i g h t r i s e

i n t h e da t a po in t s f o r the over t condition may ind ica t e t h a t an estimate

of 0 s l i g h t l y below 1.0 would improve the pred ic t ions , but t he f i t as

it stands seems adequate. Because o f space l i m i t a t i o n we have not

presented observed and t h e o r e t i c a l values comparable t o those i n Figs.

3 and 4 f o r Exp. 11. However, such analyses have been made, and the

t h e o r e t i c a l f i t s a re as good a s those obtained i n Exp. 1.-

A s ind ica ted

4/

It should be noted t h a t t h e t h e o r e t i c a l curves presented i n Figs.

3 and 4 do not involve new parameter estimates. The parameters used i n

generating these curves were the same ones used t o f i t t he da t a of Fig. 1.

14

+ U w > 0

03 k CD In * ro <u

3SNOdS3kl 133klkl03 V A 0 A1111HVHOkld

1 -

m d

+J V

k

cd m (d

a, m r= 0

a, k +J V a, k k 0 V

(d

k 0

m a, d +I, .rl

4

d % % k R rl cd c!

- r i +J a, k 0 a, A +J a d cd

z c g a, m

A-

5 bD Ti Fr

The close correspondence between the predicted and observed r e s u l t s

provides s t rong support f o r the model. I n our view the assumptions

j u s t i f i e d most s t rongly appear t o be the fixed-si.ze rehearsa l buffer

and the replacement assumptions governing the e n t r y of new items i n t o

the buffer. It i s d i f f i c u l t t o imagine a cons is ten t system without

these assumptions t h a t would give r i s e t o s imi l a r e f f e c t s . Some of the

predict ions supported by the data a re not a t a l l i n t u i t i v e . For example,

the phenomenon displayed i n Fig. 4 seems t o be contrary t o pred ic t ions

based upon considerations of negative t r ans fe r . Negative t r a n s f e r would

seem t o pred ic t t h a t a sequence of items having the same stimulus but

d i f f e r e n t responses would lead t o l a rge amounts of in te r fe rence and

hence reduce the p robab i l i t y of a cor rec t response t o the l as t item i n

the sequence. However, j u s t the opposite e f f e c t was found i n the covert-

study condition. Furthermore, the lack o f an e f f e c t i n the overt-study

condi t ion seems t o ru l e out explanations based on successive cor rec t

responses or successive zero-lag t e s t s . I n t u i t i o n notwithstanding,

t h i s e f f e c t was predicted by the model.

16

Footnote s

'This research was supported by the National Aeronautics and Space

Administration, Grant No. NGR-05-020-036, and by U. S. Public Health

Service Grant No. Usp~s-MH-6154.

'NOW a t Yale University.

3The estimation procedure uses a minimum chi-square method and i s

described i n Atkinson, Brelsford, and S h i f f r i n (1967).

The de r iva t ion of the t h e o r e t i c a l functions presented i n Figs. 4

3 and 4 a re given i n Atkinson and S h i f f r i n (1967).

i . . '

Re f e re nce s

Atkinson, R. C . , Brelsford, J. W . , and S h i f f r i n , R. M. Multi-process

models f o r memory with appl icat ions t o a continuous presentat ion

task. J . Math. Psychol., 1967, 4, 277-300. - - - Atkinson, R. C . , and S h i f f r i n , R. M. Mathematical models f o r memory

and learning. Tech. Rep. 79, I n s t i t u t e f o r Mathematical Studies

i n the Socia l Sciences, Stanford University, 1965. (To be

published i n D. P. Kimble (Ed.) Proceedings --- of the t h i r d conference

- on learning, remembering - and forge t t ing .

Academy of Science.)

New York: New York

Atkinson, R. C . , and S h i f f r i n , R. M. Human memory: a proposed system

and i t s cont ro l processes. Tech. Rep. 110, I n s t i t u t e for Mathe-

mat ica l Studies i n the Social Sciences, Stanford University, 1967

(To be published i n K. W. Spence and J. T. Spence (Eds.) - The

psychology of learning - and motivation: advances i n research - and - theory, Vol. 2. New York: Academic Press . )

Brelsford, J . W . , Jr., Kel le r , L., S h i f f r i n , R. M., and Atkinson, R. C.

Short-term r e c a l l of paired-associates as a function of the number '

of in te rpola ted pa i r s . Psychon. - Sci . , 1966, 2 , 73-74.

18

c ,

Figure Captions

Figure 1. Observed and theo re t i ca l p robab i l i t i e s of a cor rec t response

as a funct ion of l a g (Experiment I)

Figure 2. Observed and theo re t i ca l p robab i l i t i e s of a cor rec t response

as a function of l a g (Experiment 11)

Figure 3. Observed and theo re t i ca l p robab i l i t i e s of a cor rec t response

as a function o f l a g for the "all-same" and "a l l -d i f f e ren t "

conditions e

Figure 4. Observed and theo re t i ca l p robab i l i t i e s o f a co r rec t response

as a function of the number of consecutive preceding items

a l l using the same stimulus.

(Cmtinud fran lnsldr fmt covrc)

G. H. Bqy. Rmrpnr strength4 and c h d u p&&llltyc A comldmtlon of two combirutla dr. Dowdw 19,1960. On E. -1, P. Suppc, and A. T n k l (E*.), m, Methodoloqy and Phllaophy of Solma: Rocm(l~?## of the 1960 lntrmtlonrl bnqmr. Sword Unlv. h s , 19621 Pp. 400410

G. H. Ban. Appliutlon of the all-a-nonr condltlonlng modo1 to UW Irmln( d canpard mparrr. J u n 7,1961. P. Suppn a d H. Schlrg-Rry. T r t of some lounlng modo11 forddouble cmtlfW8nt n l n f o n m n t . Aupust 15, 1961. (Plshol. Re&, 1962, P. Suppr and R. Glmkg. A f u d r m n l r l m r t y of dl-or-non dr l r , blnomlrl dlrtflbutlon d m m r pia to condltlonlnp, with

J. Theia. A thred-slu Mukw model f a Iemlng. Semmbrr 22,1961. (Slmplr cadltionlng a8 two-rrr9al l-a-non lomino, p,vchd. .

G. H. Ban. G m l thm-st r te Mrkw lcrmingmodelr. September 26, 1961. R. C. Atkins&. A variable threshold model f a slepl detection. Nmnbcr 17, 1961. R. C. Atkimon. Whemat iu l models i n m a r c h on mwption a d Iemlng. Chccnkr 25, 1961, 00 Y. H. Mrx Ed.), Thra(r in

P. Suppr. l a r d s a behavlaal foundation of mathcmttiul p O f s . January 2, 1962. On K. Aldukicrricz Ed.), The F a m d 8 t l a of

appllatlon toconwpt fmnrlion In c h l l h n . Srplnbrr 20, 1961. (ptychol. Rev., 1963,2, 139-161)

k v . , 1963, E, 403-417)

Comtemparuy Psychofogy. New York: Macmillm Co.. 1963. Pp. 551-564)

Statements and Decisions: Pmcwdings of the Intmutional Colloquium on Mcthodolopy of Sciences, Stptenkr 18-23, 1961. W r r z w a : --- __I-----

PWN-Pdish Sclmtiflc Publishers, 1965. Pp. 327-3411 P. Suppr and J. L. Zinns. Basic measwment h a y . March 15,1962. (Chapter I in R. R. b h , E. H. GrlunCr, and R. D. Lucc Eds.),

R. C. Atkinson. E. C. Carterette, and R. A. Kinchla. Sequential phenomena in prychophyslcrl judgments: a themtlcal atU~ysls. Apll 20,

R. C. Atkinson. A variable sensitivity theory of signal detection. May 18, 1962. (Pe l .& . , 1963,=, 91-106) R. C. Atkimon and W. K. Estes. Stimulus sampling theory. July 1,1962. (Chaptar 10 in R. R. h h , G. H. QIatef, and R. D. Luce

P. Supen, E. Cmum, R. Weir, and E. Tnger. Some quantitative stdies of Russian c a m t phmon*disalmlnrtla. Wrkr 14, 1962. R. C. Atklmon ud R. C. Calfee. Mathenutical leaminq theory. January 2, 1963. Qn 6. B. Wdmn Qd.), SchntlfIc Psydbdq. Mew Yo&:

P. Supen, E. Crothcn, and R. Weir. Appllc8tlon of Mthematlul Iemlnp h W y md flngUlStlC ~ 1 ~ 1 1 to -1 phor*llS mlching i n

R. C. Atklmon, R. Calfee, C. Sonmer, W. Jeffrey md R. Shamkw. A &st of t h e models fs/rtlmulus cOllp0cndlqrlt)l chlldnn. J m 29,

E. Cmthwt. General Markov models for learning with intar-trlal forgetting. April 8, 1963. J. L. Mycn and R. C. Atklnson. Choice behavior and mad structm. May 24, 1963. Uamrl mth. plydd., 1M, 1, 170-203) R. E. Robinson. A set-theoretical approach to empirical meaningfulms of m.rvrmnt statanmtr. Jum 10. 1963. E. Crothers, R. Weir and P. Palmer. The role of tramulption In the leming of the orlhooRphic nprrmtrtlmr of Russ i r s o d s . J u r 17, 1963. P. Suppes. Problems of optimlzation in learning a l ist of simple Item. July 22, 1963. On M;*lrrd W. Shelly, 11 and Glmo L. Bryan E&.),

R. C. Atklmon and E. J. Crothers. Themtical note: all-or-none learning and lntcrtrld forpcttlng. July 24, 1963. R. C. Calfee. Long-term behavior of rats under pobabiiistic reinforcement schedules. October 1, 1963. R. C. Atkimon and E. J. Crothers. Tests of acquisition and retention, a x i o m f a paired-assoclate Iemlng. Dctobrr 25, 1963. U canputson

W. J. McGlll ud J. Gibbon. The genealllamma distribution and reaction t lms. November 20, 1963. 0. math. Psychol., 1965, & 1-18) M. F. Ikmn. lncnmental learning onrndomtrials. Dccenlbt, 9, 1963. U_. math. Psychol., 1964,I, 336-351) P. S t w m . n* kv r lopmnt of mathematical concepts in children. February 25, 1964. (On the behavlml foundations of n t h e m t i u l concepts.

Handbook OF Mathematical Psychology, Vol. 1. New Yak: J h Wlley, 1963)

1962. (Institute of Radio E n g i m Transactions on Infamation Theory, 1962, E, S 155-162)

--

E&.), Handbook of Mathematical Psychology, Voi. 11. New York: Wiley, 1963)

B..lc Bocks, Inc., 1965. Pp. 254-275)

RI ISS~MWW~S. December 28, 1962.

1963. g. exp. Psychd., 1964, z, 52-58)

H m n Judpnnb and Optlmallty. New York: Wlley. 1964. Pp. 116-126) -

of paid-asrociate learning models having different acquisltlon and retention axionu,.J. math. Psychol., 1964, 1, 285-315)

'37 38 39

40

. 41 42 43

44

45

46

47 48

49 50

5 1

52

53 54 55 56 57

58 59 60

61 62 63

Monslphr of the Soclety for Resrrch in Child Development, 1965,*, 60-96) b4 65

P. Suppn. Mathemtical concept formation in chlldren. Apt1 10, 1964. (Am. Psychologist, 1966, c, 139-1501 R. C. Calfi., R. C. Atkinson, and 1. Shelton, Jr. Mathemtlcal models for vabal learning. August 21, 1964. an N. Wiener and J. P. Schodr

Ed#.), Cybumtlct of the Nervous System: Propess in Brain Research. Amstenlam, Thc Netherlands: E l l c v i a Pllbllshing Co., 1965. 4.333-349)

L. K d l r , Y. Cde, C. J. Bvke, and W. K. Estes. Paired associate leamlng with differential mads. August 20, 1964. (Reward and infmmtion values of trlal outcomes In paired associate Ieming. (Psychd. Moncqr., 1965,2, 1-21)

M. F. N-. A pohbllistlc model for Free-mponding. Decembw 14, 1964. W. K. Estn md H. A. Taylor. Visual detection In relation to display size and redundancy of ultlcal elements. January 25, 1965, Revised

P. Suppn nd J. Donlo. Foundations of stlmulus-sampllng theory f a continuous-tlm pocessa. February 9, 1965.

66

67 68

69 7-165. (Percepion and Psychophysics, 1966, i, 9-16]

70 A. C. Atkimon and R. A. Kinchla. A learning model f a forced-cholce detectlon expeflments. Febrwvy 10, 1965. (E. J. math stat. Psychol., 1965, x, 184-206)

71 E. J. Crothcn. b e n t a t i o n orders for items from different categories. March 10, 1965. 72

73 74 '15 76 77

.; 80

P. Suppq, G. Groen, and M. Schiag-Rey. Some models for response latency in paid-associates learning. May 5, 1965. U_. math. Psychol., 1966, ?* 99-128)

M. V. Levine. The generalleation function in the probability learning experiment. June 3, 1965. D. Hansn and T, 5. Rodpcrj. An exploration of psycholinguistic units in Initial reading. July 6, 1965. 8. C. hdd. A c-lrted m-scheme f a a continuum of mponses. July 20, 1965. C. i z m a and W. K. e*s. peinfmemnt-test squences in paired-associate learning. August 1, 1965. S. L. Blehrt. Pattern dttcriqination learning with Rhesus monkeys. September 1, 1965. J. L. Phillips and R. C. Atkinson. The effects of display size on short-term memory. August 31, 1965. R. C. Atkimon and R. M. Shiffrln. Mathematical models f a memory and learning. September 20, 1965. P. Suppes. The psychological foundations of mathematics. October 25, 1965.

(Continued on back cover)

(Continued from inside back cover)

P. Supper. Computer-assisted instruction in the schwls: potentialities, problems, prorprct~. October 29, 1965. R. A, Kinchla, J. Towmend, J. Yellott, Jr., and R. C. Atkinson. Influence of carelalrd v i r w l cues on w d l t w SlgNl drtsCtlOn. November 2,

P. Supper, M. Jermrn, and G . Groan. Arithmtlc drills and n v i w on a computer-bard LIIeLyp.. NovOmbr 5, 1965. P. Suppes and L. Hymn. Concept learning with non-verbal geomtrlcal stirnull. Novembrr 15, 1965. P. Holland. A variation on the minimum chi-square test. November 38, 1965. P. Suppes. Accelerated popram in demntary-rchool mathematlcs -- the second year. November 22, 1965. P. Lorenzen id F. Blnford. L w l c as a dialogical gam. November 29, 1965. L. Keller, W. J. Thomson, J. R. Tweedy, and R. C. Atkinson. Thc eflects ofmlnforcemnt Intwal on thl Jcqulrltlm of p l f d - U S W h h

J. I. Yellott, Jr. Some effects on noncontingent success in human pobablllty Ieunlng. 0ecomb.r 15, 1965. P. Suppes and C. Crocn. Some counting models for First-grade performance data on slmple addltion facts. JanuUY 14, 1966. P. Suppes. Information processing and choice behavior. January 31, 1966. C. G r a n and R. C. Atkinson. Models for optlmizlng the learning process. February 11, 1966. R. C. Atkinson and D. Hansen. Computer-asslsted instruction in inltlal reading: StanFord project. Much 17, 1966. P. Supper. Probabllistic inference and the concept of total evidence. March 23, 1966. P. Suppes. The axlonutic mthod In hlgh-school mthcmatics. A p l l 12, 1966. R. C. Atkinson, J. W. B n l s f d , and R. M . Shifhln. Multl-process models for memory with app l l u t lmr l o a CmtlnuOuI p W n h t l m

P. Suppes and E. Crothers. Some remarks on stimulus-response theories oflanguage learning. June 12, 1966. R. Bjork. All-or-none subprocesses in the learning of complex sequences. June 22, 1966. E . Gammon. The statistical determination of linguistlc units. July 1, 1966. P. Suppes, L. Hyman, and M. Jerman. Linear structural models forresponse and latency performance In arithmetic. July 29, 1966. J. L . Young. Effects of intervals between reinforcements and test trials in palred-associate learning. August 1, 1966. H. A. W ~ ~ S M . An investigation of linguistic unit size in memay processes. August 3, 1966. J. T. Townsend. Choice behavior in a cued-recognition task. August 8, 1966. W. H. Batcheider. A mathematical analysis of multi-level verbal learning. August 9, 1966. H. A. Taylor. The observing response i n a cued psychophysical task. August 10, 1966. R. A. Bjork. Learning and short-term retention of paired associates in relation to spc i f i c sqwnces of intnprrsentation Intervals. August 0, 1966 R. C. Atkinson and R. M. Shiffrin. S m Two-process models for memory. September 30, 1966. P. Suppes and C. Ihrke. Accelerated proqam in elementary-school rmthcmrtlcr--thc third yew. Jan- 30, 1967. P. Suppes and I. Rosenthal-Hill. Concept formatlon by kindergarten children In a card-satinJ task. Februay 27, 1967. R C Atkinson and R M Shiffrin. Human memay: a poposed system and i ts control processes. hknh 21, 1967 Theodm 5 . R o d g n s . Llnguistic conslderations in the design of the Stanfad computcr-bascd cvriculum In Inltial reading. June 1, 1967 Jack M. Knutson. Spelling &Ills using a computer-assisted instructional system. June 30, 1967. R. C. Atklnson. Instruction in inltlal reading under computer control: the Stanford Project. July 14, 1967.

1965. (Perception and Psychophysics, 1966, 1, 67-73)

responses. Oeccmber 10, 1963.

task. April 13, 1966.

'

81 82

83 84 85 86 87 88

89 90 91 92 93 94 95 96

97 98 99

1oc 101 102 103 104 105 106 107 108 109 110 111 112 113 114 J. W. Brelsfd, Jr. and R. C. Atkinson. Recall of paid-associates as a functlon of overt and covert rehearsal poccdues. July 21. 1967.