single ordering as a processing limitation

JOURNAL OF VERBAL LEARNING AND VERBAL BEHAVIOR 21, 39--54 (1982)

Single Ordering as a Processing Limitation

WILLIAM P. BANKS

Pomona College and Claremont Graduate School

AND

HEDY WH ITE

Claremont Graduate School

The present four experiments show that subjects have difficulty independently processing two separate orderings of the same terms, even when the orderings are well learned or are based on preexperimental opinions about ordering of terms. The results support the hypothesis that this difficulty reflects a fundamental cognitive limitation in the way we can process linear series in active memory. In the first experiment subjects with two different orderings of four terms showed processing deficits relative to control groups that also had two orderings to process but whose orderings were of two different sets of items. The second experiment showed that the processing deficit remained unchanged as overall performance im- proved approximately an order of magnitude over 16 days of practice. The last two experiments show the same patterns of interference for nonarbitrary orderings based on naturally occurring conflicts in rating-scale data. It is suggested that this cognitive limitation may account for the "halo" effect observed in rating scales.

Linear orderings are an important tool of human thought. Such orderings are scates that give a completely transitive ranking of objects such that if A > B, and B > C, then A > C. We employ linear scales regularly to solve a wide variety of reasoning problems, and we use them to organize many domains of knowledge , even those in which they may not be appropriate. In apparent service of these uses, our language puts most prop- er t ies of ob jec t s into l inear , f r e q u e n t l y b ipolar , scales that pe rmi t easy ordinal ranking of objects in terms of the degree to which they possess a given property.

Exper imenta l studies of our ability to memorize and retain orderings tend to show that we are, indeed, quite facile with linear o rde r ings , bu t at the same t ime these studies expose a curious flaw in our use of orderings. This flaw shows itself in a tendency for an object 's relative rank on one ordering or attribute to influence its rank on

This research was supported by NSF Grant BNS 78-17442 and NIH Grant MH 33279. Address reprint requests to William P. Banks, Department of Psychol- ogy, Pomona College, Ctaremont, Calif. 9171t.

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a completely different ordering on an unrelated attribute. When judgments of personality attributes given on rating scales ex- hibit this sort of mutual inf luence, it is termed a " h a l o " effect (Thorndike, 1920) because the direction of influence is consistently such that a person rated high in one attribute will tend to be rated high in other attributes. DeSoto (1961) attributed the interference between unrelated orderings to a "predi lect ion for single o rders" by which people tend to collapse differing orderings of items on several attributes into a single, consistent order.

We argue in this article that the interference be tween different orderings of the same items results, at least in part, from a cognitive limitation in the number of independent orderings of the same items that we can process in active memory. We argue, further, that the predilection for single orders is not the cause of the cognitive limitation; rather, it is one strategy of several that subjects can use to process two orderings of the same items concurrent ly. The research is consequently divided into two parts. In

0022-5371/82/010039-16502.00/0 Copyright © 1982 by Academic Press, Inc. All rights of r,eproduction in any form reserved.

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the first, reported in this article, we seek to establish the case for a cognitive limitation in processing orderings. In the second part we will examine models of the limitation and strategies people use to cope with it.

Although interference between compet- ing orderings of the same items has been amply demonstrated, there is no compelling evidence that the interference comes from a cognitive limitation (as, for example, the l imited capac i ty of sho r t - t e rm m e m o r y seems to) ra ther than f rom an opt ional strategy or a bias in assimilating information about orderings. The bulk of evidence for interference between different orderings depends on differential effects of the or- ganization of sets of elements on rates of learning. Thus, for example, it has been shown that it is more difficult to learn two different orderings of the same elements than to learn orderings of two entirely different sets of elements, even though the latter case requires subjects to learn twice as many elements as the former (DeSoto, 1961). Another example is that a transitive, linear, symmetrical relational structure is more quickly learned than one that is not (DeSoto, 1960; Mandler & Cowan, 1962).

We find two major problems with these sources of evidence. One is that the results could come from learning strategies generally used by subjects rather than from essential cognitive limitations. The strategy of acquisition may, of course, be based on the "pa th of least res is tance" necessitated by cognitive limits but it could also derive from re la t ive ly t r ivial or t h e o r e t i c a l l y unin- teresting factors in the learning situation. Moeser (1979) has, for example, shown that the advantage linear orderings have over partial orderings in learning can be elimi- nated by giving subjects a prototype for the structure of the partial ordering and by not presenting in learning trials any pairs that are composed of cont iguous terms. Be- cause contiguous terms are always in se- quential order in the linear series but not in the partial ordering, presentation of contiguous terms in learning gives an advan-

tage to linear orderings for which there is no obvious exper imenta l control . Moese r ' s study thus suggests that, rather than resulting from a fundamental cognitive limitation in the intake or use of information, the advantage for linear orders in acquisition appears to result partly from a bias to- ward assuming that the order ing to be learned will be linear and partly from the unavoidable circumstance that presenting contiguous terms facilitates complete linear orders more than partial orders.

The second problem we find in experiments on serial orderings that measure differential learning rate is that they do not study skilled performance with the orderings. It is possible that the in ter ference between multiple orders occurs only during acquisition, or only for poorly learned ma- terial, and that subjects could, for example, handle multiple linear orders of the same items perfect ly well once they had mastered them. If skilled performance with linear orders did not show interference, then we could not ascribe these effects to a strictly cognitive limitation. Likewise, the " h a l o " and related effects observed in naturalistic settings could result from a priori assump- t ions a b o u t the r e l a t i ons b e t w e e n attributes, habitual modes of integrating information, or some other source of bias rather than a structural limitation in the way people can use information. On the other hand, if subjects continue to have more difficulty with multiple orderings than single orderings long after accuracy has attained a near-perfect level, then we would have a basis for the claim that the interference arises from a fundamental limitation in the way we organize relational information. Such a limitation would then be as much a property of our cognitive hardware as the finite limit to digit span or the pervasive limit of 7 _+ 2 items in perceptual information transmission (Miller, 1956).

The present research studies processing of well-learned linear orderings at asymp- to t ic l eve l s of a c c u r a c y to d e t e r m i n e whether cognitive difficulties will still be

SINGLE-ORDER LIMITATION 41

encountered. The primary dependent measure is reaction time (RT) rather than accuracy because there is little difference in accuracy once the lists are well learned. The task given the subjects is compara t ive judgment of the relative positions of items in a serial order. In the first experiment, subjects learned either two four-term orderings of entirely different sets of terms or two conflicting four-term orderings of the same four items. This experiment is analogous to DeSoto ' s (1961) comparison of learning of two different orderings of the same terms with learning a single ordering of each of two different sets of terms, and it has an analogous outcome. As will be seen, subjects have less difficulty making comparative judgments among orderings of two completely separate sets of terms than they do comparing one set on two different orderings, even though there is a larger total number of elements to be processed in the former than in the latter case. The second experiment shows that interference between the two orderings is maintained over 16 days of practice while error rates and mean RTs decline to asymptotic levels. The last two experiments show interference between conflicting orderings whose ranks are based on rated positions on natural scales rather than on arbitrary assignments.

EXPERIMENT l

Method

Subjects. The subjects were 15 female and 9 male students from the Claremont colleges, paid $3 for the approximately 45 minutes of the experiment (3 additional subjects were dropped because they had error rates over 10%). They were randomly assigned to one of two different groups.

Procedure. Subjects in both groups were given two serial lists of four items to memorize and were then tested with timed comparative judgments of the ordinal rank of pairs drawn from the lists. The two groups differed in the relationship between the lists memorized. One group (conflicting orderings) received two different orderings

of the same four terms. If the rank ordering is symbolized as 1 2 3 4 in one list, it was 2 1 4 3 in the other. The other group (nonconflicting orderings) received two separate four-term lists containing a total of eight different terms.

For both groups, one list consisted of four male names ordered in height (Sam, Len, Don, and Tom) and the other list consisted of four male names ordered in grade point average (Len, Sam, Tom, and Don for the conflicting-orders group and Jim, Bob, Ned, and Ken for the nonconflicting-orders group). Four counterbalancing lists were used for each attribute so that each term appeared once in each posi t ion. Both groups had a total of 48 different stimuli: two lists (height and GPA), two forms of the question, six different pairwise combinations of the four terms in each list, and two different permutations of the six combinations.

At the beginning of the experiment the subject was given one list to study for 3 minutes and then the second list to study for another 3 minutes. The subject was then given practice trials on the experimental task (3 blocks of the 48 l i s t - p a i r - o r - der-quest ion combinations used in the experiment, presented in random order). The experimental trials followed the practice trials without a break, but brief rest periods were permitted between blocks of experimental trials.

In RT testing the questions and the pairs of names were presented to subjects on a PDP 11/10 computer-controlled cathode- ray tube display. Subjects began each block by pressing a microswitch; immediately after they pressed it one of four possible questions ("Taller?"; "Shor ter?" ; ~'Higher GPA?"; or "Lower GPA?") appeared for 1 second on the display, and a pair of names from the lists appeared at the end of the 1 second. The subject indicated whether the name appearing on the left or right side of the display was the one specified by the instructions by pressing a microswitch on the appropriate side. The subject's response

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caused the computer to remove the pair of names, present feedback ( " c o r r e c t " or " incor rec t" ) , and begin another stimulus sequence. In each block the computer program generated a new random order for presentation of the trials. The program re- c o r d e d RTs for c o r r e c t r e s p o n s e s and number of errors (but not RTs for errors), and later in each block presented pairs to which responses had been incorrect.

In each block of RT testing all pairs from each of the two lists were presented once in each permutation and with each instruction. This procedure created 48 RT trials per block. There were four experimental blocks and thus 192 trials for each subject.

R e s u l t s

Overall, the mean RT for the group with confl ict ing orders was 337 mil l iseconds longer than the mean RT for the group with nonconflicting orders, and this difference was reliable, with F(1,11) = 10.58 (SEre =

114 msec, p < .025). Thus, it appears that processing of nonsingle orderings of a set of items is still difficult even though the orderings are well learned.

The slowed processing for two different orderings of the same items does not derive entirely from specific interitem confusions about the terms under test. That is, it might be argued that in the conf l i c t ing-o rde r group subjects receiving a given pair might simply be confused as to which dimension they were judg ing . In some cases the member of the pair with more GPA might have less height, and the subject would be confused as to which should be chosen as having more. However , even when changes in ordinal position did not produce list-to- list conflict RTs were still longer for the conflicting than the nonconflicting group. The pairs in which there was no response conflict in the conflicting condition (24, 13, 23, and 14) produced a mean RT that was 193 mi l l i seconds longer than the mean

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RT for the same pairs for the nonconflicting group. This difference was reliable, F(1,25) = 14.38, p < .01.

Figure 1 shows the position effects for the two groups for pairs separated by 1, 2, and 3 ordinal steps. The stimulus pairs are indicated along the abscissa as hyphenated pairs of numbers that give the ordinal position of the two terms combined in the pair, where 1 = tallest or highest GPA and 4 = shortest or lowest GPA. A typical result of the comparat ive judgment paradigm is a processing advantage for pairs containing end terms over pairs containing only middle terms, and the position effect for RTs is genera l ly in the fo rm of a bow-shaped curve. In the present experiment, the re- versal of the bowed position effect for the confl ict ing-orders group is striking. The pair containing the two middle terms (pair 23) produced similar RTs for each group. But for the conflicting group the two pairs containing end terms (pairs t2 and 34) produced longer RTs than pair 23. Group in- teracted reliably with the position effect, F(5,25) = 4.02 (SEm = 86 msec, p < .01). The nonmonotonici ty of the position effect for the conflicting group was also reliable; a quadratic trend test for pairs 12, 23, and 34 produced an F(1,25) = 20.47, p < .01.

While the RTs for the conflicting-orders group were generally slower than for the nonconf l ic t ing-orders group, the RT for pair 23 was 78 milliseconds faster for the same-name than the different-name group. This difference is not reliable, but it may result from the fact that for the conflicting- orders group pair 23 in one ordering is 14, the fastest pair of all, in the other ordering. It would appear that an inability to keep the orderings independent causes this speeding up of p rocess ing pair 23. By the same token, the slowing of 14 in the conflicting- orders group relat ive to the nonconf l ic t - ing-orders group seems also to have come from an influence by the ordering not being tested, since it appears as the usually slow pair 23 in the other ordering.

The conflicting-orders group produced a

robust semantic congruity effect, despite the fact that it had a drastically distorted position effect. (The congruity effect is an interaction between the term used in the comparative question and the position of the pair in the ordering. Its form is such that subjects are, for example, faster at picking the larger than the smaller of two large terms but are faster at picking the smaller than the larger of two small terms. See Banks, 1977, for more discussion of the effect.) The mean congruity interaction for end-terms with an ordinal separation of one step was 148 milliseconds for the conflicting-orders group and 178 milliseconds for the nonconflicting-orders group. For pairs with a spli t o f two ord ina l s teps (pairs 13 and 24), the average congrui ty effect was 44 mi l l i seconds for the conf l i c t ing orders and 79 mi l l i seconds for the nonconflicting orders . These differences between groups were not reliable, F < 1.00. Across condition, the overall congruity in- te rac t ion (pair × quest ion) was reliable, F(5,55) = 22.61 (SEre = 58 msec, p < .01).

The mean error rate for the 24 subjects was 4.6% and there was a positive correlation between errors and RTs across subjects and conditions, i" = .23.

EXPERIMENT 2

Although the subjects in Experiment 1 had perfect recall for the lists on which they were tested (and had very low error rates in RT testing) it could be argued that the degree or the strength of the memory for them was not perfect and that the conflicting lists were still less well learned than the nonconflicting lists. Thus, the interference effect we obtained in RTs could have resulted from differences in degree of learning rather than from cognitive limitations in processing. It seems essential to show that the interference in processing is maintained when memory for the lists and overall RT for processing approaches asymptotic limits. This experiment gives 16 daily sessions of practice in the task (8 in conflicting and 8 for nonconfl ic t ing lists) and shows that the

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processing interference is maintained with little change while performance improves and then stabilizes at an asymptotic level.

Method

Subjects. The subjects were four Pomona College undergraduate research assistants who volunteered to perform in the experiment as par t of their l abora to ry duties. They had not participated in Exper iment 1.

Procedure. The procedure was similar to that used in Exper iment 1 except a within- subjects design was used. Subjects were tes ted four t imes a week , twice in the conflicting-orders condit ion and twice in the nonconfl ic t ing-orders condit ion. The conditions were tested on alternating days, with two subjects beginning with the conflicting orders and two beginning with the nonconflicting orders. Names were coun- terbalanced so that each subject had a different set of four terms to learn as the conflicting ordering. In the nonconflicting condition subjects 1 and 2 learned the eight names appearing on the two conflicting orderings learned by subjects 3 and 4 and subjects 3 and 4 learned the eight names appearing on the two conflicting orderings learned by subjects 1 and 2. As in Experi- ment 1, in each condition the two sets of terms were o rdered on different dimensions. The dimensions used were height, grade point average, running speed, and age, with each appearing twice in conflicting and nonconfl ic t ing condi t ions . Each subject received two of these dimensions in conflicting orderings condition and two in nonconflicting orderings.

On each day of testing, the subject re- viewed the orderings used in that day ' s comparat ive judgments. In RT testing, the questions and the pairs of names were presented to subjects as in Experiment 1 except an Apple II Plus microcomputer was used. In each session, the subject received six blocks of the 48 l i s t - p a i r - o r d e r - question combinat ions drawn from the condi t ion tested that day. There were eight sessions in each of the two experimental conditions,

generating a total of 4608 RT trials per sub- j ec t : 2 cond i t i ons (conf l i c t ing vs nonconflicting) x 8 sessions x 6 blocks x 2 orderings x 2 forms of instruction (choose the term higher vs lower on the dimension) x 6 pairs x 2 permutations.

Results

As seen in Figure 2, performance, mea- sured either in overall mean RT or error rate, stabilized at a ceiling by the middle of practice. Errors dropped from 5.75% on the first session to under 1% for the last five sessions, with an overall rate of 1.56%. The analysis of variance of error rates showed a reliable effect of practice, with F(7,21) = 13.10, p < .01. The errors also showed a reliable in teract ion of pract ice with list t ype , such tha t the con f l i c t i ng o rde r s showed more of an i m p r o v e m e n t o v e r practice (from 6.5% errors to .78%) than the nonconflicting orders (from 4.9% to .70%), with F(1,3) = 12.0, p < .05. Mean error rate varied from .39 to 2.4% over the 48 cells defined by the two conditions, two orderings, two instructions, and six pairs and had an r = .46 for the correlation with RT over these cells.

The RTs declined from 1361 to 1109 milliseconds over practice, but the effect was not reliable, F(7,21) = 1.74, p > .10. How- ever, there was a reliable decline for the first half of practice, F(3,9) = 5.81, p < .05, but no reliable effects for the second half (F < 1.00). It seems that a reliable effect of practice on RT over early sessions was di- luted to nonsignificance by including the blocks of stable performance after the ceiling was reached. Both the marking effect (marked questions were processed 73 msec slower than unmarked) and the semantic congru i ty e f fec t were rel iable, F(1,3) = 39.9 and F(5,15) = 3.1, respectively, both p ' s < .05.

Figure 3 shows the mean RTs for each pair in the conflicting and nonconflicting conditions over the eight sessions of practice, using the same conventions as Figure 1. As can be seen, the general pattern ob-


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days of practice. Practice sessions alternated between conflicting and nonconflicting orderings, and means were taken across adjacent days to combine these variables. Thus, pair 1 of pairs of sessions combines the first two days of practice, pair 2, days 3 and 4, and so on.

served in Exper iment 1 holds up over all eight sessions of practice. Despite the 252 millisecond overall improvement in mean RT from first to last session, the difference between conflicting and nonconflicting orderings increased f rom 354 to 624 mil- l iseconds. The mean difference over the first four sessions, during which perfor- m a n c e was i m p r o v i n g , was 327 milliseconds, and it was 354 milliseconds over the last four sessions, after performance stabilized.

In the overall analysis, while the main effect of conflicting vs nonconflicting orderings (producing mean RTs of 1317 and 977 msec. , respectively) was not reliable, F(1,3) = 2.53, p > .10, the pair x ordering interaction was, with F(5,15) = 4.07, p < .05. The interaction reflects an absence of a reliable difference for pair 23, which was only 134 milliseconds slower in the conflicting list, F(1,15) = 3.84, .05 < p < .10, while all the o the r pairs were re l iab ly slower in the conflicting list, by a mean of 381 mi l l i s econds . O r t h o g o n a l pa i rwi se comparison tests for the five other pairs all were reliable at the .01 level: for pair 12,

F(1,15) = 31.6, for pair 34, F(1,15) = 67.7, for pair 13, F(1,15) = 18.5, for pair 24, F(1,15) = 25.9, and for pair 14, F(1,15) = 23.8.

In sum, it appears that the pattern of interference found in Exper iment 1 does not depend on differential learning of the lists. This experiment shows no tendency what- ever for the interference to be reduced over the approximately 2000 trials after performance for both lists has stabilized at approximately the same very low error rate.

EXPERIMENTS 3 AND 4

Experiments 1 and 2 showed interference with processing on conflicting orderings using totally arbitrary orderings. Experi- ments 3 and 4 use orderings based on ratings of well-known objects on common attributes. There are several reasons for using these natural orderings. First, these orderings agree with subjects' preexperimental opinions about the relative ranking of the objects and should not be subject to differential " learn ing" effects. Second, we in- t end our conc lu s ions to app ly b e y o n d newly learned, arbi t rary orderings. The

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cognitive processing limitation should op- erate as well for concurrent ly entertained orderings drawn from a semantic m e m o r y as it does for novel orderings given by the experimenter . Third, if there is any concern tha t the f irs t two e x p e r i m e n t s s tudied " o n l y " a list-processing effect, unrelated to normal thinking with natural semantic con- cepts, then these experiments should remove a large part of that concern. It is true that the testing situation is somewhat different from anything usually encountered in everyday experience, but the task engages commonly used mental p rocesses of ordering and grading, and there seems little chance that the artificiality of the testing

situation could create the effects we study. Even the repeated testing is not unlike the repetitive operations involved in such ubiq- uitous real-world tasks as grading, judging, or sorting objects.

Experiment 3

This experiment uses much the same design as Experiments 1 and 2 except that the four-term orderings were drawn from ratings. The confl ict ing order ings (1234 vs 2143) were there fore based upon conflicts that exist in the semantic scales for these items.

Method

Subjects. Subjects were male and female students from the Claremont colleges who were paid $3 for the approximately 40 minutes required by the experiment. We asked each subject who arrived for the experimental session to order the items on the scales used in the experiments. They were given three sets of four index cards in which one of the items was written on each card. They were asked to order each set of four cards to reflect the ordering on the appropriate dimension. If any of the orderings a subject gave differed at all from the ordering to be used in that subject 's experimental session, the subject was not used in this experiment. We had to screen 12 subjects in order to find the 8 subjects used in this experiment.

Materials. The rank orderings were de rived from ratings made by 32 people. The raters used a 1-to-100 scale to rate six animals on the dimensions of intelligence and weight and to rate 14 fruits and vegetables on the dimensions of sweetness and size. They were ins t ructed to use small numbers to indicate an item was low on the attribute and high numbers to indicate an item was high.

The four- term lists drawn from these ratings were as follows (mean rating on the 1-100 scale is given in parentheses after each item): Intelligence: dog (61.7), horse (47,2), rat (36.2), chicken (12.8). Weight: horse (87.9), dog (37.5), chicken (15.2), rat (6.80). Sweetness: apple (55.1), yam (48.3),


pea (21.4), lemon (10.0). Size: yam (37.2), apple (34.1), lemon (23.2), pea (2.00).

Procedure and design. A within-subject design was used in which each subject was concurrently tested on three four-term orderings. For each subject two of these lists were in a conflicting ordering (one was ordered 1 2 3 4 and the other 2 1 4 3) and one list was not. Thus, a subject would have two fruit/vegetable lists, for example, and one animal list, and the fruit/vegetable lists would be in conflicting order. Half of the subjects had the fruit/vegetable terms in conf l ic t ing order ings and ha l f had the animal terms in conflicting orderings. Each of these halves of the subjects was further subdivided into two halves depending on the nonconflicting lists. Half of those with the conflicting fruit/vegetable lists had intelligence of animal as the nonconflicting list and half had weight of animal as the nonconflicting list. Similarly, half of those who had the two animal lists conflicting had sweetness of fruit/vegetable as the nonconflicting list and half had size of fruit/ vegetable nonconflicting.

Subjects were tested as in Experiment 1, with instructions with stimulus pairs presented on a PDP 11/10 computer-controlled cathode-ray tube display. There were six experimental blocks and no practice trials. Each b lock p r e sen t ed all 72 order ing/

question/pair/permutation combinations in random order: 3 lists (2 conflicting and 1 nonconf l ic t ing ordering) x 2 ques t ions (marked vs unmarked) x 6 pairs x 2 permutations of each pair.

Results and Discussion

Figure 4 plots mean RTs for the conflicting and nonconflicting conditions for the six pairs drawn from each ordering. For the two conflicting lists, combined means are presented. The same conventions are used as in Figure 1. With the exception of pair 24, RTs were shorter in the nonconflicting condition than in the conflicting conditions. Collapsing pairs, the nonconflicting condition produced a mean RT (1213 msec) that was 62 milliseconds shorter than the mean for the conflicting condition (1275 msec), F(1,8) = 6.15, p < .05, and the condition × pairs interaction was not reliable, F < 1.00. The position effect for 1-step pairs (panel 1) is stronger in the nonconflicting than the conflicting condition, although the position effect does not reverse for the conflicting ordering, as it did in Experiments 1 and 2. End pairs 12 and 34 were processed 148 milliseconds faster than middle pair 23 in the nonconflicting condition, but only 68 milliseconds faster in the conflicting condition. The RTs did not systematically decline over the six blocks, F(5,20) = 1.14.

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48 BANKS AND WHITE

Furthermore, there was no interaction between list conflict and practice, F(10,40) = 1.05, and no other reliable interactions with practice.

Errors declined from 9.7 to 3.1% over blocks, F(5,20) = 4.79, p < .01, with a mean of 4.2%. Most of the decline with practice took place in the first two blocks. The conflicting list p roduced a mean of 4.4% errors and the nonconflicting, 3.6%. This difference was not reliable, F < 1.00, and it did not interact reliably with practice or any other effect. Across subjects errors varied from 1.9 to 9.0%. The correlation between RT and errors was .62 over the 24 condit ions defined by the six pairs, two questions, and conflicting vs nonconflicting orders.

These results show that processing interference is still encountered in concurrent judgments of relative position on conflicting scales when the scales are part of the subjec t ' s semantic repertoire. However , one remaining concern with this conclusion is that subjects may have ignored the natural orders on which our lists were based and therefore treated the items as if they were nonsense words in an arbitrary sequence. The best way to test this hypothesis is to compare the ordinal scale distance effect (prediction of RT from ordinal step difference between members of a pair) with the interval scale distance effect (prediction of RT from rating scale difference between members of a pair). If the subjects treat the orderings as arbitrary, the rating-scale differences should not predict RT.

To compare ordinal and rated difference, we first separately computed the linear regression of ordinal difference and difference in ratings on RT. This gave an r of .63 for ordinal difference and .78 for rated difference. Both r ' s are reliable with F(1,22) of 14.5 and 34.6, respectively, both p ' s < .01, but the interval scale difference does predict RT be t t e r than ordina l -sca le d i f ference . These simple r 's are only a first step, however, because the method of list construc- tion necessar i ly creates a corre la t ion between ordinal and ra ted differences, and

either one could appear to predict RT only because of its correlation with the other. To remove the effects of such a confounding, we computed the partial correlation for each holding the other constant using the SPSS mul t ip l e - r eg res s ion package . When the rated difference was regressed against RT first, adding ordinal difference raised the correlation from .78 to .79, with an F(1,21) = 1.12, n.s . , for the addit ional var iance accounted for by the ordinal difference. On the o the r hand, a f te r the ordinal e f fec t was removed, the interval differences raised the correlation from .63 to .79, adding signi- f i can t ly to the va r i ance a c c o u n t e d for , F(1,21) = 13.33, p < .01. Thus, it appears that ordinal difference between members of a pair has no correlation with RT beyond that resulting from its correlation with the rated difference. Subjects apparently used the semantic memory informat ion to the almost complete exclusion of ordinal information in processing the pairs and they did not treat the object names as nonsense syl- lables, but as meaningful words. The interference between conflicting orders therefore exists even when subjects are basing their decisions on general knowledge about natural orders.

Experiment 4

This experiment compares processing of conflicting and nonconflicting orders as the previous experiments do, and it uses orderings based on rating scales as does Experi- ment 3. It differs from Experiment 3 in two major ways: it has six-term rather than four- term orderings and it uses somewhat different patterns of conflict between lists. The main object of this experiment is thus to show that the conflict effects of the previous experiments are not confined to the particular list lengths or pat terns of confl ict we used.

Method

Subjects. The subjects were 12 male and female Pomona College students who either served to fulfill a course requirement or

SINGLE-ORDER L I M I T A T I O N 49

were paid $3 for the approximate ly 75 minutes of the experiment .

Materials. A group of 18 students enrolled in a P o m o n a Col lege course vo lun tee red to stay about 10 minutes after class to fill out four rating sheets. The sheets were as- sembled and stapled in r andom order and handed to them in their seats in the class- room. Two sheets each had the same set of 24 animal names, to be rated for intelligence on one sheet and size on the other. Two other sheets had the same 13 fruits, to be ra ted on swee tness and weight. Ratings were on a 1-to-10 scale with 1 = least of the attribute (least smart, smallest , least sweet, or lightest) and 10 = most of the attribute.

Two pairs of conflicting lists were de- rived f rom these ratings, one pair for fruits and one for animals. In both cases the ordinal relations be tween the items on the de- rived lists was the same as their relations in the ratings. Rather than the 1234 vs 2143 pa t t e rn of confl ic t p rev ious ly used, the frui ts had 123456 vs 264513 and the animals had 123456 vs 214635. The ac tua l terms are as follows, ranked from least to most on the appropr ia te scales, with their mean rating shown in parentheses: Size of fruit: cher ry (1.93), l emon (3.62), apple (4.75), p e a r (5 .20) , m e l o n (6.06), and grapefruit (7.14); Sweetness: lemon (1.44), grapefruit (2.25), pear (5.00), melon (5.47), cherry (6.25), and apple (8.20); Weight of animal: ra t (2.97), c h i c k e n (3.17), dog (5.43), deer (7.28), ape (8.03), and horse (8.59); Intelligence: c h i c k e n (3.17), ra t (4.30), deer (4.95), horse (5.80), dog (6.41), ape (8.45).

Procedure. As in E x p e r i m e n t 3, each subject was given three of the lists, two of which used terms from one set and con- flicted with each other and one of which used terms f rom the other set. Four counterbalancing three-list sets were used, with three subjects receiving a particular set. In many cases subjects disagreed with at least one ordering, but they were asked to learn the three sets of orderings and to make compara t ive judgments of the pairs consistently with the orderings even if they dis-

ag reed with them. Subjec ts we re qui te willing to adjust their sense of the relative orderings for the sake of the experiment , p robab ly because the ones about which they disagreed were always adjacent members of the series, whose rankings are subject to uncertainty. No subject repor ted a disagreement beyond one rank of ordering on a given attribute.

Results and Discussion

Figure 5 plots mean RTs for the 15 pairs for the conflicting and nonconflicting orders. As the figure illustrates, for every one of the 15 pairs, RTs were shorter in the nonconflicting condition than in the conflicting condition. The mean overall RT in the conflicting condition was 1258 and 1136 mill iseconds in the nonconfl ict ing condition, F(1,16) = 24.11, p < .01.

As Figure 5 shows, differences between the two kinds of orderings were greater for some pairs than for others, and the pair × ordering condition interaction was reliable, F(28,224) = 3.25, p < .01. These differences may be influenced to some degree by the particular amount of conflict involved in the conflicting orders, as was the case in Exper iments 1 -3 . For example , in the first three exper iments pairs 12 and 34 were op- positely ordered in the conflicting condition while pair 23 was in the same order in both lists, and more interference was exhibited for pairs 12 and 34 than for pair 23. To as- sess the effect of conflict among specific pairs, we computed for each pair the total n u m b e r of reversa ls in ordinal rank between the two orders in the conflicting condition. This measu re of rank di f ference does not count the number of steps of ordinal difference, but only the total number of reversals. The measure can vary f rom 0 to 2 for each of the two types of conflicting lists (animals and f ru i t s /vegetables) and thus from 0 to 4 when the measure is summed over the counterbalancing conditions. This summed measure is shown in parentheses below each pair along the abscissa of Figure 5. As it happened, in no case did the measure equal 4 because none of the pairs had

50 BANKS AND WHITE

600 t [ = ": S

1500 1

,.oo--[ \ , oo] '20o 1

~ 'ooo t

9°° 11 i~ 5 3~ 25 & ;4 ~5 ,& ,~ 25 36 ,5 z. ,~- ($) (i) (2) (2) (2) (o) (I) (3) (3) (I) (I) {3) (2) (I) (I)

PAIR (NUMBER OF REVERSALS IN PARENTHESES)

FIG. 5. Reaction times in Experiment 4 for conflicting and nonconflicting six-term orders based on rating scales. Plotted by the same conventions as Figure 1.

reversed orders on both of the conflicting lists in both types of list.

This measure correlates quite well with the difference between conditions across the 15 pairs, with r = .81. Furthermore, when the number of reversals is used as a covariate in the regression equation to adjust the RTs for the conflicting condition, the mean difference between conflicting and nonconflicting orders drops from 122 to 48 milliseconds. Thus, it would appear that reversals in the order of individual pairs in the conflicting lists may account for a large part of the effect of conflict, but specific reversals do not account for all of it. And, in fact, our experimental design may speed up processing time for the conflicting lists and thus reduce our estimate of nonspecific interference because it presents subjects with members of the conflicting lists twice as often as members of the nonconflicting lists.

Figure 6 gives RT as a function of the ordinal difference between members of a

pair. This plot shows, first, that the mean number of reversals in the conflicting condition decreases with ordinal difference. For the five pairs separated by one step, the mean number of reversals is 2, it is 1.75 for the pairs separated by two steps, 1.66 for the three-step pairs, 1.5 for the four-step pairs, and 1 for the one pair separated by five steps. The essentially parallel functions in Figure 6 thus show some degree of inde- pendence between reversals and conflict. Second, the parallelism also indicates that the disagreements between our subjects' own preferred orderings of the terms and the orderings we gave them did not affect the degree of conflict. This is so because disagreements never extended beyond one ordinal step. Subjects often disagreed about the relative ordering of melon and grapefruit in size but always agreed that they were both larger than pear. As the figure shows, however, the conflict is the same for all the steps of ordinal separation and thus cannot be attributed to disagreements about the


(D W 1 4 0 0 - Or)

v

1300- W

i - - 1200 -

: 7 0 F- lloo- ( J <~ w n.,- I 0 0 0 -

Z ' ~ 9 0 0 - w

ORDINAL DIFFERENCE BETWEEN TERMS

FIG. 6. Reaction time in Experiment 4 as a function of ordinal difference between members of a pair in a ranking, plotted separately for conflicting and nonconflicting orders.

orderings we used. In any event, the same order ings of the lists we used in nonconfl ict ing and confl ict ing lists and dis- a g r e e m e n t s a bou t o rder ings c a n n o t by themselves account for the effect of conflicting orders.

We performed the same analyses used in E x p e r i m e n t 3 to c o m p a r e o rd ina l and rating-scale distance as predictors of RT. Here the ordinal distance correlated .649 with RT and the rated .687. When ordinal distance was partialled out, rated distance increased the correlation from .649 to .695, with F(1.57) = 6.86 for the additional variance accounted for by rated distance, p < .05. After rated distance was removed, ordinal distance also increased the correlation to .695, but the increase is not reliable, F(1,57) = 1.17. The distance effect thus clearly shows, as it did in Exper iment 3, that subjects were influenced by semantic m e m o r y i n f o r ma t ion in pe r fo rming the comparat ive judgments.

Mean error rate was 8.0%, with a mean of 8.6% on the two conflicting lists subjects had and 6.9% on the one nonconflicting list. Errors varied from 2.3 to 17.4% over the 15 pairs, and from 2.1 to 20% over the 30 cells defined by the combinations of the 15 pairs and the conflicting vs nonconfl ict ing or-

ders. The correlation between RTs and errors over these 30 cells was r = .80.

GENERAL DISCUSSION

These e x p e r i m e n t s give, we be l ieve , good support for a cognitive limitation in the processing of orderings. Exper iment 1, using a between-group design, showed that subjects who had to process two different orderings of the same items on unrelated dimensions were slowed relative to a group that processed orderings of two separate sets of items. Experiment 2 showed that the interference between conflicting orderings does not decline at all as performance improves with a large amount of practice and thus does not simply reflect a continuation of the diff iculty people initially exhibi t when learning conflicting orderings. Ex- periments 3 and 4 show that the interference operates in processing sets of natural objects that happen to differ in their rankings on different natural semantic scales and is not res t r ic ted to arbi t rary, experiment-specific orderings. We conclude that the interference people show in processing different orderings of the same terms does not result solely from preferences, biases, or an optional strategy taken during learning. Rather, it seems that concurrent pro-

52 B A N K S A N D W H I T E

cessing of orderings has what we call a single-order limitation.

We are not prepared at this point to pro- pose a model of the single-order limitation or of the strategies subjects may use to cope with it. We can, nevertheless, point out a few cons t ra in t s on models that are suggested by our results. First, the interference between conflicting orders takes place both at the level of individual pairs and for the list as a whole. That is, it both differs from pair to pair (depending on the relation- ships between the pairs in the two orderings), and it exists for pairs that are in the same order in both lists. In Experiments 1 and 2, and to some degree in Experiment 3, we found relative facilitation for some pairs across conflicting orderings. In Experiment 4 we found a strong relationship between degree of conflict and number of reversals across conflicting orders. At the same time, in all four experiments we consistently found a substantial amount of general interference between conflicting orders that slowed processing for pairs that were in the same relative orders in the two lists. In every case but one (pair 23 in Experiment 1) the nonspecific in terference was strong enough to overcome interpair facilitation effects.

The specific effects of mutual influence among pairs argue against the proposition that the interference between conflicting orders of the same terms results entirely from the subject's uncertainty about the dimension on which to compare a pair. For example, if pear and grapefruit are ordered in one list for sweetness and the other for size, a subject might take time to decide which list to use when presented with this pair. The subject would therefore be slower when sweetness and size lists are concurrently processed than when one of these lists is concurrent with a list of entirely different terms. Such a process would, of course, predict an overall slowing of processing with conflicting lists but would not predict the specific interpair effects. On the other hand, a model designed specifically

to predict the patterns of influence among pairs would also need to explain the general interference effect. Simple associative interference and facilitation among pairs or between list members and list positions would not, for example, explain why facilitation effects are generally not sufficient to speed processing of pairs beyond the RT for the nonconflicting control condition.

Another fact with some theoretical impli- cations is that in Experiments 3 and 4, in which orderings were based on semantic memory for natural scales, performance was predicted better by ratings on the scales than by rank in the orderings. In fact, the partial correlations suggest that the natural scales completely dominate performance and that rank predicts the distance effect only because of its correlation with the ratings. This result implies that the conflict between alternative orders does not arise solely through conflict in some ordinal list-processing strategy used in short-term memory, such as scanning an array (cf. Woocher, Glass, & Holyoak, 1978, for a scanning model of comparative judgments) or putting terms into a limited number of "slots" in short-term memory. Rather, it seems that information about the relative natural scale values is used in processing the lists. The control condit ions (nonconflicting lists) show that conflicts in the natural orderings only slow processing when the two conflicting orderings are concurrently processed. Presumably, then, the conflict between orderings only causes conflict when the semantic information for confl ict ing orderings is drawn up and maintained simultaneously in memory. Conflicting orderings can reside simultaneously in semantic memory, since our conflicting orders were based on conflicts in the ratings our subjects gave.

A question of considerable interest is the relationship between the interference in concurrent processing we have studied and the interference and mutual influence between differing orderings shown by the halo effect (Thorndike, 1920; Nisbett & Wilson,


1977). The li terature on judgment shows that the halo effect is a very widespread phenomenon. In some cases it takes the form of an influence of one dimension's ranking on another , unrelated dimension (Landy & Sigall, 1974) and in other cases it is an influence of a global evaluation on rankings on other, often unrelated, scales (Thorndike, 1920; Nisbett & Wilson, 1977).

There are many ways the halo effect and the process ing in te r fe rence could be related. The relation could, of course, be ac- cidental, with the halo effect coming from a powerful a priori bias about correlat ions between attributes and the processing inter ference from some sort of short- term memory limitation. However , the a priori bias needs itself to be explained. Such a bias is somewhat dubious when the halo effect creates correlat ions be tween attributes of low intrinsic relatedness that are approximately as high as correlations between attributes that seem reasonably to be related. For example, Thorndike (1920) reported correlat ions of .50 between rated in teres t in c o m m u n i t y affairs and ra ted quality of voice and of .80 between rated intelligence (of a teacher) and rated ability to discipline a class, but overall merit as a teacher correlated only .62 with intelligence and .41 with academic preparation. In another study Thorndike reported, aviation cadets were rated by superior officers given " e m p h a t i c " instruct ions to evaluate the attributes separately, and rated intelligence correlated .51 with rated physique, .58 with rated leadership ability, and .64 with rated " c h a r a c t e r . " Thorndike notes that intelligence and leadership should give about " th ree times as c lose" a correlation as intelligence and physique. Whether or not his assessment is correct , it does illustrate that a priori biases do not correlate all attributes equally.

The high correlat ions among unrelated attributes (and small difference in correlation between seemingly related and unrelated attributes) suggests that rather than a judgmental bias, there is a general strategy

of putting all attributes on a common scale, usually of overall evaluation. The processing limitation interfering with multiple orders in active memory could well create the necess i ty for such a s t ra tegy. If act ive memory cannot handle two conflicting concurrent orderings of the same terms, people could collapse the orderings into a single one. This strategy would create distortions in the orders, but people might rationalize these distortions where t h e y could. If the tasks required that certain conflicting orderings be kept as they are given, then a single ordering could still be set up but information could be separately stored about certain pairs that disagree on the two lists. P resumably , this appended in format ion would be more fragile than the combined ordering and would be forgotten sooner, leaving only the memory of a combined ordering. It would seem that conflicts between orderings in semantic memory could continue to exist as long as they are not brought up at the same time for considera- tion in active memory. Once they are processed together, they may be put into the same order and remembered that way sub- sequently.

While the process ing in te r fe rence between multiple orders could create the halo effect, it is difficult to see how the halo effect could be, instead, the basis of the processing interference. First, in Experiments 3 and 4, we found processing interference for cases that did not show the halo effect in semantic memory. In these experiments the rated scale values for the two natural orderings of the items are not perfectly correlated (i.e., deviate from a halo-induced correlation) but show processing interference nevertheless. If processing interference were caused by the halo ef fec t it would not have been found here. Second, if the halo effect does not result from some sort of fundamental processing limit but is, ra ther , nothing more than a judgmenta l error, we do not see how it could explain p r o c e s s i n g i n t e r f e r e n c e for the small , well-learned sets of terms we used. Surely,

54 BANKS AND WHITE

if it is jus t an error in judgment we do not see how it could continue to be made with the small sets of items and high levels of practice we used.

REFERENCES

BANKS, W. P. Encoding and processing of symbolic information in comparative judgements. In G. H. Bower (Ed.), The psychology of learning and motivation. New York: Academic Press, 1977. Vol. 11.

DESOTO, C. B. Learning a social structure. Journal of Abnormal and Social Psychology, 1960, 60, 417-421.

DESoTo, C. B. The predilection for single orderings. Journal of Abnormal and Social Psychology, 1961, 62, 16-23.

LANDY, D., & SIGALL, H. Beauty is talent: Task evaluation as a function of the performer's physi- cal attractiveness. Journal of Personality and So- cial Psychology, 1974, 29, 299-304.

MANDLER, G., & COWAN, P. A. Learning of simple structures. Journal of Experimental Psychology, 1962, 64, 177-183.

MILLER, G.A. The magical number seven, plus or minus two: Some limits on our capacity for processing information. Psychological Review, 1956, 63, 81-97.

MOESER, S. D. Acquiring complex partial orderings in comparison with acquiring similar-sized linear orderings. Memory & Cognition, 1979, 7, 435-444.

NISBETT, R.E . , & WILSON, T. D. The halo effect: Evidence for unconscious alteration of judgments. Journal of Personality and Social Psychology, 1977, 35, 250-256.

THORNDIKE, E. L. A constant error in psychological ratings. Journal of Applied Psychology, 1920, 4, 25 - 29.

WOOCHER, F. D., GLASS, A. L., & HOLYOAK, K. J. Positional discriminability in linear orderings. Memory & Cognition, 1978, 6, 165-173.

(Received September 30, 1980)

single ordering as a processing limitation

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