Primacy effects and attention decrement

8/8/2019 Primacy effects and attention decrement

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Acta Psychologica 62 (1986) 293-302North-Holland

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CONTINGENCY JUDGMENT:PRIMACY EFFECTS AND ATTENTION DECREMENT *J. Frank YATES and Shawn P. CURLEYThe University qf Michigan, Ann Arbor, USAAccepted October 1985

Subjects made judgments concerning the strength and direction of the contingency between twodichotomous variables in a situation in which no contingency actually existed. The judgmentsexhibited a significant primacy effect. The effects of warning and not warning the subjects thatthey would be required to recall the frequencies of observed event co-occurrences impl ied that thisprimacy effect was due to attention decrement (Anderson 1981). According to this hypothesis,attention to contingency-relevant information diminishes after the subject is exposed to only asmall portion of the available information.

Judging the contingency between events, e.g., symptom S and diseaseD in medical diagnosis, is an important cognitive activity. The pioneer-ing work of Smedslund (1963) and Jenkins and Ward (1965; Ward andJenkins 1965) led to the recognition that people exhibit limited pro-ficiency at contingency judgment tasks. Those initial studies, as well assubsequent research, have shed much light on the nature of contingencyjudgment processes as well as the effectiveness of those processes (seereviews by Beyth-Marom (1982) and Cracker (1981)).

Suppose that events E and P are those of interest in a givensituation. The events are contingent if I( E 1E;) f P( E 1F) or, equiv-alently, P( I: 1E) f P( F 1E), where the primes indicate the comple-mentary events. The direction and strength of the contingency ismeasured by what might be called a contingency index, A = P( E I P)- P( E I F). Table 1 shows a contingency table whose axes are identi-

* It is our great pleasure to thank Robert Revnew for his assistance in carrying out the reportedresearch. This work was supported in part by U.S. Nationa l Institute of Menta l Health GrantMH16892.

Requests for reprints should be sent to J. Frank Yates, 136 Perry Build ing, Dept. ofPsychology, University of Michigan, Ann Arbor, MI 48104, USA.

OOOl-6918/86/$3.50 0 1986, Elsevier Science Publishers B.V. (North-Holland)


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294 J.F. Yates, S.P. Curley / Primacy and contingency judgm ent

Table 1Standard contingency table cell and frequency labels.Variable 1

E

Variable 2FCell Aa

FCell Bb

Total

a+b

E Cell Cc

Cell Dd c+d

Total aft b+d a+b+c+d

fied with the variables defined by E and E, on the one hand, and Fand F, on the other. The frequencies for the four possible joint eventsare denoted in the cells by lower-case letters. Assuming that observa-tions are selected at random, P( E 1F) is estimated by the frequencyratio a/( a + c), and P( E 1F) by the ratio b/(b + d). Thus, a propercontingency judgment should be based upon a comparison of theseratios or, equivalently, the frequency products ad and bc.

One reason contingency judgments are suboptimal is that peopleseem to use improper contingency rules (Arkes and Harkness 1983;Beyth-Marom 1982; Shaklee and Tucker 1980; Smedslund 1963). Thatis, the criteria by which people judge the relatedness of binary variablesdo not agree with the statistical convention. Rather than comparingu/( a + c) to b/( b + d), subjects have often appeared to judge con-tingency on the basis of the frequency a, the so-called Cell A strategy.In other words, they conclude that events E and F are contingent tothe extent that they co-occur. Another popular rule involves contrastingfrequency (a + d) to frequency (b + c). This sum of diagonals strategyis in essence a comparison of the number of cases consistent with thehypothesized contingency of events E and F to the number of casescontradicting that contingency.

Strategy selection and resulting contingency judgments are also af-fected by how the relevant data are presented (Arkes and Harkness1983; Shaklee and Mims 1982; Ward and Jenkins 1965). The simplestmeans by which one might judge the contingency of events E and Fwould be with the aid of a data summary, e.g., a contingency table suchas that contained in table 1. However, in a more naturalistic situation,information becomes available case-by-case. Even if a person wished toapply an appropriate contingency judgment rule, doing so with a serial


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J.F. Yates, S.P. Curley / Primacy and contingency judgm ent 29 5

presentation of cases would impose heavy demands on memory. Asexpected, contingency judgment is more accurate when based on infor-mation presented in summary rather than serial formats. Consistentwith the memory demand hypothesis, the Cell A strategy seems to beused more commonly when the subject is confronted with large ascompared to small numbers of cases.

Beyth-Marom (1982) has demonstrated another factor which in-fluences the strategy by which relatedness is judged. Contingencyjudgment is affected by a variables type, or how the variable isdescribed to the subject. An asymmetric binary variable is such that thename of the variable is closely identified with one of the eventsconstituting the variable, but not the other, e.g., present vs absent,when the variable is described as Pigmentation. In contrast, forsymmetric variables, the constituent events are of equal status, e.g.,dark vs light, again when Pigmentation is the relevant variable.Subjects are more likely to use contingency rules relying on only part ofthe relevant information, e.g., the Cell A strategy, when variables areasymmetric rather than symmetric.

Einhorn and Hogarth (1978) have argued that, in many real-worldsituations, people often lack some of the information needed to de-termine contingencies. Suppose, for example, that in table 1 event E issuccessful job performance and event P is predicted successful jobperformance. Employers almost never hire workers who are expectedto perform poorly. So, frequencies b and d will be unavailable, and aproper contingency assessment wil l be impossible to achieve.

Even if available, relevant information may have little or no effect onjudgments of the relatedness of variables (Alloy and Tabachnik 1984;Jennings et al. 1982; Wright and Murphy 1984). Instead, these judg-ments are often dictated by peoples expectations and intuitive theoriesabout how the variables ought to be related. The most dramaticdemonstrations of such phenomena are the intuitive correlations thatsubjects report between clinical symptoms and diagnoses in situationsin which no contingencies actually exist (Chapman and Chapman 1967,1969). Moreover, as Einhorn and Hogarth (1978) have shown, whensubjects are able to request any frequency information they desire, theyoften do not ask for all that is needed to make a legitimate contingencydetermination. Rather, they seek information that is consistent with,but not decisive for, their init ial hypotheses about the potential con-tingency.


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J.F. Yates, S.P. Curley / Primacy and cont ingency judgment 291was such that cases presented early in the sequence indicated a con-tingency in one direction; cases presented toward the end of thesequence supported a contingency in the opposite direction. In thisway, a primacy effect could be identified. Also, all subjects wererequired to recall the frequencies of case types they observed. However,only half the subjects were forewarned of the recall test; the others werenot. If the attention decrement hypothesis had credence, then theanticipated primacy effect in contingency judgments should have beenweaker for the forewarned subjects.

MethodSubjects

There were 129 paid subjec ts in the stud y. They were assigned randomly to the fourcondit ions of the experimen t described below.Stimuli

The subjects were asked to consider a hypothetical plant called the Rhododipsia.Rhododipsia were reported to grow in both Region A and Region B. Rhododipsia werealso said to com e in either of two colors , light or dark. During the experime nt, subjec tswere shown wha t were purported to be the results of a random sampling of Rhodo-dipsia from Regions A and B. Each observation wa s displayed on a slide indicating thespecim ens region and whether it wa s light or dark.Procedure

The subjects task wa s to determine whether and to wha t extent Rhododipsia regionand color were related to each other. The y we re informed that the basis for theirjudgme nts would be the results of a random sampling of Rhododipsia specim ens. Thesubje cts, who served in non-interacting groups o f three to f ive individuals, were thenshow n practice slides il lustrating all four types of specim ens that might be observed.The subjec ts were requested to pay close attention to the slides the y would see, but tonot keep written records. At the end of the experime nt, the subjec ts were a sked to recallhow many Rhododipsia from e ach region and of each color they had been show n. Ha lfthe subjec ts were forewarned of this recall tes t, while the remaining subjec ts were not.

Fig. la is a contingency table describing the distribution of Rhododipsia shown tothe subje cts. As is apparent, over the entire seque nce of Rhododipsia slides, there wa sno contingency between region and color. The comp lete slide sequence actuallyconsisted of two blocks of slides. Fig. lb sh ows the distribution of Rhod odipsia,typescontained in Block 1, which implies a contingency whereby light-colored plants tended


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Q) Overal l Distr ibution: No ContingencyREGIONA 0

LightCOLOR

Dork

b) Block I Distr ibution: Light-A ContingencyREGIONA 01

COLOR

c) Block 2 Dlstr ibutlon. Light-B ContingencyREGION

COLORLight

Dark

A B2 5

Ct5 2

Fig. 1. Distributions of fictitious Rhododipsia plants according to region and color$a) overall, (b)Block 1, (c) Block 2.to be relatively more comm on in Region A. The distribution of Rhododipsia typescontained in Block 2 is shown in f ig. lc. The contingency evident in Block 2 wa s exac tlyopposite in direction and strength to that indicated in Block 1. The presentationsequence of slides in Block 1 wa s random . The slide seq uence in Block 2 wa sisomorphic to the Block 1 sequen ce. Using letters corresponding to the cells show n intable 1, the transformation wa s: A + B, B + A, C --j D, D -+ C. That is, an observationbelonging to Cell A wa s replaced by one belonging to Cell B, one belonging to Cell Bwa s replaced by one belonging to Cell A, and so on. Half the subjects saw the slides inthe order Block l-Block 2; the others were exposed to the slides in the opposite order.

The design of the experiment wa s thus a 2 X 2 factorial. The f irst fac tor wa s whetheror not the subject wa s forewarned of the impending recall tes t. The second w as definedby the order of slide blocks .

After being sh own all the specime n slides, each displayed for 4 set, subjec ts reportedtheir judgme nts in written form . Inferred co ntingency judgme nts were derived fromresponse s to two condit ional probability questions . The subject wa s asked : Suppose aRhododipsia plant is from Region A. Wh at is the chance that it is Light in color rather


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J.F. Yates, S.P. Curley / Primacy and contingency judgm ent 299than Dark? The s ubject w as told that he or she should report 100% if you areabsolutely sure the plant would be Light, and 0% if you are absolutely sure the plantwould NO T be Light. Similar instructions defined the meaning of 50% and otherintermediate respon ses. A parallel question requested the subjects judgment of thechance that a plant would be light if it had been found in Region B.Subjects were also asked to indicate how strongly related, if at all, they felt thatRhododipsia region and color were. The y did so on a 0 to 6 scale, on which 0 mea ntthat the two features are com pletely UN RE LAT ED to each other, while 6 impliedthat they are PER FEC TLY related to each other. Whe n the rating wa s anything otherthan 0, the subject also reported the direction of the perceived relationship.

The mem ory task was the f inal one performed by the subjects. Each indiv idualcomp leted a contingency table by entering the numb ers of plants of each type recalledto have been shown in the slides.

Results and DiscussionFor each subject, the following inferred judged contingency index

was derived: A = P (Light 1Region A) - P (Light 1Region B), whereP indicates a judged rather than an objective probability. Fig. 2displays the mean value of A, as a function of slide presentation orderand recall test warning.

An analysis of variance concerning A was performed on differencesin P (Light 1Region A) and P (Light 1Region B) after these probabil-ity judgments were subjected to appropriate variance-stabilizing arcsinetransformations. As hypothesized, when subjects were not forewarnedof the recall test, a primacy effect was evident. The mean of A wassignificantly higher when the block of slides containing a Light-Acontingency was presented first rather than second (J(1, 125) = 14.78,p < 0.001). As expected, according to the attention decrement proposi-tion, there was not a significant primacy effect in the judgments ofsubjects who were forewarned of the recall test (F(1, 125) = 1.12, ns);the interaction of the warning and order factors was marginally signifi-cant (F(1, 125) = 3.76, p -c 0.06).

The mean relatedness ratings of subjects in Warning and No-Warn-ing conditions were 2.19 and 2.42, respectively. Although this differenceis consistent with expectations, it is not statistically reliable (I: < 1).The fact that subjects explicit relatedness judgments do not agree withthe judgments inferred from their conditional probability assessments iscompatible with previous results (cf. Beyth-Marom 1982). Those studiesimply that, although subjects have the capacity to report proper con-


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300 J.F. Yates, S. P. Curley / Primacy and contingency judgm ent

10.15

0.10 II

0.05-b5 0.00 -

s-0.05-

o Warning-------l No Warning

.

I ILight-A First Light-A SecondPRESENTATION ORDER

Fig. 2. Mean inferred judged contingency index, A = P (Light 1Region A)- P (Light 1Region B),as a function of presentation order and recall test warning.

tingency judgments, they fail to do so because their subjective notionsof relatedness often disagree with the accepted statistical concept.

The accuracy of subjects recollections of the frequencies of slidesshowing Rhododipsia of various origins and colors were indexed by thefollowing score:

S=CIf-71,where f represents the estimated frequency reported by the subject foreach cell in the Rhododipsia region-color contingency table, and thesummation is over all cells. The mean of S was 6.31 for subjects in theWarning conditions, and 7.52 for those in the No-Warning conditions.The observed difference is in the expected direction, but not statisticallysignificant. It might also be noted that the subjects were generally quiteaccurate in estimating the total number of slides they saw. The meansum of f was 28.05 in the Warning conditions, and 27.32 in theNo-Warning conditions. These means did not differ significantly from28, the actual total number of slides, or from each other.


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J.F. Yates, S.P. Curley / Primacy and contingency judgm ent 30 1

Over the entire sample of specimens shown to each subject, Rhodo-dipsia color and region were completely unrelated. However, if thesubject only considered the first half of the sample, that subsamplewould in fact support a color-region contingency. So a legitimatequestion to ask is whether, after seeing the first half of the sample, itwas appropriate for the subject to have decided that a contingencyexisted, and therefore stop paying attention to additional sample infor-mation. To gain some sense of the reasonableness of such an action, thecontingency of Rhododipsia region and color, based on either of thesingle-block distributions shown in figs. lb and lc, was tested accordingto standard statistical procedures. The resulting (corrected)x2 statisticwas 1.14, which is far from conventionally acceptable levels of statisti-cal significance. That is, a contingency judgment based on only the firsthalf of the available information would seem to be a hasty judgment.

In summary, it does indeed appear that contingency judgments aresubject to primacy effects. The present data also imply that theseprimacy effects are due to attention decrement; the law of smallnumbers reaches into yet another quarter. Besides being of interest inthemselves, these conclusions offer initial hypotheses for why otherpuzzling phenomena occur.

Investigators have been struck by the lack of agreement in thejudgment policies of different people - including experts - operating inthe same domains. For example, Hoffman et al. ,(1968) studied hownine gastroenterologists made ulcer malignancy judgments on the basisof seven cues discernible from X-rays, e.g., ulcer contour and thepresence of related ulcers. These specialists differed markedly in theirreliance upon the various indicators. The observed policy differencesseemed to be a major cause for the low interjudge agreement; themedian correlation between the diagnoses of pairs of physicians wasonly 0.38. It is conceivable that the types of primacy effects observed inthe present study contribute to such policy differences. Natural sam-pling mechanisms imply that small samples of cases can differ from oneanother substantially with respect to the contingencies between ulcercharacteristics and their malignancies. When neophyte physicians beginlearning to diagnose malignancy, the present results suggest that theymight be overly (and permanently) influenced by the chance con-tingencies observed in the first few cases they consider. A plethora ofdivergent judgment policies would result.


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Primacy effects and attention decrement