The role of logical and nonlogical factors in making inferences about category membership

JOURNAL

OF EXPERIMENTAL

SOCIAL

13, 517-595 (1977)

PSYCHOLOGY

The Role of Logical and Nonlogical Factors in Making Inferences about Category Membership ROBERTS. University

WYER,JR. of Illinois

Received July 28, 1976 Three postulates are proposed concerning the manner in which persons infer the validity of propositions that do not necessarily follow logically from the information available. These postulates assume that subjects first attempt to identify the propositions that are most and least likely to follow from the information given. They then use their beliefs in these propositions as anchors, relative to which the validity of other propositions is evaluated on the basis of both logical and nonlogical criteria. Two experiments are reported in which these postulates are used successfully to diagnose the logical and nonlogical factors that underlie inferences based upon both single statements and sets of syllogistically related propositions. The implications of the proposed postulates for existing formulations of social inference and cognitive organization are discussed.

Persons frequently infer the validity of general propositions about their social environment (“businessmen are Republican,” “college students smoke marijuana”) on the basis of information that bears upon them. In some instances, these inferences are the result of syllogistic reasoning. For example, a person may infer that “businessmen are Republican” on the basis of information that businessmen oppose a strong central government and that persons who oppose a strong central government are likely to be Republican. In other cases, such an inference may be inductive, based upon information about specific instances of the relation to be evaluated (for example, information that a particular subgroup of businessmen belongs to a particular Republican political organization). The role of both types of reasoning in social inference, attribution, and opinion change has been studied extensively (in the case of syllogistic reasoning, see McGuire, 1960; Wyer, 1974a, 1975b, 1976; in the case of inductive reasoning, see Abelson & Kanouse, 1966; Kanouse, 1971; Podeschi & Wyer, 1976; Wyer & Podeschi, in press). However, while this research has been productive, it has had one serious limitation: It has concentrated almost exclusively on This research was supported by National Science Foundation Grant No. SOC73-05684. Appreciation is extended to Marcia Gale, Ronald Hinkle, and Marilyn Henninger for assistance in various phases of the research. Requests for reprints should be sent to Robert S. Wyer, Jr., Department of Psychology, University of Illinois, Champaign, Illinois 61820.

577 Copyright 0 1977 by Academic Press, Inc. All rights of reproduction in any form reserved.

ISSN WZZ-1031

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S. WYER,

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the effect of information upon judgments of propositions that follow logically on the basis of formal principles of deductive and inductive inference. Yet, it is obvious that persons often accept propositions that do not follow logically from the information they receive. For example, while information that logically implies that businessmen are Republican may affect one’s belief in this proposition, it also may affect his belief that nonbusinessmen are not Republicans, or that Republicans are businessmen. These effects may occur in part because the person invokes certain auxiliary assumptions not directly implied by the information presented (e.g., he may assume that if businessmen are Republicans, then nonbusinessmen, who are antagonists of businessmen, are unlikely to be Republicans). However, they may also occur because the person applies certain nonlogical criteria that lead him to regard propositions as more or less equivalent in meaning, independent of the particular types of objects to which they pertain. General formulations of cognitive functioning must ultimately be able to identify and take into account the contributions of these nonlogical criteria. The research reported here is a first step in the pursuit of this objective. First, we propose a set of postulates concerning the process of evaluating propositions that do not necessarily follow from the information available. The validity and generalizability of these postulates are then evaluated in two experiments. The second of these provides an example of how the postulates can be incorporated into an existing formulation of social cognition, specifically, the syllogistic model developed by McGuire (1960) and extended by Wyer (1975b). The postulates we propose to describe the process whereby persons evaluate the validity of propositions are similar to those outlined in an earlier paper (Wyer, 1975b), but eliminate several conceptual ambiguities in this earlier analysis. Here, we will restrict our attention to propositions Other about class membership (e.g., “businessmen are conservative”). types of relations are undoubtedly of interest, and the factors that underlie the acceptance of generalizations about them may often be similar to the ones to be proposed here. However, the extent of this similarity will be a matter for further study. Suppose that information is available about two general categories of objects, X and Y. Eight possible propositions about membership in these categories might be evaluated on the basis of this information: X are Y, X are r(not

Y), ~(non-X)

are Y, Rare

y, Yare X, Yare&

FareX,

and Bare

R. Although certain of these propositions seem contradictory, note that all could be true with some likelihood if the implicit quantifier assigned to each subject category is not universal (for example, if X are Y is interpreted as meaning that only some X are Y). When a person is asked to judge the validity of any one of these alternative propositions, it seems likely that he will first reflect upon the information available to him (either new

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information presented in the immediate situation or information acquired in the past) that pertains to X and Y and will identify the propositions he believes are most and least likely to follow from this information. Presumably, these propositions are contradictories (e.g. ,Xare Y andXare nor Y). He will then estimate the validity of these propositions. Once this is done, the judge may infer the validity of other propositions about X and Y (such as the one he is specifically asked to evaluate) by comparing them to these standard, or “anchor,” propositions. The bases for these comparisons will be considered presently. First, however, let us restate the hypothetical process described above more formally: Postulate I. When a person is asked to evaluate a proposition about the relation between two categories, he will Jirst identify the conclusions he believes are most and least likely to follow from the information available. The perceived validity of these conclusions will then serve as positive and negative anchors (A+ and A-), respectively, relative to which the validity of the proposition to be evaluated is compared. Thus, if the information available is believed most likely to imply that X are Y. the judge’s beliefs in this proposition and its contradictory (X are ?) would serve as positive and negative anchors, respectively. The next question concerns the criteria for comparing the validity of alternative propositions to these anchors. First, note that of the eight possible propositions concerning the relation between membership in X and membership in Y, four (X are Y, Y are X, 8 are y, and Pare 8) are symmetric; that is, the subject and predicate are either both positive (X and Y) or both negative (2 or 9). The remaining four (X are y, Fare X, x are Y, and Y are 8) are asymmetric; that is, one element is negative but the other is not. Note also that the two anchor propositions differ in symmetry; if one is symmetric, the other is not. Thus, the eight propositions can be divided into two sets offour, one set having the same degree of symmetry as the positive anchor proposition, and the other set having the same degree of symmetry as the negative anchor proposition. The following, “symmetry” postulate is, therefore, suggested: Postulate 2. A person willjudge a proposition to be similar in validity to an anchor proposition if its degree of symmetry is the same as that of the anchorproposition. Thus, ifXare Y is the positive anchor proposition, the propositions X are Y, Y are X, y are y, and y are x’ will be judged as similar to it in validity, and thus as relatively likely to be true, whereas the remaining positions (X are F, Y‘ are X, etc.) will be judged as similar in validity to the negative anchor proposition, and thus as relatively unlikely to be true. While the above postulate may initially appear somewhat arbitrary, it is plausible in light of two considerations. First, Woodworth and Sells (1935)

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reported evidence that statements containing similar elements will be judged as similar in validity; for example, X are Y and Y are X should be judged similarly, as shouldxare Band pare 8(for additional evidence that subjects tend to treat such statements as equivalent, see Chapmen & Chapman, 1959). Second, note thatX are Y and Bare 8 have similar logical implications: the greater the proportion of members of X that belong to Y, the more likely it is that nonmembers of Y do not belong toX. (IfX were a subset of Y, thenall nonmembers of Y would not belong toX.) To the extent that judges take these two factors into account, Postulate 2 should follow. The second postulate divides the eight alternative propositions into two subsets of four, such that each proposition in one subset is judged more likely to be true than any conclusion in the other subset. Thus, let Pij represent a person’s estimate of the likelihood that the proposition i arej is true. Then, suppose that the positive and negative anchor propositions are X are Y and X are Y, respectively. Postulate 2 then implies the following inequality: Pxy + Pyx + P,, + P,

> P,,

+ Piy + P,

+ P,,

(1)

The final question concerns the criteria that persons use to infer the validity of propositions within each subset distinguished on the basis of Postulate 2. Two criteria have already been suggested: the similarity in Logical implications of each proposition to the anchor proposition with which it is compared and the similarity of the elements contained in the proposition to those in the anchor proposition (content similarity). A third criterion may be the similarity in form between the anchor proposition and the one being evaluated, that is, whether the subject and object of the proposition to be evaluated pertain to the same categories as do the subject and object of the anchor proposition, respectively. (For example,xare Fis similar in form to the anchor X are Y, whereas Y are X is not.) Thus, once the anchor to which a given proposition is to be compared has been identified (see Postulate 2), the following postulate may apply: Postulate 3. A person will judge a proposition to be similar in validity to the anchorproposition with which it is compared to the extent it is similar to the anchorproposition in (a) content, (b) logical implications, and (c)form.

Although this postulate is limited in its a priori predictive utility, it suggests a means of isolating the effects of different logical and nonlogical criteria upon which judges’ inferences may be based. Suppose thatX are Y and X are ? are the positive and negative anchor propositions (A+ and A-), respectively. To the extent that persons base judgments of the validity of alternative propositions upon their similarity in content to the anchor propositions, they should judge the propositionsX are Y and Y are X to be similar in validity to A +, and thus to be more valid on the average than 8 are p and Fare X. However, they should judgeX are r and Bare X

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581

to similar in validity to A - , and thus to be less valid on the average thank are Y and Y are 8; that is, Pxy + Pyx > Pg + P,

and Pxp + P;, < Pjy + P YX.-

Combining these inequalities, an overall contribution of content similarity can be assessed from the magnitude of the following inequality: Pxy + Pyx + Piy + P,

> P,, + P,

+ Pxu + P,.

(2)

Similar reasoning implies that the extent to which judgments of propositions are based on their similarity in logical implications to the anchor propositions can be inferred from the magnitude of the inequality: Pxy + P,

+ P;y + P,

> P;y + Pyx + Pxv + P,.

(3)

Finally, the extent to which judgments are based on similarity in form to the anchor propositions can be inferred from the magnitude of the inequality: Pxy + Pjy + P,

+ P,

> Pyx + P,

+ Pxp + Pxy.

(4)

Thus, in combination, Postulates 1-3 help to conceptualize the manner in which both logical and nonlogical criteria may contribute to persons’ evaluations of propositions on the basis of the information available to them. The propositions also have methodological implications. Note that the contrasts hypothesized to reflect the contributions of symmetry (Eq. I), TABLE

I

TABULATION OF EIGHT PROPOSITION TYPES AS A FUNCTION OF THE ANCHOR TO WHICH THEY ARE HYPOTHETICALLY COMPARED AND SIMILARITY IN FORM AND CONTENT TO THESE ANCHORS

Similar in content

Dissimilar in content

Statements compared to A +

Statements compared to A -

Similar in form

Dissimilar in form

Similar in form

X are Y (similar to A+ in form, content, and logical meaning)

Y are X (similar to A + in content only)

Xare P (similar to A- in form, content, and logical meaning)

P are X

fare

I are X

X are Y

YareX (similar to A - in logical meaning only)

I

(similar to A + in form only)

(similar to A + in logical meaning only)

(similar to A - in form oW

Dissimilar in form (similar to - in content only)

A

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S. WYER,

JR.

content similarity (Eq.2), similarity in logical implications (Eq. 3) and form similarity (Eq. 4) are orthogonal. This can be seen from Table 1, where the alternative propositions hypothetically compared to each anchor are tabulated as a function of content similarity and form similarity. Suppose judgments of each proposition are organized in the manner described in this table, and an analysis of variance is performed on these judgments as a function of anchor (A + vsA -), content similarity, and form similarity. The main effect of anchor reflects the magnitude ofthe contrast described in Eq. (1). The interaction of anchor and content similarity (which indicates the extent to which propositions similar to A+ are judged more valid, and conclusions similar to A -less valid, than propositions that are dissimilar to these anchor propositions) reflects the magnitude of the contrast described in Eq. (2). The interaction of anchor and form similarity reflects the magnitude of the contrast described in Eq. (4). Finally, the three-way interaction of anchor, content similarity and form similarity corresonds to the contrast defined in Eq. (3), and therefore reflects the effect of similarity in logical implications. (The contributions of each factor to judgments of statements compared to each anchor separately can of course also be isolated.) The heuristic value of the approach is further enhanced by the fact that once the relative contributions of similarity in form, content, and logical implications are known, one can theoretically predict the rank order in which each alternative proposition will be accepted. This possibility will be considered in more detail presently. The present paper presents two studies. In the first experiment, Postulates l-3 were evaluated under conditions in which the identity of the anchor propositions are clear on a priori grounds. Based upon the results of this study, predictions were made concerning the effects of information bearing upon premises of syllogisms to which the McGuire- Wyer syllogistic model of cognitive functioning (McGuire, 1960; Wyer, 1974a, 1975b) is often applied. The design of this latter study permitted the validity of anchor propositions to be varied systematically, thus enabling the effects of variation upon the acceptance of alternative propositions to be investigated. EXPERIMENT

1

To construct conditions in which there was minimum ambiguity concerning the identity of the positive and negative anchor propositions, subjects were asked to make inferences based upon single statements of the form X are Y. In each case, they were told to assume that each stimulus proposition was definitely true, and then to infer, on the basis of this proposition, the likelihood that each of eight alternative “test” propositions about members (or nonmembers) of X and Y was true. The stimulus

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proposition itself, which was identical to one of the conclusions to be evaluated, was assumed to function as the positive anchor proposition. Method Materials were constructed in four stimulus domains. Each set of materials was administered to a different group of 16 introductory psychology students untrained in formal logic. The procedure for constructing and presenting materials was similar in each domain. A series of either four or eight stimulus propositions was presented. The order of presentation varied over subjects so that each proposition occurred the same number of times in each serial position. In Domain 1, the categories described in stimulus and test propositions were designated by letters of the alphabet. Four single stimulus propositions pertained to membership in two hypothetical groups, A and B. These items were of the formA are B (specifically, “members of A are members of B”), A are B (“members of A are not members of B”), A are B (“nonmembers ofA are members ofB”), and A are B (“nonmembers ofA are not members of B “). The eight response items to be evaluated on the basis of each stimulus proposition were (in - the - order they were presented) ofthe formA are B, Bare A. B are A, A are B, Bare A, Bare A, A are B, and A are B.

In the other three domains, stimulus and response items pertained to categories of objects with which subjects were familiar. Two replications were constructed in each of these domains. In Domain 2, the two propositions denoted A ure B were “collies are dogs” and “dogs are animals”; in Domain 3, they were “businessmen are conservatives” and “conservatives are Republicans,” and in Domain 4, they were “women’s liberationists are apathetic persons” and “apathetic persons are troublemakers.” The eight alternative test propositions to be judged on the basis of each stimulus proposition were analogous to those in Domain 1. The three domains were expected to differ primarily with respect to subjects’ a priori beliefs that the stimulus proposition denoted A are B was true. Specifically, this proposition was expected to be considered definitely true in Domain 2, probably true in Domain 3, and unlikely to be true in Domain 4. Procedure. Subjects were presented each stimulus proposition in turn. In each case, they were told to assume that the proposition was definitely true, and then to estimate, on the basis of this information, how likely it was that each of the eight test propositions was true. These latter propositions were presented in a random order following the stimulus proposition; this order was the same for each stimulus item. Judgments were recorded along an 1 l-category scale from 0 (not at all likely) to 10 (extremely likely). For ease in interpreting these judgments. they were divided by 10 prior to analyses to convert them to units of subjective probability.

Results In Domains 2, 3, and 4, judgments of corresponding test propositions were averaged over stimulus replications to provide a single judgment of each type of proposition under each stimulus condition. Judgments were then relabeled to conform to the notation used in Eqs. (l)-(4) by IettingX represent the subject of the stimulus item (A orA) and letting Y represent its predicate (B or B). Thus, the specific item to which a given judgment pertains (e.g., Pxv) depends upon the particular stimulus item presented. However, in each case, judgments of the conclusions assumed to function as positive and negative anchor propositions are denoted Pxy and Pxy, respectively.

584

ROBERT S. WYER. JR. TABLE MEAN

JUDGMENTS

Type of stimulus item A A A A

is is is is M

B B B B

OF CLASS

MEMBERSHIP

2 BASED

UPON

SINGLE

STIMULUS

ITEMS

P XY

PYX

pi%

Pi;

PiY

PYi

p,

px;

.933 .928 ,919 903 ,921

.741 .679 ,653 .751 ,706

.664 ,717 ,598 ,660 ,660

.611 ,629 .626 ,704 .642

.416 ,438 .296 .363 .378

,416 ,365 ,362 .375 ,380

.319 .292 .428 .425 .366

,181 .186 ,225 .264 .214

Judgments of the eight test propositions are shown, averaged over stimulus domains, in Table 2. The contributions of the factors identified in Postulates 2 and 3 were estimated by subtracting the mean of the judgments to the right of each inequality in Eq. (l)-(4) from the mean ofthe judgments to the left of the inequality. The magnitude of these contributions, averaged over stimulus domains, is shown in Table 3 for each type of stimulus item. To investigate the significance of each contribution and its contingency upon the type of stimulus proposition and the domain involved, the eight test propositions were first organized in the manner suggested by Table 1. An analysis of variance was then performed on judgments of these propositions as a function of the anchor proposition to which the proposition being judged was theoretically compared, the content similarity of this proposition to the anchor proposition, its form similarity to the anchor, the subject of the stimulus item (A orA), and the object ofthe stimulus item (B or B). The contrasts of primary relevance to Postulates l-3 correspond in this analysis to the main effect of anchor (Eq. 1) and the interactions of anchor with content similarity (Eq. 2), with form similarity (Eq. 4), and with both content and form similarity. (The latter, triple interaction contrast reflects the contribution of similarity in logical TABLE MEAN

CONTRIBUTIONS BASED

OF RESPONSE Upon SINGLE

3

ITEM CHARACTERISTICS STIMULUS PROPOSITIONS

TO JUDGMENTS

Type of stimulus item Response item characteristic Symmetry (Eq. 1) Similarity in content (Eq. 2) Similarity in logical implications (Eq. 3) Similarity in form 0%. 4)

A are B

A are B

A are B

A are B

M

,404

.418

,372

,398

,398

,183

,146

,088

,085

.126

.096

,129

.094

,064

.O%

,069

,048

,141

,092

.088

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implications; see Eq. (3).) The results of this analysis are described below in the context of the issues of concern. Postulate I. Pxu was greater than any other judgment at all 16 combinations of stimulus proposition type and stimulus domain, while Px? was less than any otherjudgment in 15 of these 16 cases. These datajustify the assumption thatxare Y andXare Yfunctioned as positive and negative anchor propositions, respectively. Postulate 2. The mean judgment of propositions hypothetically compared to the positive (A +) anchor was consistently greater than the mean judgment of propositions compared to the negative (A-) anchor (mean difference = .398, F(1,60 = 189.96, p < ,001). The magnitude of this difference was not significantly contingent upon either domain or the nature of the subject and object of the stimulus item (in each case, F(1,60) -C 1.26). Moreover, Table 2 shows that the two sets of judgments differentiated on the basis of Postulate 2 are virtually nonoverlapping. This was also true when data pertaining to each domain were considered separately; in only 2 of 256 instances (16 comparisons pertaining to each of 4 types of stimulus proposition in each of 4 domains) was the mean judgment of a proposition hypothetically compared to A + less than that of a proposition hypothetically compared to A - . Postulate 3. The effects of similarity to anchor propositions in content, form, and logical implications were each significant, F(1,60) > 64.23, p < .OOl, and were not significantly contingent upon stimulus domain, F(3,60) < 2.20,~ > . 10. Ingeneral, similarity in content contributed most, followed by similarity in logical implications and then similarity in form. Supplementary analyses revealed that each factor contributed more to judgments of test propositions that were hypothetically compared to the positive anchor proposition than to judgments of those hypothetically compared to the negative anchor proposition; this difference was significant (p < .05) in the case of content similarity and similarity in logical implications but not in the case of form similarity. Other contingencies should also be noted. First, the effect of all three factors depended (p < .05) upon whether the subject of the stimulus proposition was positive or negative. Specifically, similarity in content to A + had substantial effect regardless of the subject of the stimulus item, but similarity in content to A - had an appreciable effect only when the subject was positive. Similarity in logical implications also had greater effect when the subject was positive f.112) than when it was negative (.079), while similarity in form contributed less in the former condition (.058) than in the latter (. 116). Predictions of rank order ofjudgments. If Postulate 2 is valid and if the relative contributions of the three factors identified in Postulate 3 are determined, the rank order in which test propositions are accepted as valid should be predictable. Note from Table I that of the four propositions hypothetically compared to each anchor, one is identical to the anchor

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ROBERT S. WYER. JR

proposition while the others are similar to it in one and only one way. Thus, if similarity to an anchor in content contributes most to judgments of a proposition’s similarity in validity to the anchor, followed by similarity in logical implications and then similarity in form (see Table 3), then among the four propositions compared to A + ,X are Y (the proposition identical to A+) should be judged most valid, followed in order by Y me X (the proposition similar to A + in content), p are R (the proposition similar to A + in logical implications), and then x are p (the anchor similar to A + in form). Moreover, of the propositions compared to A -, X are y should be judged least valid, followed in order by Fare X, Y are 8, anddare Y. These predictions are summarized in the following inequality: Pxy > Pyx > P,

> P,; > P,, > P,

> P,

> P*u.

(5)

This rank ordering is a necessary implication of the assumption that content similarity contributes most to judgments, followed by similarity in logical implications and then form similarity. While the data described above indicate some contingencies in the validity of this assumption, it is nevertheless of interest to determine the extent to which this rank ordering, which is based upon data averaged over stimulus conditions, is able to predict the relative judgments of test propositions within each stimulus condition considered separately. Equation 5 predicts the direction of 28 possible paired comparisons between judgments of the eight test propositions. The number of times that the actual mean difference between two judgments was in the same direction as the predicted difference was determined for each of the 16 combinations of stimulus proposition type and stimulus domain. Actual differences were in the direction implied by Eq. (5) in 402 and 448 instances (90.1%). When comparisons involving P,, and P,y (i.e., judgments of items identical to the anchors) are eliminated from consideration, the equation still predicted correctly in 197 of 240 cases (82.1%). This accuracy could, of course, be increased further if contingencies in the contributions of the three factors upon the type of stimulus item were taken into account.’ EXPERIMENT

2

In Experiment 1, the proposition assumed to serve as the positive anchor was identical to the stimulus proposition, and therefore was typically ’ If the response scale used by subjects is interval, a more rigorous test of the generality of the formulation is possible. That is, knowledge of the contributions of each of the factors identified in Postulates 2 and 3 theoretically enables the relative magnitudes of the judgments of the eight test propositions to be positioned along a scale bounded by the judgments of the two anchor propositions (A + and A -). Therefore, ifjudgments of the two anchor propositions under any given stimulus condition are known, point predictions may be made ofjudgments of alternative test propositions under this condition. While this possibility was not investigated in the present study, it may be worth pursuing in future research in which Postulates l-3 are applied.

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judged to be true with a likelihood approaching unity. In more realistic situations, where the information available is usually more complex and its implications are more equivocal, this is unlikely to be the case. However, if Postulates l-3 are valid, factors that affect the strength ofjudges’ beliefs in the proposition they consider most likely to follow from the information available should also have predictable effects on their beliefs in alternative propositions. For example, suppose that similarity in content has the greatest influence upon judges’ evaluations of test propositions, followed by similarity in logical implications and then similarity in form. Then, ifX are Y is the proposition judged most likely to follow from the information presented, factors that affectjudges’ beliefs in this proposition (Pxu) should also have an effect, similar in direction but less in magnitude, upon their beliefs that Y are X (Pyx) that Pare R (Py,& and that R are P (P&. The relative magnitudes of these effects should be predictable from Eq. (5). Moreover, the factors that change P xy should also change beliefs in the negative anchor proposition (Px;) in the opposite direction, and similar, although less pronounced, changes should occur in beliefs corresponding to P,, P,, and Pjy. A convenient paradigm for exploring these possibilities is that typically used to test the syllogistic model of cognitive functioning proposed by McGuire (1960) and extended by Wyer (1974a, 1975b). This model has the general form Pb

=

pap,,,

+

PtiPbki,

(6)

where a and b are two propositions, Pb is the belief that b is true, P, and Ph are beliefs that a iS and is not true, respectively, and P,%,,aand Pb,, are conditional beliefs that b is true ifa is and is not true, respectively. In effect, this model describes the relation between beliefs in a conclusion (b) and beliefs in two mutually exclusive sets of premises [a; ifu, than b J and [not-u; if not-u, then b 1, each of which, if true, would imply this conclusion. Specifically, the model implies that if information has independent effects upon ajudge’s belief that a is true (P,) and his belief that a implies b (P&a), it will have multiplicative effects on his belief in b; (Pb); that is, Pb should increase with Pb,a; moreover, the increase should be greater when P, is high than when it is low. Similarly, if information affects a judge’s belief in a and his belief that b is true if a is not true (P&, it should also have multiplicative effects upon his belief in b; specifically, P, should increase with Pb,,, but in this case, the increase should be greater when P, is low (or P, is high) than when P, is high (P, is low). Previous research has consistently supported these predictions (Wyer, 1970, 1975a, 1976). If Eq. (6) is a valid description of the manner in which syllogisticallyrelated information combines to affect beliefs in b, this information should also affect beliefs in propositions other than b in a manner implied by Postulates 1-3. For example, if b is a proposition of the form X are Y, the information should not only affect the belief in this proposition, but also

588

ROBERT S. WYER. JR.

beliefs that Y are X, that8 are F, etc. Moreover, these effects should differ in relative magnitude in a manner implied by the results of Experiment 1. The present experiment investigated these possibilities. Method Overview. Subjects were 64 introductory psychology students who participated in the study to fulfill a course requirement. Sixteen subjects received materials pertaining to each of the four stimulus domains constructed for use in Experiment 1. In each domain, subjects received 18 sets of statements that were designed to establish all possible combinations oftwo levels of P,, three levels of P,,, and three levels of Pbiti, as these beliefs are defined in Eq. (6). In each case, b was a proposition of the formX are Y. On the basis of each set of statements, subjects inferred the validity of b, followed by the validity of each of the other seven test propositions to which Postulates l-3 pertain. This design allowed the effects of informational manipulations upon judgments of the logically implied conclusion and also other propositions to be determined, and enabled the contributions to these judgments ofthe factors postulated in Postulates l-3 to be isolated. Preparation of stimulus materials. Sets of stimulus statements were prepared in a manner analogous to that used in other recent studies in which the implications of Eq. (6) have been investigated (Wyer, 1975a, 1976). Within each stimulus domain, 18 sets of statements were constructed, each corresponding to a different combination of P, (high or low), P*,, (high, moderate, or low) and Pbis (high, moderate, or low). Each of these probabilities was manipulated through the use of the adverbs usually, sometimes, and rarely to describe the likelihood of the relation of concern; these three adverbs were selected on the basis of normative data(Wyer, 1975a) which indicate that they convey probabilities of .81, .44, and .16 when applied to hypothetical relations among persons and objects. The stimulus statements presented in each domain were of the same general form. In Domain 1, where abstract categories were used, the statements used to convey different levels of pa, Pm, and Pbia were, respectively:

Members of group A usually (rarely) belong to group B If members of group A belong to B, they usually. (sometimes. rarely) If members of group A do not belong to B, they usually (sometimes, group C.

belong to group C. rarely) belong to

The eight test propositions evaluated on the basis of each set of stimulus statements pertained to the relation between membership in A and membership in C (that is, the likelihood that a member ofA was a member of C, that a nonmember ofA was not a member of C, etc.) These propositions were presented in the same order for each stimulus set. Specifically, the proposition equivalent to b in Eq. (1) (i.e., members of A are members of C) was presented first, followed in order by propositions corresponding to C are A, care A, ii are c, Care A, c are 6, d are C, and A are c. Stimulus propositions in the other three domains were constructed similarly. In Domain 2, the categories corresponding to A, B, and C were “collies,” “dogs,” and “animals”; in Domain 3, they were “businessmen,” “conservatives,” and “Republicans,” respectively, and in Domain 4, they were “women’s liberationists,” “apathetic persons,” and “troublemakers,” respectively. Thus, in Domain 2, the three stimulus statements were ofthe form: Collies are usually (rarely) dogs. If collies are dogs, they are usually (sometimes, rarely) animals. If collies are not dogs, they are usually (sometimes, rarely) animals.

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The propositions evaluated on the basis of these statements were then “colhes are animals,” “animals are not collies,” etc. Stimulus and test propositions in the other two domains were analogous. Each set of stimulus and response items was typed on a separate page ofthe questionnaire. The 18 pages were then arranged in a different order for each subject in such a way that averaged over subjects, the mean serial position of each stimulus set was roughly the same. Procedure.Judges were introduced to the study with instructions that its purpose was to find out how persons estimate the likelihood of different events on the basis of verbal information about them. They were told to read the three statements at the top of each page and then, based upon this information, to estimate the likelihood of each of the eight propositions following it. These judgments were recorded along an 1l-point scale from 0 (not at all likely) to 10 (extremely likely), and were divided by 10 prior to analysis to convert them to units of subjective probability. Results

The syllogistic model described by Eq. (6) predicts four effects of informational variables on beliefs in 6 (or in this case, the belief that X are Y). Specifically, beliefs inb should increase with the manipulated values of bothI’*,, andP,,,; however, the first effect should be greater when P, is high than when it is low, while the second should be greater when P, is low than when it is high. The effects of these variables on beliefs in the contradictory of b, orX are Y, should be analogous, except that in this case, the effect of each conditional belief should be negative rather than positive. Finally, if Postulates 1-3 are valid, beliefs in the validity ofXare Y andXare Bshould serve as anchor propositions relative to which the validity others are compared and evaluated on the basis of criteria specified in Postulate 3. (Incidentally, whileXare Y andXare p were anticipated to serve as the two anchor propositions, which of these conclusions is most likely to follow from the information given depends upon the implications of this information. Thus, to avoid confusion, we will refer to these anchors by the specific proposition to which they pertain, rather than as “positive” or “negative.“) Three orthogonal analyses were performed. First, to determine the effect of the anchor per se (Postulate 2), judgments of the four conclusions hypothetically compared to each anchor were averaged and then analyzed as a function of the three manipulated informational variables (P,, Pbla, and Pelti>, anchor proposition (Xure Y vsXure Fj and stimulus domain. Figure 1 shows the interactive effects of (a) P, and Pbta and (b) Pa and PO,; on the mean judgment of test propositions compared to each anchor. Each interaction was significant, F(2,120) > 58.19, p < .OOl, and of the nature expected. Therefore, these data support not only the assumption that Eq. (6) is a valid description of how subjects combine the information presented to arrive at judgments under the conditions constructed in this study, but also the assumptions underlying Postulate 2.

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The interactive effects of informational variables on judgments of each of the four propositions hypothetically compared to each anchor were similar in form to the overall effects described in Fig. 1. However, the magnitude of these effects differed. If the results of Experiment 1 generalize to the present study, similarity to the anchor in content should contribute most to judgments of test propositions, followed by similarity in logical implications and then similarity in form. To investigate this matter, judgments of propositions compared to each anchor were analyzed separately as a function of the three informational manipulations (P,, Pbla, and Pb,;), the content similarity of the proposition being judged to the anchor, and the form similarity of the proposition being judged to the anchor. The contribution of each factor to judgments of propositions compared to a given anchor may be inferred from the sum of squares associated with its interaction with each combination of informational variables predicted to affectjudgments on the basis of Eq. (6) (specifically, Pbia,P,,;, P,, and Pbiain combination, and P, and PO,; in combination).2 The sums of squares accounted for by these interactions are shown in Table 4. The relative contributions of similarity in content, logical implications, and form to judgments of propositions compared to X are Y are in accord with expectations. However, similarity in logical implications typically contributed more than similarity in content to judgments of propositions compared toX are 8; moreover, similarity in form contributed very little to

High LOW

o+----

Moderote

pb/.

pb/O

PO PO

High pb,O

I

FIG. I. Interactive effects of P, and P*,,, and of P, and P,,;;, on judgments of propositions hypothetically compared to (a) X are Y and (b) X are r. 2 The contribution of similarity in logical implications is reflected by the interactive effects of form similarity and content similarity; see Table 1.

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4

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ITEM

EFFECTS

OF INFORMATIONAL

CHARACTERISTICS

pm

pax pm

pax pm

1. Conclusions compared to X and Y Similarity in Content 4.97** Logical implications .42** Form .21*

5.10** .65** .27*

2. to** .59** .48**

1.98** .26** .32**

2. Conclusions compared to X are F Similarity in Content .64** Logical implications 1.92** Form .ll

.92** 2.51** .13

.75** .16 .07

.22* .32* .08

*p < .05. **p < .Ol.

these judgments.3 Possible implications of these deviations from prediction will be discussed presently. Additional considerations. In evaluating the results reported above, some additional considerations are worth noting. First, neither the predicted effects of informational variables nor their contingencies upon response item characteristics were significantly contingent upon stimulus domain. This does not indicate that persons’ previously formed beliefs have no effect on the conclusions they draw on the basis of information bearing on premises. Evidence that they do is of both early and recent vintage (Janis & Frick, 1943; Wyer, 1976). However, in the present study, these effects may have been constant over informational conditions, and therefore did not interact with the effects in question. One discrepancy from predictions based upon Eq. (6) is worth noting, however. Specifically, a small but significant interaction of Pbla and Pi,, occurred in analyses of statements hypothetically compared to X are Y, F(4,240) = 2.92, p < .05. This interaction is not predicted by Eq. (6). An equally small but significant interaction between these variables was detected in earlier research (Wyer, 1975a). Both interactions are attributable to the fact that when the implied value of both conditionals was low, judgments were less than would be expected if the effects of these conditionals were independent. Thus, while there appear to be some 3 Supplementary analyses of judgments of each test proposition separately confirm these implications. Among the four propositions compared toX are Y, the four predicted effects of informational variables accounted for the most variance in judgments ofX are Y, followed in order by judgments of Y are X, F are x and then x are y. However, among propositions compared to X are F, these effects accounted for the most variance in judgments ofX are y, followed in order by judgments of Yare x (the proposition similar in logical implications to the anchor), Fare X (the proposition similar in content), and then x are Y.

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JR.

consistent discrepancies from predictions based upon Eq. (6), these discrepancies are small in magnitude and may be of more theoretical than practical significance. (In this regard, a corresponding interaction was not detected in analyses of data pertaining to conclusions hypothetically compared to X are F, F(4,240) = .98.) A few other scattered effects were also significant in the three analyses described above. However, these effects were small, difficult to interpret, and not of obvious theoretical or empirical interest. Of the total sums of squares accounted for in analyses of judgments compared to X are Y, 68% was accounted for by the 35 df pertaining to the four predicted effects of experimental manipulations and their interactions with content similarity, form similarity and similarity in logical implications, while the remaining 252 &accounted for only 32 %. The corresponding percentages in analyses of judgments compared to X are F were 77 and 23%, respectively. Thus, it seems reasonable to conclude that the effects obtained were primarily concentrated in the sources theoretically predicted on the basis of Eq. (6) and Postulates l-3. DISCUSSION

The two experiments reported in this paper provide some insight into the factors that affect inferences that do not follow logically from the information available. Moreover, they demonstrate the utility of Postulates l-3 in conceptualizing and identifying the contributions of these factors. The heuristic value of these principles is increased by virtue of the fact that their applicability does not appear to depend upon the particular categories of persons and objects to which inferences pertain; this suggests that the effects of factors identified through the use of these postulates are not restricted to any particular stimulus domain. Two contingencies are worth noting. First, the relative contributions of content similarity, similarity in logical implications, and form similarity depended to some extent upon whether the subject category of the anchor propositions was positive or negative (independent of the nature of the objects to which the category pertains). Differences between the manner in which persons process negations and the manner in which they process affirmations has often been detected, both in the present research program (Wyer, 1976) and more generally (Meyer, 1973; Wason, 1959). The nature of these differences, and the reasons they occur, are not clear. The existence of these contingencies in the present study adds complexity to the task of predicting a priori the contributions of the factors postulated to affect judgments of “nonlogical” conclusions. However, it does not call into question the validity of Postulates l-3 as a basis for conceptualizing the processes underlying these judgments. Other contingencies are suggested by the evidence in Experiment 2 that

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the contributions of response item characteristics to judgments of propositions compared to X are p differed in relative magnitude from their contributions to judgments of propositions compared to X are Y, and also differed from their relative contributions to judgments of propositions compared to similar anchor proposition in Experiment 1. The first of these differences may be yet another reflection of a general difference between the processing of affirmations and the processing of negations. The second is somewhat more disturbing. Postulates l-3 assume thatjudgments of test propositions are based exclusively upon a comparison of these propositions to the ones most and least likely to follow from the information presented. To this extent, the contributions of factors to these judgments should not depend upon the manner in which the anchor propositions are identified. The difference between experiments in the contributions of response item characteristics when the anchor proposition was of the form X are a suggests that judgments of certain propositions may be based to some extent upon a direct consideration of the information presented, and may not be mediated entirely by the processes outlined in Postulates l-3. As a consequence, caution should be taken in generalizing the relative contributions of the factors implied by these postulates to different inference situations than those considered here. Nevertheless, the approach taken in this paper provides a valuable diagnostic tool in determining the nature and extent of this generality. Interest in the proposed postulates is increased by virtue of the fact that they can potentially be incorporated into existing formulations of social inference, and thus can extend the range of inference phenomena to which these formulations potentially apply. This possibility was demonstrated in Experiment 2 with reference to the syllogistic model of cognitive functioning proposed by McGuire (1960) and Wyer (1974a, 1975b). However, to the extent that other theoretical formulations are able to generate a priori predictions of the effects of information upon beliefs of the form considered in this paper, Postulates l-3 may be used to extend the applicability of these formulations as well. Postulates l-3 may also have implications for models of cognitive organization. For example, Eq. (6) has been used to describe not only the manner in which new information combines to affect beliefs about a hypothetical object or event but also the manner in which a subject’s previously formed beliefs about actual persons and objects are organized (Wyer, 1976). Moreover, subjects appear to regard beliefs that are not related in the manner implied by this equation as inconsistent (Henninger & Wyer, 1976), and modify their own beliefs to make them more consistent once these beliefs are made salient (McGuire, 1960; Rosen & Wyer, 1972; Wyer, 1974a). If Postulates l-3 are valid, they suggest a broader criterion for cognitive inconsistency than that implied by Eq. (6). That is, a subject may be induced to alter his beliefs in a direction of greater

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consistency, not only by making salient the four beliefs comprising this equation, but also by making salient beliefs in propositions that are not syllogistically related to the premises. The research reported in this paper has been restricted to a consideration of a single type of relation among elements, namely, an existence relation (X are Y). However, it is important to note that a similar approach may be taken to investigate factors that govern inferences about other types of relations. One obvious relation of interest is a sentiment relation (e.g., X like Y). Principles analogous to Postulates l-3 could potentially be developed for describing the effects of information bearing directly upon one such relation (e.g., X like Y) upon other sentiment relations such as Y like X, non-Y like non-X, etc. In light of the continued interest in cognitive balance phenomena (Heider, 1958), the role of factors analogous to form similarity, content similarity, and logical relatedness in inferences about sentiment relations may be worth exploring. REFERENCES Abelson, R. P., & Kanouse, D. The subjective acceptance of verbal generalizations. In S. Feldman (Ed.), Cognitive consistency: Motivational antecedents and behavioral consequences. New York: Academic Press, 1966. Chapman, L. J., & Chapman, J. P. Atmosphere effect reexamined. Journal of Experimental Psychology,

1959, 58, 220-226.

Heider, F. The psychology ofinterpersonal relations. New York: Wiley, 19.58. Henninger, M., & Wyer, R. S. The recognition and elimination of inconsistencies among syllogistically-related beliefs: Some new light on the “Socratic effect.” Journal of Personality and Social Psychology, 1976, 34, 680-693. Janis, I., & Frick, F. The relationship between attitudes toward conclusions and emors in judging the logical validity of syllogisms. Journal of Experimental Psychology, 1943, 33, 73-17. Kanouse, D. Language, labeling andattribution. Morristown, N. J.: General Learning Press, 1971. McGuire, W. J. A syllogistic analysis of cognitive relationships. In M. J. Rosenberg, C. 1. Hovland, W. J. McGuire, R. P. Abelson, &J. W. Brehm(Eds.),Attitude organization and change. New Haven, Conn.: Yale University Press, 1960. Meyer, D. E. Verifying affirmative and negative propositions: Effects of negation on memory retrieval. In S. Komblum (Ed.), Attention andperformance IV. New York: Academic Press, 1973. Podeschi, D., & Wyer, R. S. The acceptance of generalizations based upon inductive and deductive evidence. Journal ofPersonality and Social Psychology, 1976,34,496-509. Rosen, N. A., & Wyer, R. S. Some further evidence for the “Socratic effect” using a subjective probability model of cognitive organization. Journal of Personality and Social Psychology, 1972, 24, 420-424. Wason, P. C. The processing of positive and negative information. Quarterly Journal of Experimental Psychology, 1959, 11, 92- 107. Woodworth, R., & Sells, S. An atmosphere effect in formal syllogistic reasoning. Journal of Experimental Psychology, 1935, 18, 451-460. Wyer, R. S. The quantitative prediction of belief and opinion change: A further test of a subjective probability model. Journal of Personality and Social Psychology, 1970,16, 559-571.

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Wyer, R. S. Cognitive organization and change: An information-processing approach. Potomac, Md.: Lawrence Erlbaum Associates, 1974. (a) Wyer, R. S. Some implications of the “Socratic effect” for alternative models of cognitive consistency. Journal ofPersonality, 1974, 42, 399-419. (b) Wyer, R. S. Functional measurement analysis of a subjective probability model of cognitive functioning. Journal of Personality and Social Psychology, 1975, 31, 94-100. (a) Wyer, R. S. The role of probabilistic and syllogistic reasoning in cognitive organization and social inference. In M. Kaplan & S. Schwartz (Eds.). Human judgment and decision processes. New York: Academic Press, 1975. (b) Wyer, R. S. Effects ofpreviously formed beliefs on syllogistic inference processes.Journal of Personality and Social Psychology, 1976, 33, 307-316. Wyer, R. S., & Podeschi, D. M. The acceptance ofgeneralizations about persons, objects and events. In R. Revlis & R. E. Mayer (Eds.), Human reasoning. Washington, D. C.: V. H. Winston & Sons, in press.