Linking Structures and Sensitivity to Judgment ...

ATTITUDES AND SOCIAL COGNITION

Linking Structures and Sensitivity to Judgment-Relevant Information in Statistical and Logical Reasoning Tasks Yechiel Klar

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Tel Aviv University, Tel Aviv, Israel It is proposed that in solving statistical and logical reasoning tasks, reasoners form a bilateral linking structure connecting the 2 problem focal categories with each other. This structure includes two links. Each link may be conceived as full or partial. A full versus partial link, relevant to the inference, was predicted to promote unqualified and confident conclusions and to decrease sensitivity to incoming judgment-relevant information. Similar, though weaker, effects were predicted for the converse (irrelevant) link. Undergraduates (N = 248) were exposed to 1 of the 4 possible linking structures and then performed a series ofjudgmentsrelatedto pseudodiagnosticity, insensitivity to sample size, judgmental overconfidence, and so on. Strong evidence for the relevant link hypothesis and some evidence for the irrelevant link hypothesis were found.

Over the past two decades, the literature on human reasoning has put a substantial premium on the discovery and study of specific instances of insensitivity to judgmental considerations. For example, the statistical-reasoning literature has described "insensitivity to sample size (Tversky & Kahneman, 1971), judgmental overconfidence (Lichtenstein, Fischhoff, & Phillips, 1982), insensitivity to the base rate (Bar-Hillel, 1984), and pseudodiagnosticity (Doherty, Mynatt, Tweney, & Schiavo, 1979). The logical-reasoning literature has identified tendencies such as false affirmation of the consequent (AC) and false denial of the antecedent (DA; Taplin & Staudenmayer, 1973) and the verification bias (Wason, 1968). To date, much research has been conducted on each of these separate phenomena (see Borgida& Brekke, 1981; Dawes, 1988; Evans, 1982; Hogarth, 1987; Kahneman, Slovic, & Tversky, 1982; Manktelow 1981; Markus & Zajonc 1985; Nisbett & Ross, 1980; Skov & Sherman, 1986, for reviews). Recently, however, several writers within the logical domain (Evans, 1989; Newell, 1980), the statistical domain (Hogarth, 1981; Sherman & Corty, 1985), and across these two domains

This article is based on a doctoral dissertation that was supported by the Josef Buchmann Doctoral Fellowship at Tel Aviv University and received the Society for Experimental Social Psychology Dissertation Award. I gratefully acknowledge precious advice Ireceivedfrom Arie Kruglanski, my adviser. I am also thankful to Jonathan Baron, Reuben Baron, Ruth Beyth-Marom, Nyla Branscombe, Thomas Malloy, and four anonymous reviewers for valuable comments on drafts of this article. I appreciate the assistance of Ruth Bry, Yael Vagner, and Leonardo Wallmer at Tel Aviv University and of Ellen Amore, Eliza Goodell, and Richard Mendola at the University of Connecticut. Correspondence concerning this article should be addressed to Yechiel Klar, Department of Psychology, Sharet Building, Tel Aviv University, Ramat Aviv 69778, Tel Aviv, Israel.

(Baron, 1988; Klayman & Ha, 1987; Kruglanski & Ajzen, 1983) have recommended shifting the focus of study to a level beyond the separate phenomena to identify underlying cognitive processes related to subjects' behaviors in a variety of reasoning tasks. In this article, I wish to take a step in this direction.

Common Structural Properties of Reasoning Problems: Categories and Links Table 1 presents six experimental problems selected from the logical- and statistical-reasoning domains. The first column in this Table provides informal descriptions of the reasoning problems. The second column specifies the particular reasoning task in each of these problems. The third column indicates the specific kinds of judgmental insensitivity depicted in each problem. I argue that all the reasoning problems in Table 1 and many other similar problems deal, explicitly or implicitly, with two or more sets of cognitive categories and the possible relations between these categories. This can be appreciated by examining the fourth and fifth columns. Reasoning problems relate to different cognitive categories (i.e, events, qualities) that are denoted here as x,, x 2 ,. . . xn and as yl5 y 2 ,. . . yn. In the first example, they are the events of mowing the lawn (x,), washing the car (x2), and doing nothing (x3; different domestic work situations) and other types of events such as receiving $5 (y!), receiving $10 (y2), and receiving nothing (y3; different monetary rewards situations). In the second example, they are traveling to Manchester (x,) and traveling to Leeds (x2; different destinations) and traveling by train (yt) and traveling by car (y2; different kinds of transportation). In other examples, these are particular qualities, such as a Bears Club member, a Lions Club member, a professor, a mechanical writer, a computer science major, or a blue bird. An alternative way of conceiving cognitive categories may be as discrete values

Journal of Personality and Social Psychology; 1990, Vol. 59, No. S, 841-8S8 Copyright 1990 by the American Psychological Association, Inc. 0022-3514/90/S00.75

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(//)• That is, subjects do not consider the professors are Bears Club members, but only some Bears Club prior probability of the inferred H quality (the base rate) when members are professors, and some are not"). Some evidence for judging the probability that a particular instance (or group), M, this tendency was presented using deductive and probabilistic known to possess a D quality, also possesses the //quality. It was tasks (Bar-Hillel, 1984; Chapman & Chapman, 1959; Eddy, argued that in doing these judgments, subjects relied only on 1982; Smith, 1982). Also, asymmetrical structures are more eas- the degree of resemblance between the D quality to the H qualily jeopardized in memory than symmetrical structures. A ity (Kahneman & Tversky, 1973). For example, when asked to full-partial link ("all the Bears Club members are professors, predict the probability that a particular student, Tom W, but only some of the professors are members of the Bears Club") known to possess the quality of mechanical writing style (£>), may be transformed in memory into a partial-full link ("all the would turn out to be a computer science major (//), subjects professors are Bears Club members, but only some of the Bears were insensitive to the actual proportion of computer science Club members are professors") and vice versa. This type of majors among the student population (the base rate), and they confusion, termed by Dawes (1988) as the confusion of the in- based their predictions on their assumption of the representaverse, cannot happen with symmetrical structures. tiveness of mechanical writing style among computer science majors. Thus, subjects were influenced by specific target information but not by the base rate of the inferred quality (see Bar-Hillel, 1984; Borgida & Brekke, 1981; Kahneman et al, Statistical and Logical Reasoning Tasks 1982; Kassin, 1979; forreviewsand research examples).

Statistical Tasks

In statistical reasoning tasks, the reasoner is asked to assess the probability of a particular hypothesis (//; eg., M is a professor) given a particular datum (D; e.g., M is a Bears Club member). In terms of the current model, statistical problems are concerned with the bilateral relations between an observed D category and an inferred H category. When judging the probability of// on the basis of a given D, subjects are often found to be insensitive to several sources of informationreflectingstatistical consideration (Fischhoff & Beyth-Marom, 1983; Kahneman et al, 1982; Nisbett & Ross, 1980). Some of the most researched examples are briefly illustrated here. Pseudodiagnosticity occurs when the subject is relatively insensitive to the denominator in the likelihood ratio, P(D/H)/ P(D/not H), (Beyth-Marom & Fischhoff, 1983; Doherty et al, 1979; Klayman & Ha, 1987; Skov & Sherman, 1986; Snyder & Swann, 1978; Trope & Bassok, 1982). That is, the subject is

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The aforementioned four basic linking structures describe affirmative relations (e.g, all . . . are . . . , every . . .) between positive properties (e.g, professors, Bears Club members), and only by implication do they deal with negative relations and with the negations of these categories. This focus does not imply that people may not be interested, sometimes, in negative relations or that they are not capable of directly representing links between negations of categories (e.g, nonprofessors are not members of the Bears Club). However, it is assumed that the more basic function of linking structures is to represent what actual categories of things are and how they are linked with other actual categories. Reasoning about negatives is generally found to be more difficult than reasoning about affirmative statements and positive categories. This article only marginally touches the complex issues of reasoning with negatives (see Evans, 1982; Klayman & Ha, 1987; Wason & Johnsoniaird, 1972). 3 1 am indebted to a journal reviewer for suggesting this form of illustration.

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Much of the research in this tradition is concerned with inferences from conditional statements. Subjects are presented with a statement in the form of "if p then q" (&g, if M is a Bears Club member [p], then Mis a professor [q]"). The p category and the q category are called antecedent (p) and consequent (q). Then subjects are presented with one of the categories as an observation (e.g, M is a Bears Club member) and they are asked to determine whether a particular conclusion (&g, M is a professor) logically (i.e, necessarily) follows from the original statement. Thus, logical problems are concerned with the bilateral relations between the p category and the q category. The two links in these problems are p-q and q-p. Four possible inferences can be made on the basis of the "if . . . then" statement: (a) M has been identified as a Bears Club member, therefore M is a professor (modus ponens [MP]—a valid inference), (b) M has been identified as a nonprofessor, therefore M is not a Bears Club memberfynodustollens [MT]—a valid inference, (c) M has been identified as a professor, therefore M is a Bears Club member (affirmation of the consequent [AC]—invalid inference), and (d) M has been identified as a nonmember of the Bears Club, therefore M is not a professor (denial of the antecedent [DA]—invalid inference. Research on reasoning with conditionals (see Evans, 1982, for a review) showed that unlike MP, the remaining three inferences, AC, DA, and MT pose considerable difficulties to subjects. Subjects tend to sometimes mistakenly affirm the consequent and deny the antecedent when logically this is unjustified and sometimes mistakenly reject the MT inference. In addition, when asked to test the truth or the falsity of a conditional statement such as, "If a Bears Club member (p), then a professor (#)," subjects often disregard as irrelevant potentially falsifying not-q evidence (in fact, they do not select for testing a person known to not be a professor). This bias was designated in the literature as a verification bias (see Griggs, 1983; Manktelow, 1981; Wason, 1983 for reviews of research in this task). In the next section, I argue that the linking structure with which subjects enter a given problem plays an important role in their subsequent sensitivity to judgmental considerations in both statistical and logical domains.

Influence of Linking Structures on Inference Hypothesis 1: Effect of Full Versus Partial Relevant Link

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Consider a prediction task in which subjects are presented with some information about a certain M, who possesses the quality x, (is a Bears Club member), and they are asked to judge the probability that Malso possess the quality y, (is a professor). Therelevantlink for this inference is the x,-y, link (Bears Club members-professors). I propose that for a reasoner who approaches the task equipped with a full x,-y, link (e.g, "all Bears Club members are professors" or "a Bears Club member is necessarily a professor"), concluding that M, the Bears Club member, is a professor is a simple task of drawing an obvious conclusion from a general belief (i.e, "if all the Bears Club members are professors, then any particular member of this club is a professor"). On the other hand, for a reasoner who

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enters the task with a partial x^y, link ("only some Bears are professors, and some are not" or "a Bears Club member is not necessarily a professor), a Bears Club membership is not fully indicative of being a professor. Thus, the problem presents an uncertain inference. I, therefore, hypothesize that entering the problem with a full rather than a partial x,-y, link will result in higher judgmental confidence in the prediction that M is a professor and decreased sensitivity to potentially relevant incoming judgmental information. More specifically, the fulllinked reasoner will be less likely to use statistical heuristics such as consulting the base rate (the percentage of professors in the population), taking the sample size into account (the number of Bears Club members who have already been observed as professors or non-professors), or evaluating the evidence for diagnosticity (the frequency of Bears members among professors as compared with their frequency among nonprofessors). Furthermore, nonstatistical target information (e.g, specific attributes in M that are representative of a professor) will also be less sought and used in the full, rather than partial, x,-y, link condition. Finally, logical tasks are hypothesized to be affected as well: When required to test the truth and the falsity of the following assertion, "if someone is a member of the Bears club, then this person is a professor," the full-linked reasoner (assuming, on the basis of the linking structure, that the statement is empirically true) will also be less inclined to actively seek for potentially falsifying cases (i£, people known as nonprofessors, to see whether they are Bears Club members). Also, when presented with the following statement as a true statement, "all the professors (p) are Bears Club members (#)," the full rather than partial x{-y{ linked reasoner will be more ready to endorse the following conclusions as though they logically follow the aforementioned statement: (a) "If someone is a Bears Club member (q), then this person is a professor (pf (the affirmation of the consequent inference), and (b) "if someone is not a professor (not p), then this person is not a Bears Club member (not qf (the denial of the antecedent inference), because these conclusions seem to be empirically true in light of the linking structure. Evidence supporting this general hypothesis can be found in regard to a variety of reasoning tasks. In the statistical domain, Nisbett et al. (1983) demonstrated that when the judged category was perceived to be heterogeneous rather than homogeneous, the sensitivity to sample size increased. A heterogeneous category (e.g, "some shreebles, D, are blue colored, H, and some shreebles are of other colors, not H) is an example of a partial D-H link. Real-life beliefs about D-H relations were found to affect the sensitivity to the base rate that was provided by the experimenter (Evans, Brooks, & Pollard, 1985). In the logical arena, Van Duyne (1976) showed that subjects were more likely to select the not q evidence in the Wason (1968) selection task when the statements they were asked to test appeared to them (on the basis of theirreal-lifeknowledge) as only sometimes true (a partial p-q link) rather than always or necessarily true (a full p-q link; see also Pollard & Evans, 1981). Similarly, Markovits (1984) showed that subjects' awareness to the fact that the p-q link is possible rather than necessary was associated with better logical performance in conditional reasoning tasks. Also, contents involving category-subcategory relations (e.g, "if this is a bird [p], it must be a turkey [q]") were argued to invoke the AC

and DA inferences more than problems about subcategorycategory relations (e.g., "if this is turkey, it must be a bird; Adams, 1980). It can be seen that in thefirstbut not the second condition, a full q-p link (i.e, "all turkeys [q] are birds [/>]") is, by definition, always the case. Whereas all thesefindingsare consistent with the full versus partial link hypothesis, they were not designed to test it. What is needed is a more direct test of this hypothesis in a variety of reasoning tasks, statistical and logical alike. I predict that subjects entering these tasks with a full rather than partial relevant link will be less sensitive to the aforementioned types of information and considerations as compared with the partial relevant link. This hypothesis can be portrayed as a main effect for the relevant link (e.g, FF and FP < PF and PP, when x,-y, is the relevant link). Hypothesis 2: A (Weaker) "Ecological" Effect of Converse Link In addition to the relevant link, which may be full or partial, the second link (e.g, yi-xt) may also be full Call the professors are Bears Club members") or partial ("only some professors are Bears Club members"). Note that normatively speaking, this link is irrelevant to the prediction of whether or not M, the Bears Club member, is a professor (it does not matter if all or only some of the professors are Bears Club members). However, this link may also have some effects on the inference. A number of factors may be combined to contribute to this possible converse effect. First, in some cases, the links may be mixed up with each other (Dawes, 1988; e.g., "are all the Bears Club members professors, or are all the professors Bears Club members?"), or both of them may be converted into a simpler symmetrical structure (e.g, a partial-full structure may be converted into a full-full or a partial-partial structure). In addition, the converse link may exert some ecological influence by its mere presence in the structure: The existence of the converse partial link may promote some judgmental caution, even in inferences that are based on therelevantfull link, and the existence of the converse full link in the structure may decrease judgmental caution, even in inferences that are based on the partial relevant link. I thus predict that the converse (irrelevant) link effects will be in the same direction as the effects of the relevant link, although the magnitude of the later effects will be considerably lower in order. In fact, a main effect for the converse link (e.g, FF and PF < FP and PP) is predicted. The combination of both Hypothesis 1 and 2 main effects should result in an FF < FP < PF < PP order. Some suggestive evidence for a converse link effect on inference was already reported: Bar-Hillel (1984) suggested that the base-rate neglect in prediction tasks may be attributed, at least in part, to subjects' inability to distinguish between the two conditional probabilities P(H/D) and P(D/H) (see also Eddy, 1982). An additional and independent implication of the bilateral nature of the linking structures is that when the link that is relevant for the inference is switched (e.g, from x^-y^ to ^,-jq), a marked change should result in the sensitivity to judgmental information in the asymmetrical structure conditions (FP and

LINKING STRUCTURES

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PF), but not in the symmetrical conditions (FF and PP). For example, a reasoner who believes in a full-partial Bears Club membership-professorship relation (e.g., all Bears Club members are professors, but not all professors are Bears Club members) who is given the information that M is a Bears Club member will be likely to conclude with confidence that M is a professor without making much use of judgmental calculated strategies (the conclusion is based on the full link in the structure). However, the same reasoner, given the information that M is a professor, will be more hesitant in concluding that M is a Bears Club member and will make more use ofcalculated strategies (the conclusion is based on the partial link in the structure). Overview of the Study In the first phase of the study, subjects were presented with a selection of 50 two-sided fictitious ID cards taken from members of several social clubs in a large community center. These cards enabled subjects to learn the specific set of relations prevailing in one section of a large community center between (a) being a member in a particular social club (x) and (b) preferring a certain leisure activity (y). This stimulus set was designed to correspond to one of the four linking structures: FF, FP, PR or PP. In the second phase, subjects were presented with a second set of social clubs and leisure activities taken from a different section of the community center. This time, subjects could not observe the ID cards, and the experimenter informed them that no information was available about the new clubs and activities. I assumed that the linking structures pertaining to the initial set of clubs and leisure activities would continue to exert influence when making judgments about the new clubs and activities. Subjects were asked to perform a series of judgment and inference tasks; each task assessed a different reasoning behavior (e.g, interest in the base rate). In some of the tasks, subjects were supposed to make inferences involving the clubsactivities link; in the remaining tasks, subjects were supposed to make inferences involving the activities-clubs link. Given the variety of reasoning tasks investigated, the presentation of the study is divided in this article, so that each major reasoning task is separately discussed. The order of presentation, however, corresponds to the manner in which the study was originally conducted.

Method Subjects The subjects were 248 undergraduates, 169 women and 79 men, at Tel Aviv University. The study was presented as an evaluation of social judgment. The subjects participated as part of their requirements in an introductory psychology course. Subjects were tested individually, and each was randomly assigned to one of the four linking structures groups and later to the four additional experimental variations within groups, described subsequently.

First Phase: Induction of Linking Structures The experimenter informed the subjects that the study dealt with social judgment and would include several different tasks of judgment

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and information processing. The subjects then received the following written background information: In a certain town B,fivehundred people in their 30s and 40s are affiliated with a large community center. Within the center there are 20 social clubs that are divided into four sections. Every member in the center may belong to only one club. [This information was followed by a list of the four sections containing S clubs each. The names were arranged in alphabetical order, they were all names of trees or minerals, for example, Aspen, Birch].4 Each member of the community center has been issued an ID card. You will be presented with a set of these ID cards that have been collected from various members. Your task will be to review the cards, and when you are done, you will be asked a number of questions about the cards. You are free to take notes if you like. The subject was then given a selection of 50 plastic membership cards to examine. One side of the card listed the following information: the member's name (first and last) and the name of an activity preferred by the person (i.e., tennis, bridge, chess, computer games, or photography). The name of one of thefivesocial clubs was listed on the opposite side of the card. The club-activity and the activity-club relationship in the set of cards selected corresponded to one of the four linking structures: FF (full-full, a full clubs-activities link; a full activities-clubs link). All the members of each specific club preferred the same activity. In addition, all the people with a certain activity preference were members of the same club. In fact, each one of the five social clubs matched only one of thefiveactivities and vice versa. FP (full-partial: a full clubs-activities link, a partial activities-clubs link). All the members in each club preferred the same activity. However, not all the people with the same activity preference were necessarily in the same club. In this selection, three activities were distributed amongfiveclubs. Two of the activities were preferred by members of two different clubs; the remaining activity was preferred by members of only one club. PF (partial-full: a partial clubs-activities link, a full activities-clubs link). Not all the members of any particular club necessarily had the same activity preference. However, all the people with a certain activity preference were members of the club. In this selection, five activities were divided between three clubs. Two clubs included two activities each; the remaining club included only one activity. pp (partial-partial: a partial clubs-activities link, a partial activities-clubs link). Not all the members of any particular club necessarily had the same preference. In addition, not all the people with the same activity preference necessarily belonged to the same club. In this selection, four activities were distributed among four clubs, and (as in the other groups) there was one match between a club and an activity. In this way, each subject was exposed to one of the four linking structures. To promote the learning of the clubs-activities and activities-clubs relations and also to give subjects some rationale for their inspection of the cards, subjects were asked to complete a short task in which they had to specify the probability that a person preferring a particular activity (e.g., tennis) was a member of a particular club (e.g., Aspen) and also the probability that a person in the sample who was a member of a particular social club preferred a particular leisure activity. Subjects were able toreferto the ID cards in completing this task. Except for 1 subject, all 248 subjects were able to complete this task in a way indicating understanding of the linking structure into which they were assigned. This task may be also conceived as an initial check of the manipulation. This task concluded the first phase of the study.

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Similar Hebrew names were used in the experiment.

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Second Phase: Reasoning Tasks

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After a short recess, the experimenter approached the subject again with a closed box, displaying the names of a new set of five clubs. The experimenter told the subject that in this part of the experiment, she or he would be asked to perform a series of judgment tasks about members of other clubs about which she or he did not receive prior information. The experimenter added, "In this part you will not receive any information in advance about the different clubs and the different activities. As a matter of fact, I do not know what happens in the other sections of the community center" (the experimenter pointed to the closed box). Following this general introduction, the experimenter handed the subject the first reasoning task.

Task 1: Pseudodiagnostic Judgment According to the current approach, when a full clubs-activities link is perceived to be the case—that is, when a specific club membership (D, the Bears Club) is fully indicative of a given professional group (H, being a university professor) and the target member is known to be a Bears Club member—information about alternative professional groups is quite irrelevant. Similarly, in the present context, entering the task with a full D-H link between club membership (D) and leisure preference (and to a lesser degree also a full H-D link) should reduce interest in people with other leisure activities, and the susceptibility to pseudodiagnostic judgments should increase.

Method Subjects were presented with a task adapted from Beyth-Marom and Fischhoff(1983): You have met Mr. Danieli at a party where only people who jog or play basketball in their leisure time were invited. The only thing you know about Mr. Danieli is that he is a member of the Hickory Club. You are asked to assess the probability that Mr. Danieli is a jogger by asking one, two, three, or four of the questions given below. However, before asking them, you are asked to evaluate their relevance to the task. A relevant question is one where the answer will help you in your assessment. Please evaluate each of the questions separately and indicate the degree that it is relevant or irrelevant for your task [on a 0-7 scale]. 1. What percentage of the people at the party are joggers? [PI(H) ] 2. What percentage of the Hickory Club members are at the party? [Afilleritem] 3. What percentage of joggers at the party are members of the Hickory Club? [P(D/H)\ 4. What percentage of the basketball players at the party are members of the Hickory Club? {P(Dfao\ H)]

Results Figure 1 contains the mean relevance judgments of the three informational items P/(H), P(D/H), and P(D/not H) made in the four linking structures groups. The critical item in this task is Item 4, F(D/not H), which reflects the sensitivity to the likelihood ratio. A 2 X 2 (Relevant Link X Converse Link) analysis of variance ANOVArevealeda significant relevant-link main effect, F(l, 243) = 34.05, p < .001. The PF and PP groups, with the partial clubs-activities (D-H) link, which is the relevant link in this task, were significantly more interested in Item 4 (M =4.16 and 3.59, respec-

full-partial

full-full P(H)

partial-full P(D/H)

partial-partial P(D/not H)

Figure 1. Mean relevance ratings of P(H), P(D/H), and P(D/not H) in the party task, in the four linking structures groups.

tively) as compared with the full clubs-activities linked groups, FF and FP (M = 1.74 and 2.53, respectively). However, there was no main effect of the converse (H-D), activities-clubs link and no significant Relevant Link X Converse Link interaction, F(l, 243) = 2.3, p = .13. Thus, the first hypothesis—suggesting a relevant-link effect—received clear support, whereas the second hypothesis—suggesting some additional effect to the converse link—was not supported. Task 2: Sensitivity to Sample Size and Degree of Judgmental Confidence I predicted that subjects' sensitivity to the sample size would be influenced by their prior linking structures. When subjects believe in a full rather than a partial (relevant) D-H link and, to a lesser degree, when they believe in a full rather than a partial (converse) H-D link, their tendency to make extreme probabilistic predictions on the basis of a small sample (see Nisbett et al, 1983), to attribute high confidence to these predictions (Borgida & Nisbett, 1977), and to berelativelyuninterested in reviewing additional corroborative information should be heightened.

Method After the subject completed the pseudodiagnosticity task, the experimenter approached the subject with a closed box (containing the second series of ID cards). The experimenter took from this box, supposedly at random, one of the ID cards and gave it to the subject. On one side of this card appeared the name Hickory Club. On the other side, there was a member^ name and jogging as a preferred leisure activity. Thus, subjects were presented with a single observation ofa jogger who was a member of the Hickory Club. The experimenter then opened the box again and took out another supposedly random card. This time, the experimenter put the card, which carried the name Hickory Club, on the table face up. The experimenter told the subject that the card must not be turned over this time and that the next task would be focused on this person whose card was lying on the table (the subject was not able to see the target person's preferred leisure activity). After

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LINKING STRUCTURES the experimenter left, the subject was asked to make the following judgment: "The probability, in my view, that the Hickory Club member whose card is lying on the table will have jogging as his preferred leisure activity is %." Degree of confidence in the prediction and interest in additional information were assessed by two related hems: (a) "My degree of certainty in the prediction I have just made i s . . . (a rating ranging from very little [0] to very high [7]). (b) "Receiving additional information seems to me at this point..." (a rating ranging from Useless [0] to very useful [7]).

Results This document is copyrighted by the American Psychological Association or one of its allied publishers. This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.

Prediction Task Subjects' probabilistic estimates that the Hickory Club member whose card was lying on the table would be a jogger, after viewing one jogger/Hickory Club card are presented in Figure 2. A Relevant Link X Converse Link ANOVA revealed a strong main effect to the relevant link, F(l, 240) = 89.13, p < .001, and a weaker but still highly significant main effect to the converse link, F(l, 240) = 22.33, p < .001. The mean probabilistic judgments followed FF > FP > PF > PP (M = 74,66,53, and 35, respectively) as predicted by the two hypotheses. Degree of Confidence in the Prediction The two judgments pertaining to judgmental confidence are presented in Figure 3. The degree of confidence in the judgment was found to decrease according to the predicted FF > FP > PF > PP order (M= 4.57,4.03,2.95, and 1.98, respectively), and the degree of interest in receiving additional information was found to increase according to the same theoretical order {M = 4.28, 4.78, 5.3, and 5.48, respectively). A multivariate analysis of variance (MANOVA) conducted on these judgments revealed a strong effect of the relevant link, Hotelling's T2 - .26, p< .001, and a weaker but still significant effect of the converse link, Hotelling's T2 = .03, p = .02. On the univariate level, there were highly significant main effects of the relevant link on the confidence judgment, F(l, 240) = 46.08, and on the informational need, F(l, 240) = 47.53, ps < .001, a significant main

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Figure 2. Mean probability (percentage) that the person whose ID card is lying on the table is a jogger, after viewing a single-case sample, in the four linking structures groups.

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Figure 3. Mean confidence in judgment and interest in receiving additional information, after viewing a single-case sample, in the four linking structures groups.

effect of the converse link on judgmental confidence, F(l, 240) = 7.77, p < .01, but not to the informational need, F(l, 240) = 1.62,/? =.20. Overall, these results demonstrated that the linking structures affected subjects' sensitivity to sample size considerations, as reflected by their probabilistic predictions and by their degree of confidence in the predictions.

Task 3: Sensitivity to Base-Rate and Target Information The sensitivity to the base-rate information can be assessed in several ways: (a) by measuring subjects' degree of interest in acquiring base-rate information (e.g, Beyth-Marom & Fischhoff, 1983; Lyon & Slovic, 1976), (b) by comparing predictions made under different base rates (Fischhoff, Slovic, & Lichtenstein, 1979; Kahneman & Tversky, 1973; Lynch & Ofir, 1989) and confidence in these predictions (Bar-Hillel & Fischhoff, 1981; Manis, Dovalina, Avis, &Cardoze, 1980), (c) by comparing the relative effects of the base rate and the nonstatistical target information on subjects' predictions (e.g, Kahneman & Tversky, 1973; Manis et al, 1980). According to the present view, all these measures of sensitivity to base-rate information should be influenced by the relevant link and, to a lesser degree, by the converse link. Furthermore, the linking structure should affect the sensitivity to any kind of incoming information related to this link. Thus, one may also predict that the sensitivity to and the use of non-statistical target information (e.g, information that would enable subjects to know if the psychological profile of the specific person studied matches a profile of a jogger) should be influenced by subjects' linking structures exactly in the same manner expected for the statistical base rate and other instances of statistical information such as the likelihood ratio and the sample size already reviewed.

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Method

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Overview of Procedure and Experimental Design The hypotheses about the base-rate and target information call for an experimental design in which the sensitivity to each type of information will be independently measured within the different linking structures groups. In addition, for each type of information, both the initial interest in receiving the information and the degree of the information use after it is granted was assessed. After completing the sample size task, the subjects in each experimental group were divided into two conditions. In the base-rate-first condition, the subjects were first offered information about the leisure preferences distribution among the 500 members in the community center of which Hickory members are a fraction). In the target-information-first condition, subjects were first offered a short personality sketch of the target person (the person whose card was lying on the table). Subjects were asked to rate their degree of interest in receiving the information. Subjects then actually received the information, which was described to them. Here they were divided into two additional conditions. In the supportive-information condition, the additional information was consistent with the jogger hypothesis (i.e, either that a relatively high proportion of joggers belonged to the community club or a jogger-matching personality description of the person). In the nonsupportive-information condition, the information was inconsistent with the jogger hypothesis (either that a very small percentage of joggers belonged to the community center or a jogger-mismatching personality sketch). Subjects made a prediction and then were offered a second set of information (either target information or base rate). They completed the related tasks about this information too. The second set of information corresponded to the first set in being jogger supportive or nonsupportive. After making each probabilistic judgment, subjects were asked to rate again their confidence in their prediction in light of the new information. This experimental procedure resulted in 16 different experimental conditions (4 linking structures groups X 2 orders of presentation X 2 levels of information supportiveness). A more detailed description of the experimental procedure follows.

Interest in Receiving Base-Rate and Target Information

Actual Application of Base-Rate and Target Information After rating the potential usefulness of the source of information, the subject was actually presented with that information. Base-rate information. Subjects were presented with a diagram describing the distribution of the 500 community center members according to their preferred leisure activity. In the low-base rate condition, this diagram indicated that 25 (5%) of the members chose jogging as their preferred leisure activity. In the high-base-rate condition, the diagram indicated that 120 (24%) of the members chose jogging. Target information. Subjects were presented with one of the following versions of a personality description supposedly written by a psychologist about the particular person whose card was lying on the table: [Jogger-inconsistent [consistent] personality description] Jacob, 38, is quite intelligent but [the "but" omitted] he also seems to be unwilling [willing] to invest a lot of effort and to persevere. He shows a poor [very good] ability of effort endurance and a poor [very good ] ability to sustain effort in moments of strain. It seems likely that Jacob will choose tasks which are below his capabilities [reflect these capabilities] and will be choosing activities that do not demand [that demand ] focused effort, perseverance, and coping with strain. After presentation of the information (base-rate or target information), subjects were asked to make a probabilistic prediction about the target person and a confidence judgment. Afterwards, subjects in the base-rate-first condition received the tasks related to the target information and vice versa.

Results Interest in Receiving Base-Rate and Target Information Interest in base rate. The means of the interest ratings in receiving the base rate in the four linking structures groups are presented in Figure 4. A 2 X 2 X 2 ANOVA (Relevant Link X Converse Link X Order of Presentation) did not reveal any effect for order of presentation; that is, subjects showed the same degree of interest in seeing the base rate whether they saw it before or after the target information. Consistent with the two

Subjects were presented with one of the following descriptions: [Base-rate information first] A diagram found in the office of the community center describes the distribution of the S00 community members according to their preferred leisure activities. One can learn from this diagram how many of the members from the center have chosen each of the activities as their preferred leisure activities. [Target information first ] A psychologist working for the community center wrote a short personality description of each of the members in the center. The psychologist's written description is based on a series of projective tests which he administered to each of the members. [This description followed Kahneman and Tversky (1973).] [Both conditions] Please indicate the degree in which receiving this information (the diagram; the profile of the person under consideration) might be useful to you in correctly estimating the probability that the Hickory Club member whose ID card is lying on the table prefers jogging as a leisure activity.

full-full

full-partial

Base rate

partial-full

partial-partial Target

The scalerangedfrom this information will be ofno use at all (0) to this Figure 4. Mean interest in receiving base-rate information and target information, in the four linking structures groups. information will be of very great use (7).

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prediction. Figure 5 presents the probabilistic judgments made in the two base-rate conditions (low vs. high) nested in the four different linking structures groups. The critical tests for the two hypotheses in this task were the different comparisons between the two base-rate conditions (low vs. high) in each of the linking structures groups. As predicted, there was a significant interaction between the base-rate values and the linking struc40ture conditions, F(3,239) = 7.2 p < 001. Comparisons between the base-rate-value conditions in the different groups revealed that in the FF group, there was no difference between the two 20base-rate-value conditions; in the FP group, there was a nonsignificant tendency toward difference, p = .09; there was a large effect in the PF group, F(l, 240) = 72.7 p < .001; and there was an even larger effect in the PP group, F(l, 240) = 93.2, p < .001. full-full full-partial partial-full partial-partial These results follow the order of effects (FF < FP < PF < PP) predicted by the combination of the relevant and converse link, • Low base rate E^ High base rate thus they support the two hypotheses. Figure 5. Mean probabilistic judgment, after receiving the base-rate, Use oftarget information. Figure 6 contains the probabilistic by the base-rate-condition (low vs. high) and by the linking structures judgments made in the different conditions after receiving the groups. target information. Once again, there was a significant interaction between the base-rate-value conditions and the linking structures groups, F(3, 239) = 6.8, p < .001. Comparisons within different linking structures groups revealed that in the theoretical predictions, there was a highly significant main efFF group, there was no effect for the target information (i.e, fect of the relevant link, F(l, 240) = 13.84, p < .001, and a near whether the target person possessed jogger attributes), F(l, significant effect of the converse link, F(l, 240) = 3.54, p = .06. The FF, FP, PI? and PP groups' mean interest in the base rate were 245) = 1.2, ns; however, this time there was an informational effect in the FP group, F(l, 240) = 17, p < .001; there was a 3.17,3.5,3.97, and 4.77, respectively. considerably larger effect in the PF group, F(l, 240) = 101, p < The study included an additional measure of sensitivity to .001; and the largest effect was in the PP group, F(l, 240) = 203, the base rate. As was pointed out by Beyth-Marom and Fischp < .001. Thus, the predicted order of effects was followed here, hoff (1983), whose party task was used in the present study too, supporting both hypotheses. (Task 1), the first item of their task is concerned with the perIncremental judgmental confidence after receiving the addiceived relevance of P(H), the base rate (i£, the percentage of tional information. After each informational item (base-rate or joggers attending the party). In this judgment, there was a sigtarget information), subjects were asked to rate their current nificant main effect of the relevant link, F(l, 243) = 26.76, p < degree of confidence in the prediction they had just made. .001, but not of the converse link. The relevance ratings of the Full-linked subjects exceeded their partial counterparts after FI5 FP, PI; and PP groups were 4.47,4.34,5.9, and 6 respectively. Overall, there was strong support for the first hypothesis and evidence for the second hypothesis on one of the two measures. Interest in Target Information. Similar analyses were conducted on the judgment of the interest in the target information (see Figure 4). The findings generally replicated theresultsobtained with the base rate. Here, too, there was no main effect 60nor any two-way interaction involving the order of presentation; however, there was a three-way ordinal interaction, involving the order factor, F(l, 240) = 4.87, p < .03; there was a significant 40main effect of therelevantlink, F(l, 240) = 6.46, p < .02, and a near significant main effect of the converse link, F(l, 240) = 3.61, p = .059. The mean interest in the information in the FIS 20FP, PF, and PP groups were 3.28, 3.7, 3.72, 4.31, respectively. Thus, the data were consistent with the two research hypotheses.

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oo,

Actual Use of Base-Rate Information in Revising Probabilistic Predictions A crucial question is whether the linking structures would affect, in addition to the initial degree of interest in receiving the base-rate information, the actual base rate impact on the

full-full

full-partial

Unsupportive

partial-full

partial-partial

Supportive

Figure 6. Mean probabilistic judgment, after receiving the target information, by the target information condition (unsupportive vs. supportive) and by the linking structures groups.

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YECHIEL KLAR

receiving the base-rate information (M= 4.93 and 4.48, respectively), F(1,236) = 3.66, p = .057, and after receiving the target information (5 and 4.05, respectively). Judgmental confidence was unrelated to the base-rate value (F < 1), or to the target-information value, F(l, 236) = 1.98, p =. 16. When the incremental gained confidence was assessed (the difference between the confidence before and after receiving the additional judgmentrelevant information), it revealed that partial-linked subjects, as compared with full-linked subjects, revised their confidence ratings more after reviewing the base rate. There was a main effect of the relevant link on these scores, F(l, 240) = 25, p < .001, and of the converse link, F(l, 240) = 7.58, p < .01. The means reflected the order predicted by the two hypotheses (Ms .28, .97,1.59, and 2.43, respectively). Similar results were found for the target information: a main effect of the relevant link, F(l, 240) = 10.77, p = .001, and for the converse link, F(\, 240) = 4.52, p < .05. The means of the confidence gained reflected the predicted order (Ms = .41, .98,1.3, and 1.87). Discussion All the different measures of sensitivity to additional information used in this part of the study lend strong support to the first hypothesis. The relevant link affected subjects' degree of interest in receiving judgment-relevant information (base-rate or target information), the degree of their actual use of the information, and the gained confidence in the prediction. The effects of the converse link were considerably weaker; however, evidence for this effect was found in six out of the seven measures ofsensitivity to the base-rate/target information. The similar effects for the base-rate information and for the target information suggest that the linking structures effect has generality beyond the use of statistical judgmental information (likelihood ratio, sample size, base rate) and that it can be applied to nonstatistical judgmental information (eg, target information) as well. The design of the study enabled testing whether the type of information (base-rate vs. target information) affected the degree of interest in receiving it. According to the base-rate literature, subjects are more interested in receiving the target information than the statistical base rate (the linking structures hypothesis is silent on this particular point). As can be seen from looking at Figure 4, no general preference for the target information was found. A repeated measures ANOVA corroborated this impression; it failed to find any effect that was due to the type of information. This finding suggests that no bias for or against the base-rate information was discovered in this particular paradigm. Lack of inherent bias against base-rate use was also recently reported in a different paradigm by Lynch and Ofir (1989). Another typical finding not found in the present study is the traditional "seesaw effect" between the use of the two types of information. That is, in a typical base-rate study, the more subjects take one source of information (e.g, the target information) into account, the less they will take other information (e.g, base-rate information) into account (e.g, Birnbaum & Mellers, 1983; Borgida & Brekke, 1981; Ginossar & Trope, 1980,1987; Hinsz et al., 1988; Kassin, 1979; Lynch & Ofir, 1989). In the present study, the reverse happened: In the same conditions in which the base rate was sought and used (partial

D-H link), the target information was used and vice versa. A plausible explanation for this difference is that in the present study, there was no built-in competition between the two types of information, as is the case in most base-rate studies (i.e, in which the two types of information lead to opposite conclusions, so that accepting one type of information necessarily means rejecting the other). When no such competition between the two sources of information exists and the sensitivity to each type of information is independently assessed, the relations between the degree of sensitivity to the two types of information appear to be of a positive rather than a negative nature. That is, in some conditions (e.g, perceived partial D-H link), subjects are receptive toward both types of information, whereas in other conditions (e.g, perceived full D-H link), they are attentive to none of them. Taken together, these findings add to a growing consensus that the degree of base-rate use can be best described in terms of general conditions affecting the use of judgmental information (e.g, sensitivity to judgmental information, the perceived relevance of the information), rather than by a specific cognitive deficit in attending to this particular type of information (Bar-Hillel, 1984; Ginossar & Trope, 1987; Lynch & Ofir, 1989). Task 4: AC and DA Logical Fallacies In a typical task in the logical reasoning literature, subjects are provided with a statement in the form of "If p then q" and asked which of the four possible inferences—the MP, MT, AC, and DA—are also true if the given statement is true. As was already discussed, two typical responses are the nonjustifiable endorsements of two inferences, AC and DA (see Evans, 1982, for a review). The linking structure approach predicts that the AC and DA inferences should be endorsed more often when the q-p link is perceived as full rather than partial. That is, when the subject is asked to regard a statement such as "all Hickory Club members (p) prefer jogging (qf as a true statement and this subject also believes that people with a particular activity (e.g, joggers) can only be in a particular club (e.g, Hickory Club; a full activitiesclubs link), the AC ("if a jogger, then a member of Hickory Club") and the DA ("if not a member of Hickory Club, then not a jogger") inferences seem to also be true statements. In addition, a converse effect would be predicted here, as in the other tasks. Note that in this particular experimental task, unlike the previous tasks, therelevantlink is the activity-club link. Therefore, the major comparisons should be made this time between the groups with the full activity-club link, FF and PF, and the groups with the partial activity-club link, pp and FP. More specifically, unlike the previous tasks, the FP group (full clubactivity link, partial activity-club link) should be superior in these tasks to the PF group (partial club-activity link, full activity-club link). However, this change in the link for the inference should not affect the two symmetrical groups, FF and PP. Method Procedure After completing all the base-rate/target information tasks, subjects in the different experimental groups were divided again into two order groups: One halffirstreceived the four inferences task, while the other half first received the Wason selection task (to be later discussed).

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LINKING STRUCTURES After completing the first assigned task, each group received the other task.

Four Inference Tasks

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Subjects received the following written instructions: Assume for a moment that the statement "All the members of the Hickory Club are joggers" is true. Under this hypothetical assumption please evaluate for each of the following four statements the degree that they are also true. Please evaluate each of the following statements separately: (1) If someone is a member of the Hickory Club, then he is a jogger