perception of social distributions

Journal of Personality and Social Psychology1985, Vol. 48, No. 2, 297-311

Copyright 1985 by the American Psychological Association, Inc.0022-3514/85/S00.75

Perception of Social Distributions

Richard E. Nisbett and Ziva KundaUniversity of Michigan

Accurate representation of the distribution of social attitudes and behaviors canguide effective social behavior and is often essential for correct inferences. Weexamined the accuracy of people's beliefs about the distributions of a largenumber of attitudinal and behavioral dimensions. In two studies we measuredactual attitudes and behaviors in a student population, and we assessed beliefs byasking subjects to estimate the distribution of 100 students on these dimensions.We examined the accuracy of subjects' perceptions of the means, standarddeviations, and distribution shapes. Subjects showed a number of systematicbiases, including overestimation of dispersion and overestimation of the means ofbehavioral distributions and a false consensus bias, but their overall accuracy wasimpressive.

Approximate knowledge of the distribu-tions of important social variables wouldseem to be essential for effective social func-tioning. Reasonably accurate guesses aboutthe dispersion and central tendency of im-portant behavioral and attitudinal dimensionscould serve to guide one's behavior and self-presentation in unfamiliar social situations.Such knowledge could allow one to adhereto accepted norms of behavior and conver-sation and to steer away from controversialtopics so as to avoid offending others whohold different opinions. Indeed, one's effec-tiveness in group situations often depends onthe ability to gauge the extent of support forone's own position. Politicians have long ap-preciated the value of knowledge about others'opinions, and contemporary ones are willingto spend large sums of money on polls de-signed to obtain very precise knowledge ofopinions.

Approximate knowledge of the parametersof social distributions also would seem to beessential in order to make appropriate infer-

This research was supported by National ScienceFoundation Grant SES-8218846 and National Instituteof Mental Health Grant 1RO1 MH38466-01. We thankJ. E. Keith Smith for advice on the analysis of the dataand Henri Zukier for theoretical suggestions. Keith Hol-yoak, Daniel Kahneman, Jon Krosnick, Darrin Lehman,and Lee Ross provided thoughtful criticism of an earlierdraft of this article. Sara Freeland provided able editorialhelp.

Requests for reprints should be sent to Richard E.Nisbett, Institute for Social Research, University of Mich-igan, Ann Arbor, Michigan 48106.

ences about the meaning of social behavior.In fact, Kelley (1967) considered "consensusinformation," that is, information about thedistributions of people's attitudes and behav-ior, to be a major factor in his analysis ofvariance (ANOVA) scheme for inferences aboutcausality in the social domain. More recently,Thagard and Nisbett (1982) have argued thatknowledge about the variability of kinds ofobjects, including social objects, is re-quired for appropriate generalizations. Nis-bett, Krantz, Jepson, and Kunda (1983) havedemonstrated that such knowledge mediatesother types of statistical inference as well.

Despite the importance of people's percep-tions of social distributions, there are veryfew studies that have examined the degree ofpeople's accuracy in perceiving the centraltendency, dispersion, or shape of behavioraland attitudinal distributions.

Some indirect evidence comes from workon perception of physical objects, which in-dicates that people are highly sensitive to allthree of these parameters. It has long beenknown that people are quite able to estimatethe central tendencies of perceptual distri-butions (e.g., Peterson & Beach, 1967; Posner& Keele, 1968). More recent work by Friedand Holyoak (1984; Flannagan, Fried, &Holyoak, 1984) shows that people are alsosensitive to dispersion and distribution shape.They presented subjects with computer-gen-erated variations on a particular visual theme,for example, a pattern of light and darkpatches on a grid or a pattern of coloredrectangles.

297

298 RICHARD E. NISBETT AND ZIVA KUNDA

Subjects were more willing to classify agiven variant as an exemplar of a particulartype of pattern if the previous exemplars werehighly variable on the dimensions composingthe type, than if previous exemplars were lessvariable. Subjects were also highly sensitiveto distribution type. When the dimensionsfrom which exemplars were constructed weredistributed in a normal bell-shaped curve,subjects readily learned to classify a patternas being of the particular type that in factgenerated it. The probability of assigning apattern to its parent type was greatest nearthe center of the dimensions underlying thetype and fell off in proportions dictated bythe shape of the normal curve.

When subjects were instead presented withpatterns generated by bimodal, U-shaped di-mensions, their classifications did not trackthe actual frequencies of the dimension values.Instead, subjects made their guesses aboutclassification as if they believed the distribu-tions of the dimensions were normal. Evenafter a very large number of trials exposingthem to different patterns, subjects failed todistribute their guesses in the same fashionas the actual dimensions. Instead, their guesseswere distributed in an essentially flat fashionacross the dimensions.

Work on the perception of physical dimen-sions thus indicates that people can be quiteaccurate in assessing central tendency anddispersion and that they have a very heavybias toward perceiving normality in distri-bution shapes. Given the apparent frequencyof normal distributions in nature, it is possiblethat this bias might serve to make perceptionmore accurate and efficient. Observation ofa very few exemplars would serve to give afair idea of central tendency, and, if normalityof the dimensions is presumed, variance orstandard deviation could also be estimatedwith fair accuracy. Thus the classification ofnew objects or events would be maximallyefficient in a statistical sense, so long as theunderlying dimensions are in fact distributedapproximately normally.

Although it is possible that people are alsoaccurate about the central tendency and dis-persion of social distributions and have auseful bias toward assuming their normality,there are good grounds for suspecting thatthey might not be very accurate. This isbecause beliefs about social dimensions are

subject to some unique sources of bias. Thefollowing potential errors in the perceptionof social distributions have been identified(cf. Nisbett & Ross, 1980):

1. People seem likely to be influenced bythe availability of exemplars (Tversky &Kahneman, 1973). Because extreme behaviorsand opinions are likely to be salient (indeedpeople with extreme dispositions and opinionsare likely to take steps to guarantee that theywill be salient), their overrepresentation inmemory may lead to an overestimation ofthe variability of social distributions. Indeed,it has been shown that individuals with ex-treme physical or social characteristics aremore available in memory and are conse-quently estimated as more frequent than cor-responding numbers of less extreme individ-uals (Rothbart, Fulero, Jensen, Howard, &Birrell, 1978).

2. A special case of availability, that is,knowledge about one's own value on socialdimensions, might produce systematic errorsin estimates of central tendency. One's per-ception of the entire distribution might beshifted toward one's own location. This falseconsensus tendency has already been docu-mented for a number of attitudes (e.g. Fields& Schuman, 1976) and behaviors (Ross,Greene, & House, 1977).

These investigators and others whom theycite (as well as subsequent studies, e.g., Judd& Johnson, 1981 and van der Pligt, 1984),have shown that people tend to assume thata higher fraction of the population sharestheir own views, or would behave as theyhave, than is the case. The work gives us littleindication, however, of the degree of distortionthat this produces in estimates of centraltendency and no indication at all of theeffects on estimates of dispersion or distri-bution shape.

3. There is a well-known tendency of groupmembers to exaggerate the differences be-tween themselves and out-group members(e.g., Campbell, 1967; Child & Doob, 1943;Quattrone, in press; Sherif, Harvey, White,Hood, & Sherif, 1961; Tajfel, 1970; Vinacke,1949). This suggests the possibility that peoplemight have a bias toward assuming bimodalityfor social distributions—"my kind" and "notmy kind" (a tendency actually found in onestudy by Judd & Johnson, 1981).

Current theory and some evidence therefore

SOCIAL DISTRIBUTIONS 299

suggest that people may not be as accuratein their perceptions of statistical parametersfor social distributions as in their perceptionsfor physical distributions. Additional supportfor this expectation is suggested by researchon inferential errors. Substantial evidenceshows that people do not make proper infer-ences when reasoning about problems involv-ing social distributions. For example, Hamill,Wilson, and Nisbett (1980) showed that peo-ple may draw essentially the same conclusionsabout a population when told that an extreme-appearing case is a highly biased sample ofthe population as when they are told that thecase is drawn from the center of the popula-tion distribution.

It is possible to explain errors such as theseeither in terms of people's inadequate com-mand of the requisite statistical rules (Kahne-man & Tversky, 1972, 1973; Tversky &Kahneman, 1974) or in terms of their in-ability to picture the relevant social distri-butions. Recent work shows that faulty beliefsmay play a bigger role in producing inferentialerrors than originally thought.

It appears that people may have someappreciation of statistical rules but that thesemay be applied only to domains that lendthemselves to accurate representation of thecentral tendencies and dispersions of the rel-evant distributions (Fong, Krantz, & Nisbett,1984; Jepson, Krantz, & Nisbett, 1983;Kunda & Nisbett, 1984; Nisbett et al., 1983).For example, people seem to be able toreason statistically about abilities and aboutsports events but to have more difficultyreasoning statistically about personality traitsand social behaviors.

This seems to be the case because it iseasier to perceive the distributions of theformer sorts of events than of the latter. Theunits of measurement for abilities and sportsevents are usually clear (score on the test,number of baskets shot), and they are oftenobserved in situations that are relatively fixed,therefore permitting comparisons amongpeople.

Traits and most other social behaviors arenot so clearly measurable: There are noobvious units for shyness or honesty, forexample; and it is rare to observe large num-bers of people in situations that can be pre-sumed identical, so that their behavior canbe directly compared. These results suggest

that beliefs about social distributions mightbe quite inaccurate, perhaps due to the kindsof biases discussed earlier.

Thus it is important to determine howaccurate people's perceptions of social distri-butions are, both because of the "first order"importance of accuracy about social distri-butions for purposes of social conduct andbecause of the "second order" importance ofaccuracy for purposes of inferences aboutcausality and meaning.

The results of an investigation of the ac-curacy of perception of social distributionsalso would have educational implications. Ithas been shown that instruction in statisticsimproves people's ability to answer statisticalquestions about everyday social objects andevents (Fong et al., 1984; Krantz, Fong, &Nisbett, 1984). If it should turn out thatpeople have very inaccurate beliefs aboutsocial distributions, however, then this wouldimply that training should also focus onteaching people how to represent social dis-tributions accurately.

Study 1: Perception of Behavioral andAttitudinal Dimensions

Method

Selecting Dimensions

In Study 1, we examined the accuracy of subjects'perceptions of the mean, standard deviation, and shapeof a number of behavioral and social distributions. Tochoose the dimensions, we tacitly denned a space ofsocial attitudes and behaviors including public and privateones, socially desirable and socially undesirable ones, andseemingly important and trivial ones. From these wechose dimensions haphazardly within the constraint thatwe wanted to include a large number of nonnormaldistributions in order to see whether subjects would bebiased toward seeing them as normal.

Thus, we tried to include dimensions that wouldproduce bimodal distributions and J distributions withthe central tendency far to the right or left of the scaleof logical possibilities for the dimension. The resultingset of items is very arbitrary and cannot be consideredan unbiased sample from any precisely denned universeof behaviors and attitudes. It is unclear, of course,whether any procedure could approximate such a sample.

Subjects and Procedure

Subjects were 247 University of Michigan studentsenrolled in introductory psychology classes. Only 14% ofthe subjects had had any training in statistics. Theyparticipated in groups of 3 to 8. Sixty-two of the subjectswere asked to indicate the frequency of their actualbehavior on each of 17 dimensions, and 87 subjects were


asked to indicate their attitudes on each of 21 dimensions.Forty-eight subjects were asked to estimate the distribu-tions of 100 of their fellow University of Michiganstudents on each of the behavioral dimensions (i.e., theirreports of their behavior), and 50 subjects were asked toestimate the distributions of the attitudinal dimensions.

Behavioral Items

Subjects were asked 17 questions about behavior. Thesewere all answered on the scale below:

married? (c) How do you feel about women being allowedto have an abortion on demand? (d) How do you feelabout Ronald Reagan's conduct of the Presidency todate? (e) How do you feel about U.S. intervention tosupport the government in El Salvador? (f) How do youfeel about increasing defense spending? (g) How do youfeel about the University's plan to eliminate some schoolsand departments in order to generate money for newprograms? (h) How do you feel about Harold Shapiro'sconduct of the University Presidency to date?

The objects that subjects were asked to evaluate on 5-point scales were the following: (a) the actress Jane

Never Oncea year

2-5timesa year

6-11timesa year

Once amonth

2-3times amonth

Oncea week

2-3times

a week

4-6times

a week

Daily

The questions asked were the following: (a) How oftendo you play tennis? (b) How often do you shoot pool?(c) How often do you smoke marijuana? (d) How oftendo you have any trouble getting to sleep? (e) How oftenare you bothered by nervousness? (f) How often are youtroubled by headaches? (g) How often do you feel blueor down? (h) How often are you bothered by nightmares?(i) How often do you attend religious services? (j) Howoften do you go to concerts? (k) How often do you go toparties? (1) About how often do you get drunk duringthe year? (m) How often do you go to bars or nightclubs?(n) How often do you drink alcoholic beverages? (o) Howoften do you go to movies? (p) How often do you getangry with someone? and (q) How often are you late toclass?

Attitudinal Items

Subjects were asked eight questions about attitudes on10-point scales, and to make sure that our findings aboutaccuracy would not be limited to the case of the 10-point scales, with their particular format, subjects werealso asked to evaluate 13 objects on 5-point scales. Thetwo scales are reproduced below:

Fonda, (b) the television anchor Dan Rather, (c) themovie Raiders of the Lost Ark, (d) the movie Star Wars,(e) Pepperidge Farm cookies, (f) McDonald's hamburgers,(g) Saudi Arabians, (h) the Moral Majority, (i) Campbell'schicken noodle soup, (j) Ritz crackers, (k) the modelBrooke Shields, (1) former Secretary of State AlexanderHaig, and (m) international oil companies.

Results

We examined subject accuracy about dis-tribution parameters—central tendency anddispersion—in three complementary ways,(a) We calculated average correlation, acrossitems, between a given subject's estimatesand the actual values. This measure providesan indication of the extent to which peopleare calibrated about the ranking of the itemson each of these parameters, that is, abouttheir relative magnitudes, (e.g., a high corre-lation between subjects' estimates for themeans of different behaviors and the actual

Very Stronglystrongly disapprove

disapprove

Dislikevery much

Disapprove Somewhat Slightly Somewhat Approve Strongly Verydisapprove disapprove approve approve strongly

approve

Dislike somewhat Neither like nor dislike Dislike somewhat Dislikevery

much

The questions asked on 10-point scales were the fol-lowing: (a) How do you feel about people your own agetaking hard drugs? (b) How do you feel about peopleyour age living with another person while not being

values for the means, would indicate thatsubjects are knowledgeable about the relativefrequency of behaviors of different kinds.)


(b) We calculated simple average absolutedeviation of the estimates from the actualparameter. This measure provides an indica-tion of how close the estimates of the averageperson are to the actual parameters, for theaverage dimension, (e.g., small average abso-lute discrepancies of estimates of behaviormeans from actual behavior means wouldindicate that subjects are highly accurateabout the absolute frequency of various be-haviors.)

(c) In order to provide a way of evaluatingthese absolute deviations and assessing theirimplications, we also looked at the numberof cases, drawn randomly from actual distri-butions, that was required to equal the ac-curacy of the average subject's guesses aboutparameters as measured by absolute devia-tions. This measure indicates the size of thesample, drawn from the actual distribution,that would provide estimates of the parame-ters that were as accurate as those of theaverage subject. This measure was based oncomputer-drawn, randomly generated samplesof different «s from the actual distribution ofeach item.

For each item we drew 10 samples of eachn. We calculated the mean and standarddeviation of each such sample and then cal-culated, as we did for subjects' estimates, theabsolute deviations of these statistics fromthe parameters of the actual distributionsfrom which each sample was drawn. Thesewere averaged over items for each samplesize, and the resulting average absolute devia-tions were compared to those of the subjects'estimates. Accuracy is estimated by the num-ber of cases in the random samples requiredto equal subjects' discrepancies from actualvalues. The more cases required, the moreaccurate subjects are.

For each of these analyses, the basic datumwas our computation of the estimated param-eters, based on subjects' histograms. To avoidcircumlocutions, however, we will refer tosubjects' "estimates of parameters" ratherthan to our computation of the parametersbased on subjects' estimates of distributionsacross scale points. (Similarly, we asked sub-jects about their reports of behavior ratherthan measuring their behavior, but to avoidcircumlocutions we will refer to these as

"actual behavior" rather than as "reportedactual behavior.")

Although significance levels for analyses oftype (b), absolute average deviation, are re-ported, these are descriptive merely, becausethe various estimates are not independent.The results of these analyses are summarizedin Table 1.

Accuracy About Central Tendency

Behavioral dimensions. As may be seenin the top row of Table 1, subjects' perceptionsof the means of behavioral dimensions weremoderately accurate on the whole. The aver-age correlation between a given subject's es-timates of the means of the 17 behavioraldimensions and the actual means of thedimensions was .42 ± .06.' The average ab-solute error of estimates of the means ofbehavioral distributions was only 1.19 on the10-point scale. Because actual means rangedfrom 2.66 to 5.95, the accuracy was not dueto limits on the range of possible error. Therewas, however, a systematic bias in the subjects'estimates of behavioral distributions towardoverestimating behavior of all kinds. For 13of the 17 distributions, the average estimateof the mean was significantly higher than theactual mean for the dimension.2

Partly because of the overall bias towardoverestimation of the frequency of behaviors,subjects' guesses about means were not ter-ribly accurate when compared with the resultsof computer-drawn random samples of theactual distributions. On the average, a sampleof only 2 cases from behavioral distributionscame as close to the actual means as did theguesses by a typical subject.

Attitudinal dimensions. Subjects weremore accurate about the means of attitudinaldimensions. The average correlation betweena given subject's estimate of the means of theattitudinal distributions (pooling the resultsfor 10-point scales and 5-point scales) andthe actual means of the distributions was.73 ± .05. The average subject's guess aboutthe mean of 10-point scale items was only.89 away from the actual mean. (Actual means

' AH intervals represent 95% confidence intervals forthe correlations.

2 All p values reported are based on two-tailed tests.


Table 1Summary of the Results of Study 1

Average correlation ofeach subject's

estimates with theactual parameters

Central tendencyBehaviors .42 ± .06Attitudes .73 + .05

(5-point)Dispersion

Behaviors .47 ± .05Attitudes .26 ± .08

(5-point)

Average absolutedeviation of

Overestimation estimates fromof parameters parameters

yes 1.19no .89

.48

13% .459% .63

.18

Size of randomly drawnsample with sameabsolute deviation

23.57

610.57

ranged from 2.91 to 6.14.) The average sub-ject's guess about the mean of the 5-pointscale items was only .48 away from the actualmean. (Actual means ranged from 2.26 to4.12). There was no systematic distortion ofthe location of the mean toward either endof the scale. Subjects as a group were signif-icantly wrong in their estimates of only 12 ofthe 21 means; 5 of these were overestimatesand 7 were underestimates. On average, itrequired a random sample of 3.57 cases froman attitudinal distribution to equal the accu-racy of the typical subject's guess about themean.

Accuracy About Dispersion

Behavioral dimensions. Subjects' estimatesabout dispersion were also fairly accurate,despite a bias toward overestimating variabil-ity. The average correlation between the stan-dard deviation calculated for a given subject'sestimates of the behavioral distributions andtheir actual standard deviations was .47 ±.05. On average, subjects overestimated thestandard deviation of behavioral distributionsby 13%.

The results of t tests contrasting standarddeviations of estimated distributions withstandard deviations of actual distributionsyielded nine significant overestimates andonly four significant underestimates. The ab-solute discrepancy of standard deviation es-timates from actual standard deviations was.45 for the average subject, across dimensions.(The range of actual standard deviations was

from 1.15 to 2.40.) It required a randomsample of 6 cases to equal this level ofaccuracy.

Attitudinal dimensions. The average cor-relation between a given subject's estimatesof the standard deviations of the attitudinaldistributions and their actual standard devia-tions was .26 ± .08. Subjects overestimatedthe standard deviations of attitudinal dimen-sions by 9% on the average. Results of t testscontrasting standard deviations of estimateddistributions with standard deviations of ac-tual distributions yielded nine significantoverestimates and only two significant under-estimates.

The absolute discrepancy of standard de-viation estimates from actual standard devia-tions was .63 for the average subject for 10-point scales (where the actual range was 1.81to 3.19) and .18 for 5-point scales (actualrange .68 to 1.26). It required a randomsample of 10.57 cases to equal this level ofaccuracy.

It is striking that it required a substantiallylarger random sample of the actual distribu-tion to equal subjects' average accuracy aboutstandard deviations than to equal subjects'average accuracy about means. Because thestatistician's calculation of standard deviationis substantially more complicated than thecalculation of a mean, this is surprising onits face. On the other hand, it is distinctlypossible that subjects' rough-and-ready esti-mates of dispersion are actually easier forthem to compute and less prone to errorthan their rough-and-ready estimates ofmeans.


Table 2Percentage of Subjects Who Estimated a Given Distribution Shape for Each Typeof Actual Distribution Shape

Actualdistribution

shape

JLef tNormalJ RightBimodal

JLef t

3012

19

Estimated distribution

Normal J

44643851

shape

Right

24

436

Bimodal

24201834

A statistician can obtain a quite goodestimate of the standard deviation of a sampleof 20 cases simply by dividing the range by4 or 5 (cf. Snedecor, 1946, p. 198). Nocomparably easy estimate of the mean of 20cases exists. In addition, any rough calculationof the standard deviation relying on the rangerequires memory only for two values—thehighest and the lowest observed—and thesevalues would tend to be quite memorable.Comparable accuracy for the mean wouldrequire either remembering many more casesthan that or forgetting just the right ones!

A seeming anomaly in the attitude datashould be mentioned. Although the accuracyof mean estimates was considerably higherthan the accuracy of standard deviation esti-mates as measured by correlations, the reversewas true as measured by the size of therandomly drawn sample with an equally largeabsolute deviation. We suspect that this wastrue in part because subjects' estimates of thestandard deviations for attitudes in generalwere very close to the true range of standarddeviations, whereas the actual differencesamong standard deviations for attitudes werevery small.

This latter fact resulted in extreme trun-cation of range for standard deviations ofattitudes. Thus, although subjects were ingeneral very close to the actual values inevery case, they were not very well calibratedto the slight differences that existed betweencases.

Accuracy About Distribution Shapes

Subjects' guesses about distribution shapesshowed a heavy bias toward assuming nor-mality. All distributions, both actual andestimated, were denned (by a set of criteria

that were necessarily somewhat arbitrary) tobe either J Left (that is, central tendency onthe extreme left of the scale), J Right, Bi-modal, or Unimodal Symmetric (i.e., resem-bling a normal distribution).3 Approximatelyhalf of the distributions defined by thesecriteria were coded as normal and a thirdeach of the remainder as J Left, J Right, andBimodal.

Table 2 shows the cross-tabulation of esti-mated and actual distribution types, pooledacross behavioral and attitudinal dimensions.Subjects were overwhelmingly accurate atidentifying normal distributions. Where thedistribution was nonnormal, subjects' guesseseither favored the actual distribution shapeor favored a normal distribution, with theactual distribution shape coming in a strongsecond. These data indicate (a) very substan-tial accuracy in perception of distributionshapes and (b) an even more substantial biasin favor of seeing distributions as unimodalsymmetric.

An interesting view of subjects' accuracyabout all distributional parameters, includingshape, may be seen in Figures 1 and 2. Figure1 presents 16 of the 17 actual behavioraldistributions and the average of all subjects'estimates about the distributions. (One of thethree questions about alcohol consumptionis not included to save space, but it is notnotably different in any respect from theothers.) Figure 2 presents all 8 of the 10-

3 For example, to be designated unimodal symmetric,the highest point of a subject's Id-point scale distributionhad to be within slots 3-8 and the second highest pointhad to be adjacent or, if not, then the difference betweenthe second and third highest points had to be less than5%. Figures 1 and 2 show how various curves ended upbeing classified by the system.


point attitudinal scale distributions and 8 ofthe 13, 5-point attitudinal scale distributions(the dropped distributions are not notablydifferent from the retained ones). The curveshape for each actual distribution is indicatedat the top of each distribution.

The reader is warned that the averaging ofall estimated distributions allows for the pos-sibility of greatly overestimating individualsubject accuracy. With that caveat, it may beobserved that accuracy about distributionshapes, at the group level, is remarkableindeed. Whatever individual biases there arein the perception of social distribution pa-rameters, they tend to cancel out, save forthe previously mentioned overestimates ofthe sheer amount of behavior of all kindsthat people engage in and the mild overesti-mate of the standard deviation of both be-

havioral and attitudinal distributions. Amongother things, this means that when 2 or morepeople pool their estimates of social distri-butions they normally would come closer tothe truth rather than compounding their in-accuracy due to shared biases.

We have not yet examined the possibilitythat subjects show a substantial false consen-sus effect. Note that the overall accuracyportrayed in Figures 1 and 2 as well as theapparent bias toward normality could theo-retically be produced entirely by false consen-sus. If each subject estimated the distributionby constructing a unimodal distribution witha mode corresponding to his or her ownposition, all the errors would cancel eachother out when pooled together, and theresulting aggregated picture would be similarto that portrayed in Figures 1 and 2. Such a

Have Trouble Getting to Sleep

B

Get Drunk

Come Late to Class

Go to Concerts Smoke Marijuana

JL

Play Tennis Go to Parties

Figure 1. Actual and estimated distributions for behavioral items. Letters at the top of each distributiondenote coded shape of actual distribution: N = Normal, JL = J Left, JR = J Right, B = Bimodal.


heuristic could also produce the apparentbias toward normality, because it is true evenfor the nonnormal distributions that the po-sitions of a large proportion of subjects arelocated in the middle range of the scale; ifthese subjects used their own position as thesole basis for judging central tendency theywould estimate the distribution to be normal.But such a strategy could not possibly produceany accuracy about dispersion—one's ownposition on a distribution provides no infor-mation about the variability of the distribu-tion nor does one's own position on differentdistributions provide any information abouttheir relative variability.

Examination of false consensus bias canonly be achieved by asking the same subjectsabout their estimates of the population dis-tributions and about their own locations inthe distributions. (In Study 1, we did not

want to contaminate estimates about distri-butions with reports of own behavior andattitude, or vice versa.) In Study 2, we askedboth sets of questions of the same subjects.This made it possible to examine the degreeof false consensus in estimates. The previousliterature on false consensus does not allowfor a very good estimate of the degree oferror because in most studies the data weredichotomized, and it was shown merely thatsubjects tended to overestimate the numberof people who behaved in the rough way theydid or who held the approximate opinionthey did.

Study 2: False Consensus in the Perceptionof Social Distributions

MethodOne hundred three University of Michigan students

enrolled in introductory psychology classes were presented

University's Budget Cuts Unlwslty President's Conduct

JL

U.S. Intervention In El Selvedor Increeslng Defense Spending

International Oil Compsnles

JR

Moral Majority CsmpbeirsSoup

JR JL-

Ssudl Arabians

Figure 2. Actual and estimated distributions for attitudinal items. Letters at the top of each distributiondenote coded shape of actual distribution: N = Normal, JL = J Left, JR = J Right, B = bimodal.


Table 3Summary of the Results of Study 2

Average correlation ofeach subject's

estimates with theactual parameters

Central tendencyBehaviors .55 ± .04Attitudes .56 ± .10

(5-point)Dispersion

Behaviors .44 ± .04Attitudes .25 ± .06

(5-point)

Average absolutedeviation of

Overestimation estimates fromof parameters parameters

yes .95no 1.18

.60

9% .4315% .63

.26

Size of randomly drawnsample with sameabsolute deviation

22.36

77.29

with the behavioral items in Study 1 and were askedboth to indicate their own position on the scale and todistribute 100 students enrolled in introductory psychol-ogy over the 10 scale points. (The reference populationdiffers from that in Study 1, where subjects were askedabout University of Michigan students. The match betweenactual population and the description of the populationgiven to subjects was thus closer in Study 2 than in Study1.) Another 120 introductory students were presentedwith the attitudinal items in Study 1 and were askedboth to indicate their own position on the scale and todistribute 100 introductory students over the 10 (or 5)scale points. For both behavioral and attitudinal items,half the subjects answered for themselves first and halfgave estimates about the distributions of other subjects'reports first. Procedure was otherwise identical to that inStudy 1.

Results

As may be seen in Table 3, the majoranalyses produced results virtually identicalto those of Study 1. Significance levels tendedto be higher, however, because the N wasgreater.

False Consensus and Accuracy about Means

There was a decided false consensus effect,but it was not of great magnitude, either forbehaviors or for attitudes.

Behaviors. The average correlation, acrossdimensions, between subjects' own behaviorallevel and the mean of their estimated distri-butions was .28 (p < .01; the correlation was.23 when subjects indicated their own re-sponse first and .34 when they gave estimatesabout the distribution first). For all of thebehavioral dimensions the average subjectestimated the mean of the distribution to becloser to its actual mean than to the subject'sown level: All but one of the estimated means

were closer to the actual mean than to thesubject's own level at p < .01 (though it shouldbe noted that these are descriptive only be-cause of lack of independence). The averagediscrepancy between the subject's guess aboutthe mean and the actual mean was .95,whereas the average discrepancy between thesubject's own value and the actual mean was1.95;tfll8) = 12.95, p<.001.

Attitudes. The average correlation betweensubjects' own attitudes and the mean of theirestimated distributions was .32 (p < .001;the correlation was .34 when subjects indi-cated their own attitude first and .28 whenthey gave their estimates about the populationfirst). For all but one of the attitudinal di-mensions, the average subject estimated themean of the distribution to be closer to itsactual mean than to the subject's own attitude.All but seven of the estimated means werecloser to the actual mean than to the subject'sown attitude at p < .01. The comparison ofthe overall average discrepancies, which were.80 for estimate versus actual and 1.17 forown versus actual, was highly significant,f(98) = 9.95, p<. 001.

Subjects' estimates of means are thus influ-enced by their own values, but this influenceis not great and their estimates of the meansare substantially closer to the actual meanthan to their own level. Thus, subject's ownvalue is not the exclusive, or even the major,contribution to accuracy about means.

False Consensus and Distribution Shape

There was a decided relation between sub-jects' own positions and the shape of their


Table 4Percentage of Subjects Whose Position Corresponds to J-Left, Normal, or J-Right Curves, Estimatingthe Curve to be Each of the Possible Curve Shapes, for Curves That are in fact J Left, Normal, and JRight*

Actualcurve

JLeft

Normal

J Right

n

196199

9

2321602

73

25409250

Subjects'position

JLNJR

JLNJR

JLNJR

Subjects' estimates

JLeft

42180

3378

05

10

Normal

345044

376927

16438

J Right

33

12

12

29

83269

Bimodal

212944

292136

762014

* Actual bimodal curves were not included in this analysis because a subject's position cannot correspond to a bimodalcurve.

estimated distributions, suggesting that ownposition played a significant, though not asingular role in determining subjects' esti-mates of shape. To examine this relation wepooled together all the J-Left curves, all theNormal curves, and all the J-Right curvesfor attitudes and behaviors. For each curveshape we identified the subjects whose ownpositions were located at the extreme left ofthe distribution, the subjects whose own po-sitions were in the middle range, and thesubjects whose own positions were at theextreme right of the distribution.

If subjects were relying entirely on theirown position (estimating the curve to beunimodal with a mode located at their ownposition), then these three groups of subjectswould be expected to estimate the curveshapes, respectively, as J Left, Normal, and JRight, and no subject would be expected toestimate the curves as Bimodal. Table 4presents, for curves that are J Left, Normal,or J Right, the percentage of subjects whoseown positions were in each of the three rangecategories who estimated the curves to beeach of the possible shapes.

It may be seen first in Table 4 that ownposition clearly played a role in estimates ofcurve shape. For example, in the first andsecond rows of Table 4, for J-Left curves,subjects whose own positions were at theextreme left favored J-Left curves in theirestimates, whereas subjects whose own posi-

tions were in the central range favored normalcurves. And a similar pattern is found for J-Right curves, where subjects whose own po-sitions were at the extreme right overwhelm-ingly favored J-Right curves in their estimates,whereas subjects whose own positions werein the central range favored normal curves.Further, for each actual curve shape thehighest accuracy rate (i.e., percentage of cor-rect identifications) is found for subjects whoseown positions corresponded to the actualdistribution shape.

Thus there is no question that subjects'own positions influenced their guesses aboutdistribution shape. But it is equally clear thatfalse consensus could not be the only mech-anism influencing subjects' guesses. First, asnoted earlier, if false consensus were the onlymechanism, no subject would estimate thedistribution to be bimodal. Yet, on average,27% of the guesses are bimodal.

More strikingly, in most cases the majorityof subjects do not believe the distributionshape to correspond to their own positions.The only two exceptions to this are for caseswhere subjects' own positions do in factcorrespond to the actual curve shape. Further,it may be seen that subjects appear to knowwhen their own position is extremely differentfrom that of the modal person. Thus, for J-Right curves, not one of the subjects whoseown positions were in the extreme left rangemade the serious error of estimating the


curve to be J Left, and for J-Left curves only12% of the subjects whose own positions werein the extreme right estimated the curves tobe J Right.

The overall extent of false consensus maybe gauged from the following comparison.The average probability of estimating thedistribution shape as corresponding to one'sown position when one's own position doescorrespond to the actual distribution shapeis 60%. But the average probability of esti-mating the distribution shape as correspond-ing to one's own position when one's ownposition does not correspond to the actualshape is only 28%. The difference betweenthe two percentages reflects the impact offorces other than knowledge of one's ownposition that affect subjects' estimates.

Another important finding in Table 4 isthat the apparent bias toward normality ap-pears to have been due in part to falseconsensus. Subjects whose own positions werenot in the normal range show only a slightpreference for normal curves. These datasuggest that the tendency to view distributionsas normal is a rather weak default for subjectswho are not themselves located fairly nearthe center of the distribution.

Discussion

In general, we find subjects' estimates aboutsocial distribution parameters to be surpris-ingly close to the actual values. They werenot overwhelmingly accurate about any singleparameter, as evaluated by any given type ofanalysis, and they showed several types ofsystematic bias. The errors, however^ werenot very large and the biases underlying theerrors do not seem to be of very great mag-nitude. We begin with a review of the biasesand then return to an assessment of the likelyreal world accuracy that people might beexpected to display.

Biases in the Perception ofSocial Distributions

The results provide strong evidence forfour different sources of bias in estimates ofdistributional parameters for social dimen-sions.

1. Subjects overestimated the degree ofdispersion. The extent of the overestimation

is not great—a little more than a 10% over-estimate of standard deviation on averageacross studies and across types of social di-mensions—but the overestimation was quitesystematic. The most natural way to under-stand this error is in terms of the availabilityheuristic. Extreme behaviors and attitudesare more salient than nonextreme ones, en-tirely aside from the fact that people whobehave in extreme ways or who hold extremeattitudes often take steps to ensure that theirbehavior or attitudes are highly salient. Whenpeople try to estimate dispersion, the extremeexamples will be more available than theyare frequent.4

2. Subjects overestimated the means ofbehavioral distributions. The extent of theoverestimation was not great, but it washighly reliable. It is not clear why peopleshould overestimate the sheer frequency ofbehavior of most kinds. Perhaps the expla-nation is similar to the explanation for over-estimation of dispersion. Behavior is moresalient than nonbehavior, thus when onecomes to estimate the frequency of behaviorfor people on some dimension the behaversare more salient than the nonbehavers andcontribute disproportionately to the outcome.There is of course no comparable phenome-non for attitudes, because it is both extremesof the dimension that are salient rather thanjust one, and we in fact found no systematictendency to displace the means of attitudescales in one direction or the other. Thisexplanation is consistent with the literatureon the feature-positive effect, which docu-ments people's tendency to ignore or underusenonoccurrences when making judgments andsolving problems. This effect has been dem-onstrated for a diverse range of domainsincluding, for example, animal and humanlearning (Jenkins & Sainsbury, 1970; Sains-bury, 1983), judgment of contingency (Nisbett& Ross, 1980; Ward & Jenkins, 1965), andself-perception (Fazio, Sherman, & Herr,1982).

4 An alternative explanation for the overestimation ofdispersion should be noted. This is the trivializing pos-sibility that our method of presenting the subjects withhighly dispersed scale values encouraged them to usethose extreme values, whereas had they spontaneouslygenerated, say, a range, they might not have overestimateddispersion.


3. Subjects skewed the central tendenciesof distributions in the direction of their ownlevel on the distribution, for both behaviorsand attitudes. The average distortion of theseparameters due to false consensus was notgreat, however. Subjects' estimates of distri-bution shapes were also influenced to someextent by their own positions. The mechanismunderlying these false consensus effects isagain most probably the availability heuristic.One always has an estimate for at least one'sown level on a given dimension. Only underspecial conditions, such as having unequivocalknowledge of a number of people's positions,or holding a theory that one is unusual on aparticular dimension, does it seem likely thatknowledge of own position would fail to havean effect on the estimate for the distributionas a whole.

4. Subjects showed a weak bias towardcharacterizing distributions as normal. It isour guess that this tendency would worktoward producing accuracy in most circum-stances. It is of course impossible to know,because of unanswerable sampling questionsand scaling questions, whether normal distri-butions are the rule for social events. If theyare, the bias is clearly useful. People wouldbe well-served by using their point estimates(knowledge of their own levels on particulardimensions and those of their friends) asinputs into a formula assuming normality.This typically would produce a characteriza-tion of the distribution that is accurate andthat is expressible with great economy interms of psychological parameters corre-sponding to mean and standard deviation.

Accuracy in the Perception ofSocial Distributions

The biases noted would not serve, of them-selves, to produce serious inaccuracy in theestimation of social distributions. And oneof them, the false consensus bias, is a veryuseful heuristic to employ in the absence ofother knowledge: For most of the distributionswe examined, the majority of people wouldbe right to assume that most other people'sstances are not very different from their own.

Indeed, the major lesson that we drawfrom our data is that people are skilled inestimating social distributions of populations

with which they are familiar. They knowwhat major kinds of distributions are possibleand they know which of these are most likely.For all distribution types examined, theyshow a strong tendency to guess the correcttype. In addition, their estimates of the centraltendency and dispersion of distributions arefairly well-correlated with the actual param-eters. For estimates of the means for distri-butions, a random sample of 2 to 4 casesfrom actual distributions would be requiredto exceed the accuracy of the average subject'sguesses; for standard deviations a randomsample of 6 to 10 cases would be required.

Our data thus make it clear that the errorspeople make in inductive reasoning aboutsocial events are not due to any fundamentalincapacity to characterize the central tenden-cies, dispersions, and shape of social distri-butions.

Note also that the reference population isnot one that would be expected to displaysubjects' abilities for parameter estimation totheir best advantage. The University of Mich-igan undergraduate body is a large and highlydiverse population. Had we studied a smallcollege population or had we asked our sub-jects to estimate parameters for some subsetof the Michigan population with which theywere personally extremely familiar, such aspeople in their major field or fellow athletesor sorority members, there is every reason toassume we would have found more accuracythan we did (cf. Judd & Johnson, 1981).

On the other hand, it should be clear thatalthough our studies do not display subjects'parameter estimation abilities to their bestadvantage, they probably also do not displaythem to their worst advantage or even at theirecologically typical level. There is good reasonto suspect, for example, that people wouldbe far less accurate about dispersion for groupsof which they are not themselves members.Work by Quattrone (in press; Quattrone &Jones, 1980) indicates that people substan-tially underestimate dispersion for outgroups.

What our studies show is that when subjectsare explicitly requested to generate socialdistributions for a large and diverse group ofwhich they are members, they can do so withsubstantial accuracy. This does not mean thatpeople spontaneously recall or construct socialdistributions for most of the social judgment


problems that require them. On the contrary,there is evidence in the work by Nisbett,Krantz, Jepson, and Kunda (1983) that thedistributions of social dimensions are oftennot salient and that it is only when subjectsare specifically cued to the necessity of con-structing them that they do so. Without suchcuing, subjects sometimes made inferences asif they believed that the relevant populationwas either uniform or essentially infinitelyvariable. For the purposes of education, then,it might be profitable to emphasize the ne-cessity of considering social distributions forvarious classes of problems. The present workindicates that college students, at least, willnot need much help in constructing suchdistributions when they understand the needfor doing so.

Constructing Social Distributions

How do people construct social distribu-tions? Our attempts to answer this questionwill be necessarily speculative, inasmuch asour studies were not designed to address it.

Everyone knows his or her own locationon each of the dimensions we examined, andthis could serve as a beginning referencepoint in estimating distribution parameters.Indeed, it is highly likely that our subjectsdid use this as a reference point, given thatthere was a false consensus effect for estima-tion of the mean and of the distributionshape.

Our data also indicate strongly, however,that false consensus could not possibly be theonly factor influencing the construction ofsuch distributions. False consensus cannotaccount for the considerable accuracy aboutdispersion, because one's own position doesnot provide any relevant information. Andour data demonstrate that false consensuscannot fully account for the accuracy aboutcentral tendencies and distribution shapeseither. Estimated means were closer, on av-erage, to the actual values than to subjects'own positions, and subjects estimated thedistribution shapes as corresponding to theshapes implied by their own positions muchmore when there was a genuine correspon-dence than when there was not.

We therefore believe that when constructingdistributions, subjects rely not only on their

own position but also on additional accurateknowledge. For most of the dimensions weexamined, subjects could be expected to havereasonably accurate memories for the locationof at least several other people. Some of thesememories could produce more error thanaccuracy, if they are more memorable thanthey are typical. But in general, memory ofactual cases could be expected to promoteaccuracy.

In addition to memories of actual casesand knowledge about the specific item athand, subjects undoubtedly have theoriesabout the kind of item in question and aboutsocial behavior and attitudes in general. Forexample, although subjects might have littleknowledge about the actual attitudes of manyof their fellow students toward increasingdefense spending, they might view this issueas the kind of issue heavily saturated withright-left ideological orientation and mighthave reasonably accurate estimates of thepercentage of the student population occu-pying various locations on this continuum.And, at the most general level, people seemto have tacit beliefs about the likely distri-bution shapes for social dimensions, just asthey do for physical dimensions. Givenknowledge about one's own position, reason-ably accurate memory for a few cases, and agood guess about the shape of the underlyingdistribution, subjects could generate quiteaccurate estimates of the mean and standarddeviation of the distribution.

These considerations make it seem lessmysterious why subjects were as accurate asthey were in their guesses about variousparameters of social dimensions. But it shouldbe remembered that they are purely posthoc. Indeed, as should be clear by now, wewere quite surprised by the accuracy subjectsdisplayed. Prior to conducting the research,we thought only of mechanisms that mightproduce error.

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Received May 21, 1984

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