oscillation in beliefs and decisions - galileo co

B A S I C I S S U E SO s c i l l a t i o n i n B e l i e f s

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Oscillation in Beliefs and Decisions

E DWA R D L . F I N KS TA N A . K A P L O W I T ZS U S A N M C G R E E V Y H U B B A R D

John Dewey, in his classic How We Think,stated that thinking “involves a jump, a leap,

a going beyond what is surely known to some-thing else accepted on its warrant. . . . The veryinevitableness of the jump, the leap, to some-thing unknown only emphasizes the necessityof attention to the conditions under which itoccurs” (Dewey, 1991, p. 26). Our research onattitude and belief change and decision makinghas attempted to explicate the cognitive forcesat work as individuals think, consider alterna-tives, and resolve issues.

All of us can recall when our decisions havecome about after vacillation, wavering, oroscillation. We believe that such oscillation isan important phenomenon. This chapter re-views our most recent research about oscilla-tion of beliefs. It also suggests a possible newdirection for research by examining chaos-

based measures to understand these oscilla-tions.

Lorenz (1977) posited that “any self-regulating process in whose mechanisms in-ertia plays a role tends toward oscillation”(p. 237). Because there is evidence that cogni-tion has such an inertial principle (see, e.g.,Saltiel & Woelfel, 1975), it is reasonable toexpect oscillatory dynamics for cognition.

With a few exceptions (e.g., Lewin, 1951),until the late 1970s, the theory and researchon attitudes and decisions focused on the out-come of the process rather than on its dynam-ics. For example, a review of the decision-making literature (Abelson & Levi, 1985)focused on models predicting decisions basedon the probability of and utility of variousoutcomes. In attitude research, the majoremphasis during this time has been on how

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AUTHORS’ NOTE: Portions of this chapter are based on Kaplowitz, S. A., & Fink, E. L. (1996). Cybernetics ofattitudes and decisions. In J. H. Watt & C. A. VanLear (Eds.), Dynamic patterns in communication processes(pp. 277-300). Thousand Oaks, CA: Sage.

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source, message, and receiver characteristicsinfluence an attitude, typically measured onlyonce after an experimental treatment. Thus,those investigating decision making and atti-tude change have generally failed to measurethe time course of variables associated withthe underlying psychological dynamics.

However, understanding dynamics in gen-eral and cognitive oscillations in particular iscritically important. First, understanding thetime course of attitude and belief change mayadd considerably to our understanding ofthe forces causing this change, thereby allow-ing the creation of a model that governs theprocess.

Second, because beliefs are typically mea-sured at one point in time, the existence ofoscillations can introduce what appears to beunreliability into the measurement of beliefs.In other words, systematic change, in the formof oscillation, can be mistaken for the randomdisturbances in a measurement, which we usu-ally think of as unreliability. Determining thetime parameters of such oscillations may al-low us to separate unreliability from instabil-ity in the measurement of an attitude or abelief (see, e.g., Heise, 1969). It also may tellus how long we need to wait for the attitude toreach equilibrium or “settle down.”

Both attitude and decision researchers haverecently begun paying more attention to pro-cess and dynamics. In the attitude area, notonly have thoughts been considered an impor-tant intervening variable (see, e.g., Chaiken,Liberman, & Eagly, 1989; Petty & Cacioppo,1986), but a number of studies (Liberman &Chaiken, 1991; Millar & Tesser, 1986) sug-gest that thinking is sufficient to bring aboutattitude change. Thus, McGuire (1989) statedthat those who study attitudes increasinglyview them as an interacting dynamic system.The decision-making literature has also shownincreasing concern with the dynamics of theprocess (see, e.g., Janis & Mann, 1977;Tversky & Shafir, 1992).

COGNITIVE OSCILLATION:INDIRECT EVIDENCE

From studying post-decisional attitudes,Walster (1964) and Brehm and Brehm (1981)have found that people often initially regret achoice that they have just made. Only later dothey reduce their post-decisional dissonancewith that choice (see also Landman, 1993).The regret-dissonance reduction process may,in fact, be one cycle of oscillation in beliefs;dissonance researchers did not measure atti-tudes with sufficient frequency in any experi-ment to know whether attitudinal oscillationmight continue.

Gilbert, Krull, and Malone (1990) showedthat an idea must first be entertained as truebefore it can be rejected as false. If correct, thisidea suggests that an individual’s beliefs mustchange at least once in the process of rejectinga proposition. Moreover, Latané and Darley(1970) stated that bystanders experiencingthe stress of an emergency can “cycle backand forth” between beliefs such as “the build-ing’s on fire—I should do something” and“I wonder if the building’s really on fire”(p. 122). For other evidence relevant to thepossibility of cognitive oscillations, see Pooleand Hunter (1979, 1980) and Wegner (1989,pp. 34, 113).

How have cognitive oscillations been ex-plained? Lewin (1951) posited that as weapproach a goal, both the attractive and repul-sive forces associated with the goal getstronger, but the repulsive forces increasemore rapidly than the attracting ones. Thus,whereas at great distances the net force isattractive, as the goal is approached, the netforce becomes repulsive (see Lewin, 1951,p. 264). Similarly, in Brehm and Brehm’s(1981) analysis of reactance, moving towardone choice alternative threatens the freedomto choose another choice alternative. This pro-cess causes the previously rejected alternativeto become more attractive. Both of these

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approaches suggest an oscillatory decision tra-jectory.

A SPATIAL-SPRINGMODEL OF COGNITIVE FORCES

A spatial-spring model of attitude change anddecision making has two basic components.First is a geometry of cognition in which simi-larity in the meaning of concepts is indicatedby their distance from each other (see Woelfel& Fink, 1980) and in which the degree towhich a concept is positively evaluated is indi-cated by how close it is to some other concept(e.g., “things I like”) indicating positive evalu-ation (see Neuendorf, Kaplowitz, Fink, &Armstrong. 1986).

Second, cognitive oscillation suggests theexistence of restoring (negative feedback)forces. Such restoring forces are built into thismodel by assuming that there are associativelinkages between concepts and that these link-ages are spring-like (see Fink & Kaplowitz,1993; Fink, Monahan, & Kaplowitz, 1989;Kaplowitz & Fink, 1982, 1988, 1992, 1996;Kaplowitz, Fink, & Bauer, 1983; for earliertreatments, see Barnett & Kincaid, 1983;Kincaid, Yum, Woelfel, & Barnett, 1983;Woelfel & Fink, 1980, esp. pp. 158-159).Consistent with the operation of a mechanicalspring, we assume that the forces attractingone toward an alternative increase in strengthas the individual cognitively moves away fromthat alternative.

We found the spring imagery especiallyattractive for two reasons. First, a spring sys-tem fits our geometric model in making theforces dependent on the instantaneous dis-tances among concepts. Second, as discussedmore fully in what follows, a spring analogyhelps to make sense of the tension people feelwhen experiencing opposing forces.

A model incorporating spring-like forcesassumes that a linkage between two concepts,

A and B, creates a force satisfying the follow-ing equation:

FA,B = KA,B[dEq(A,B) – d(A,B)], (1)

where FA,B is the force between the concepts,dEq(A,B) is the equilibrium distance of the link-age, d(A,B) is the distance between those con-cepts in the receiver’s cognitive space, andKA,B is the restoring coefficient of the linkage.This model posits that on either side of theequilibrium location, the net force is directedtoward the equilibrium location.

People often see a choice alternative asconsisting of both attractive and unattractivefeatures (cf. value conflict as discussed inLiberman & Chaiken, 1991). In this choicesituation, there should be spring-like linkagespulling in opposite directions. The equilib-rium of the system is that point at which theopposing forces balance; the relevant restor-ing coefficient is the sum of the effects of allthe individual linkages.

We now consider the motion of a systemconsistent with Equation (1). From Newton’slaws of force and motion, acceleration is pro-portional to the product of the distance of aconcept from its equilibrium location and K,the net restoring coefficient computed fromall linkages on a concept. If K is constant overtime, then this equation leads to a sinusoidaltrajectory of undamped oscillations (i.e., witha constant amplitude and a constant period ofoscillation). Moreover, the period of oscilla-tion is a decreasing function of the restoringcoefficient.

Sometimes people manifest no perceptiblecognitive oscillation. Furthermore, even whenthey do oscillate, it appears that such oscil-lations usually die out. Just as mechanicalsystems have friction, which serves to damposcillations, we assume a cognitive dampingprocess whose force is proportional to, andin the opposite direction from, the velocity ofthe concept in motion. Whether the system

Oscillation in Beliefs 19



exhibits oscillation depends on the size of thedamping coefficient as compared to therestoring coefficient.

Like Lewin (1951), we see the forces on aperson’s decision as depending on the cogni-tive distance from an alternative. The spatial-spring model, however, explains Lewin’s adhoc assumption that as one approaches a goal,the repulsive force increases more rapidlythan the attractive force. In addition, the spa-tial-spring model’s explicit equations of forceand motion enable us to predict the timecourse of change more precisely.

THE PSYCHOLOGICALMEANING OF THE MODEL

Equilibrium Length

The equilibrium length of a linkage is thedistance between concepts that the linkageimplies when one ignores the effect of otherlinkages. The equilibrium length of the link-age between an attribute and an evaluativeconcept represents the evaluation of theattribute, again ignoring the effect of otherlinkages. Thus, for most people the linkage be-tween good pay and jobs I want has a smallequilibrium length, whereas the linkage be-tween long hours and jobs I want has a largeequilibrium length.

We extend the model to persuasion byassuming that a message linking concepts Aand B establishes a linkage between them,whose equilibrium length, dEq(A,B), is the dis-similarity between A and B specified in themessage. Thus, the equilibrium length is theposition advocated by the message.

Restoring Coefficient

The restoring coefficient reflects the impor-tance of the attribute in the decision calcu-

lus. Attributes that are more important havegreater restoring coefficients. The cognitionand memory literature (e.g., Anderson, 1983)suggests that more frequent associations be-tween concepts cause stronger linkages andthat the lack of recent co-occurrence causesthese linkages to weaken. Thus, we see the re-storing coefficient as related to co-occurrence(for exceptions, see, e.g., Bornstein & Pittman,1992).

Although messages are assumed to establishspring-like linkages between concepts, theydo not fully determine the receiver’s newview. The force created by a new message link-age is opposed by and ultimately in balancewith the preexisting forces from the networkof other linkages in the receiver’s cognitivesystem. These anchoring linkages representthe strength of the receiver’s initial view andare the result of prior messages.

Thus, our model posits two distinct spring-like linkages. One is called the message link-age and is represented by the symbol KA,B. Theother is called the anchoring linkage and isrepresented by KR. Given Equation (1), wefind that when the system is in equilibrium,attitude change can be predicted by the fol-lowing equation:

∆PK Dp

KKA B

RA B= +,

, , (2)

where Dp is the discrepancy (between the po-sition advocated by the message and the initialposition of the receiver.

KA,B should be an increasing function offactors that enhance attitude change such assource credibility and argument strength. How-ever, because various studies (e.g., Aronson,Turner, & Carlsmith, 1963) have shown thatas discrepancy increases, attitude changebecomes a smaller proportion of the discrep-ancy, KA,B should be a decreasing function ofmessage discrepancy.

The strength of the anchoring linkage KR isexpected to be an increasing function of pre-

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message factors that inhibit attitude changesuch as the strength of the initial attitude (orvalue-relevant involvement [see Johnson &Eagly, 1990]).

We have stated that all linkages are assumedto decay over time (see Ebbinghaus, 1964);however, new messages or self-generatedthoughts may have the effect of strengtheningthese linkages.

Frequency andAmplitude of Oscillation

The frequency of oscillation of a spring is anincreasing function of its restoring coefficient.Because the total restoring coefficient is thesum of the coefficients of the message linkageand the anchoring linkages, we can derivesome interesting hypotheses based on the pre-ceding discussion of these factors:

Hypothesis 1: Other things being equal, thefrequency of oscillation is an increasingfunction of (a) source credibility, (b) argu-ment strength, and (c) strength of initialopinion.

Hypothesis 2: Other things being equal, thefrequency of oscillation is a decreasingfunction of message discrepancy.

We now examine determinants of theamplitude of oscillation. The spatial-linkagemodel predicts sinusoidal trajectories that aresymmetric about the equilibrium location andthat have amplitudes that are greatest at thestart of the cognitive trajectory. Thus, themaximum possible amplitude is the distancebetween (a) the equilibrium location of a con-cept after persuasion and (b) the concept’soriginal location. By definition, this distance isthe final attitude change. Thus, we have thefollowing hypothesis:

Hypothesis 3: The greater the attitude change,the greater the amplitude of oscillation (cf.Kaplowitz & Fink, 1982).

As indicated previously, attitude change ispredicted to be an increasing function ofsource credibility and argument strength and(usually) of discrepancy, and it is predictedto be a decreasing function of the strength ofthe receiver’s initial belief. Combining thesewith Hypothesis 3 leads us to the followinghypothesis:

Hypothesis 4: The amplitude of oscillation isan increasing function of (a) source credibil-ity, (b) argument strength, and (usually) (c)discrepancy, and it is a decreasing functionof (d) the strength of the receiver’s initialbelief.

TESTING THEPREDICTIONS OF THIS MODEL

To summarize, the spatial-linkage model hasvery elegant and clear predictions. It predictsoscillatory trajectories with constant frequen-cies, which are either damped (getting stead-ily smaller in amplitude) or totally undamped(staying the same in amplitude). Moreover,the amplitude and frequency should be func-tions of the persuasion variables discussedpreviously.

Our first study to examine oscillations(Kaplowitz et al., 1983) used more than 1,000participants, each of whose attitude was mea-sured only once. However, their attitudeswere measured at different times from thereceipt of the persuasive message. We thentreated the mean response of all participantswho received the same experimental treat-ment and who responded at the same timeafter the message as if it were a point on thetrajectory of a single individual. We treatedthe within-cell variance as measurement error.




We found modest but significant support forthe existence of oscillations; however, therewas no evidence of damping.

Aside from time until measurement, ourother independent variable in that study wasmessage discrepancy. Consistent with Hy-pothesis 4, the message with the greatest dis-crepancy not only induced the most attitudechange but also induced the trajectory withthe greatest amplitude. But inconsistent withHypothesis 2, no relationship between dis-crepancy and the frequency of oscillation wasfound.

Obviously, the technique used in theKaplowitz et al. (1983) study has seriousdrawbacks, and we have since developed bet-ter ways to measure oscillation. The techniquewe have used most often requires participantsto think about an issue and use a computermouse to indicate their instantaneous opin-ions about the issue. Mouse position is re-corded at least every 18 milliseconds, therebygiving us trajectories of individual attitudes ordecisions. When participants determine thatthey have made a final decision, they press themouse button, and this signal indicates the endof the trajectory.

We tested Hypotheses 1 through 4 with astudy that had 99 participants. We provided amessage that manipulated discrepancy andsource credibility and then had the partici-pants use the mouse while thinking about theissue. We measured attitude trajectories fortwo separate issues. One issue was the appro-priate sentence for a convicted armed rob-ber (a scenario used in Kaplowitz & Fink,1991). The other issue was the appropriateincrease in tuition at the students’ university (ascenario used in Fink, Kaplowitz, & Bauer,1983).

There were some very striking qualitativefindings that came from examining the nearly200 trajectories generated by this study. Thefirst is that oscillatory trajectories, in whichparticipants’ mouse motion reverses direc-

tion, are quite common. In both scenarios,more than half of the participants changeddirection at least once. This finding has beenconfirmed with other decision problems aswell (see Table 2.1).

However, the oscillatory trajectories do notlook like the trajectories predicted by the sim-ple version of the spatial-spring model dis-cussed earlier. That model predicted constantperiods and amplitudes that either remainedconstant or got steadily smaller (i.e., weredamped). None of the oscillatory trajectoriesfound showed constant periods. Moreover,some amplitudes suddenly got larger, andoscillations abruptly ended with no gradualdamping (see Figure 2.1).

Because we did not have regular trajecto-ries, we could not measure frequency andamplitude in the usual way. Our analogue toamplitude became the pseudo-amplitude (halfof the difference between the maximum andminimum values of the decision trajectory).We created two analogues to the frequency.One was the total number of changes of direc-tion the participant made. The other was thepseudo-frequency (the number of changes ofdirection divided by the decision time).

In determining the number of changes ofdirection, we wanted to distinguish mousemotion that reflected attitude change fromunintentional motion. Thus, any change hadto be at least 4% of the range of the scale for usto consider it a true change of direction. Inaddition, spike-like changes, in which the par-ticipant, on reaching a position, immediatelymoved in the opposite direction, were alsointerpreted as unreliable motion. We assumedthat the participant, having overshot a “true”position, was hastening to correct it.

Although credibility was successfully ma-nipulated, contrary to Hypothesis 1a, it hadvirtually no effect on number of changes ofdirection. For both scenarios, the Pearson cor-relation between credibility and number ofchanges was less than .08. Contrary to Hy-

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pothesis 3, for both scenarios, the Pearson cor-relation between discrepancy and number ofchanges was slightly positive, but it was notsignificantly different from zero in either sce-nario. We also found our independent vari-

ables to have no significant effect on pseudo-frequency.

Hypothesis 4a predicts that the greater theattitude change, the greater the amplitude.Using the pseudo-amplitude (and counting the


TABLE 2.1 Statistics From Online Oscillation Studies

CriminalSentencing Tuition

College Admission(Wang Experiment 2)a

College Admission(McGreevy)b

ContinuousDiscreteness

ContinuousDiscreteness

DichotomousDiscreteness

DichotomousDiscreteness

Easy Difficult Easy Difficult

Sample size 99 91 31 36 50-51 47-51

Percentage changingdirection at least once 72.7 59.3 77.4 97.2 64.7 76.5

Number ofchanges ofdirection

Adjustedgeometricmeanc 1.33 0.91 1.66 5.04 0.89 1.60

25thpercentile 0 0 1 3 0 1

Median 1 1 2 5.5 1 2

75thpercentile 2 2 3 9 3 4

Maximumd 7 11 14 14 12 18

Decisiontime(seconds)

Adjustedgeometricmeanc 26.59 26.60 17.20 38.81 6.38 45.05

25thpercentile 15.60 15.93 8.01 23.96 1.00 4.00

Median 27.67 26.85 18.02 40.98 6.50 58.00

75thpercentile 42.40 45.37 35.98 57.75 40.50 103.00

Minimum 4.84 4.89 3.00 9.00 0.00 0.00

a. Wang Experiment 2 is the experiment described in this chapter.

b. For McGreevy, the results reported in the table are only from the post-message phase.

c. Let log(x + c) be the transformation used to create a functional form whose skew was approximately zero, wherex is the variable of interest and c is a constant. Adjusted geometric mean xxx (antilog of the mean of transformedvariable) – c. If c were zero, the adjusted geometric mean would equal the geometric mean.

d. For this variable, the minimum was zero in all experiments.



amplitude as missing when there were nochanges in direction), strong support for thishypothesis was found, but only for the sen-tencing scenario. For the criminal sentencingscenario, the Pearson correlation betweenamplitude and final attitude change was .45(p < .01). However, for the tuition scenario,the Pearson correlation between these vari-ables was only .08 (ns).

Although several of our findings discon-firmed our hypotheses, other evidence byVallacher, Nowak, and Kaufman (1994) wasconsistent with the spatial-spring model. Inthat study, participants evaluated a stimulusperson as they thought about that personand used a computer mouse to record theirinstantaneous judgments. Consistent with ourspring model, they found in their Experiment1 that the further someone’s attitude is fromits equilibrium position, the greater the accel-eration.

To summarize, we have some support forthe idea that people oscillate, but not for the

more specific predictions of the spatial-springmodel. One obvious explanation of this out-come comes from the logic of the model it-self. We have assumed that every message aparticipant receives creates a new linkage. Butas is well-known, as people process an exter-nal message, they often send themselves mes-sages (i.e., cognitive responses) (see, e.g., Petty& Cacioppo, 1986; Petty, Ostrom, & Brock,1981). If these self-generated messages createnew linkages and affect the receiver’s attitude,they will lead to trajectories that are far morecomplex and chaotic than those implied by thesimple model. We now consider other vari-ables that may affect the trajectories.

AMBIVALENCE,ELABORATION, DISTRACTION,AND NEED FOR COGNITION

Janis and Mann (1977) predicted that “vacil-lation” occurs when the conflict felt by the

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Figure 2.1. Mean Number of Changes in Direction, by Phase and by Object Similarity



decision maker involves a “serious risk fromthe current course of action” or a “serious riskfrom a new course of action” and when “abetter solution may be found” (p. 78). Simi-larly, Bruss (1975) attributed “a wavering inthe process of deliberation” to

an unclear ranking of preferences or incommen-surable preferences, vague or uncertain beliefsabout how well an object or act will satisfy apreference, what the available alternatives areand the relative probabilities of attaining each,and unresolved notions of the risk that is war-ranted or tolerable if a chosen alternative fails.(pp. 557-558)

Katz (1981) also argued that ambivalent atti-tudes tend to be unstable—a finding sup-ported by Bargh, Chaiken, Govender, andPratto (1992).

Situations in which people are ambivalenttend to be experienced as situations involvinga great deal of tension. In these situations,people often are said to feel torn, pulled apart,or strained by conflicting demands of compet-ing roles (see, e.g., Goode, 1960) as well as bythe difficulty of making some decisions (see,e.g., Festinger, 1957; Heider, 1958). Such sit-uations are clearly ones of great tension orstress. Thus, we predict the following:

Hypothesis 5: Oscillation is more likely forissues on which the respondent is ambiva-lent (i.e., most likely to have conflictingfeelings) and for which a decision isdifficult.

Those studying cognitive responses to persua-sion (see, e.g., Petty & Cacioppo, 1986; Pettyet al., 1981) have shown that such cognitiveresponses have a strong relationship to atti-tude change. This idea suggests the following:

Hypothesis 6: The number of cognitiveresponses should be positively correlatedwith the number of changes of direction.

If oscillation requires cognitive elaboration,it is more likely when people have the abilityand motivation to elaborate (see Petty &Cacioppo, 1986). The ability to elaborateshould be related to the availability and acces-sibility of the decider’s thoughts (see Fazio,1989; on the availability heuristic, see alsoTversky & Kahneman, 1974) and should bemore likely when the decider has a detailed orcomplex schema for understanding the issue(see, e.g., Tetlock, 1983a, 1983b). It shouldalso be more likely when the decider is not dis-tracted from concentration (see, e.g., Petty,Wells, & Brock, 1976).

Based on the Elaboration Likelihood Model,the motivation to elaborate should also be afunction of the individual’s need for cognitionand of the importance of the issue to the de-cider. If thoughts have the effects we expect,then the number of changes of direction willbe related to the number of cognitive re-sponses. Thus, we have the following hypoth-eses:

Hypothesis 7: Oscillation is more likely forissues the respondent considers important.

Hypothesis 8: Oscillation is more likely forthose who are high in need for cognition.

Hypothesis 9: Distraction will cause feweroscillations.

Our study employing criminal sentencingand tuition increases as the topics for con-sideration by the participants provides someevidence in support of Hypothesis 5. Respon-dents clearly regarded the tuition issue asmore important to themselves, and a signif-icantly greater percentage (47%) showed os-cillation in this scenario than in the sentencingscenario (35%).




The results dealing with ambivalence aremore extensive. We did a self-report study (seeFink & Kaplowitz, 1993, p. 261) in whichparticipants were given a set of hypotheticaldecision problems (scenarios) and asked forpaper-and-pencil responses to them. Consis-tent with Hypothesis 5, those who reportedthe decision to be difficult were more likely toalso report having oscillated.

Similarly, Vallacher et al. (1994) providedother evidence that ambivalence contributesto oscillations. In their studies, participantsreceived information about a stimulus personthat was either positive, negative, or mixed(ambivalent) and then indicated how theirinstantaneous evaluations of the stimuluschanged. Although participants in all condi-tions were likely to oscillate initially, the am-plitude and frequency of oscillation of thosereceiving the positive or negative informa-tion declined, whereas the oscillations of theambivalent participants did not.

Several of our online studies (i.e., those inwhich the participant employs a computermouse to encode the trajectory of thoughtswhile thinking) have also examined the effectof ambivalence on oscillation. In the criminalsentencing and tuition attitude study, we mea-sured ambivalence in two ways. One was byasking participants to list their thoughts aboutthe sentence and the tuition. The other was bya set of closed-ended questions asking the par-ticipants’ views on these issues.

Ambivalent participants were those whoagreed with the arguments on both sides of theissue. For example, the following statementindicates a belief system that might opposesevere punishment for criminals: “Two wrongsdo not make a right. Even though the criminalhas behaved badly, this does not justify societyviolating the criminal’s human rights.” Bycontrast, the statement, “ ‘An eye for an eye’ isan appropriate principle of justice,” indicatesa belief system that might favor severe punish-

ment. Ambivalent participants were thosewho might agree with both of these positions.

In the study described previously, ambiva-lence had no significant relationship with thenumber of changes of direction in the attitudetrajectory. Moreover, contrary to Hypothesis6, the Pearson correlation between number ofthoughts and number of changes of directionwas less than .10 (ns) in each scenario.

We have also experimentally manipulatedambivalence by varying the difficulty of thedecision the respondents are asked to make. Inthese studies, participants were asked tochoose which of two fictitious candidatesshould be admitted to their university. In onecase, the information was designed so thatparticipants would find it to be a difficult deci-sion. In the other case, the information wasdesigned to make it likely that the participantswould see one candidate as more suitable. Asparticipants thought about the admissionsdecision, they used a computer mouse to indi-cate their instantaneous opinions as to whichapplicant should be admitted. At one end ofthe scale (from 0 to 100) was definitely admit[Candidate A]; the other end was definitelyadmit [Candidate B]. At intermediate pointson the scale, the respondents could indicateleaning toward one candidate without totalcertainty.

In the first of these studies (Wang, 1993),one of the candidates for admission was Blackand the other was White. To vary the decisiondifficulty, the hypothetical Black applicantwas described either in an individuated way(i.e., in ways that the participants consideredatypical of Black applicants) or in a stereo-typical way. Note that in neither conditionwere evaluatively negative terms or beliefsused to describe either applicant. From the lit-erature on racial attitudes, (e.g., Bobo &Kluegel, 1991; Jackman & Senter, 1983) andon individuation (see, e.g., Wilder, 1978,1981), we expected White participants tohave a more positive attitude toward the Black

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applicant when the Black applicant was in-dividuated than when he was stereotypical.Consequently, we expected participants tofind the admissions decision to be more diffi-cult (i.e., more ambivalent) when the Blackapplicant was individuated than when he wasstereotypical. Thus, we expected a greateramplitude and a greater number of changes indirection in the decision trajectory of the indi-viduated than in the stereotype-consistentcondition.

In this study, we also manipulated distrac-tion. In the high distraction condition, therewas distracting noise on the tape-recordedinstructions, and the experimenter rustledpapers and snacked on crunchy foods. Inthe no distraction condition, neither of thesethings happened. Manipulation checks showedthat both independent variables were manipu-lated successfully. We also measured need forcognition using Petty and Cacioppo’s (1986)scale.

Of the 67 participants, 59 (88%) had atleast one change of direction. Moreover, theindividuation manipulation created signifi-cantly greater self-reported decision difficulty.Individuation also had positive and significant(at p < .01) linear correlations with (a) thenumber of direction changes in the partici-pant’s decision trajectory (r = .541), (b) deci-sion time (r = .460), and (c) pseudo-amplitude(r = .401). The linear correlations with self-reported decision difficulty were less strong(perhaps because of unreliability of the manip-ulation check of decision difficulty). Althoughindividuation and decision difficulty were sig-nificantly correlated with each other (r =.372, p < .01), neither individuation nor de-cision difficulty was significantly correlatedwith pseudo-frequency (for individuation, r =.003; for decision difficulty, r = .086). Inshort, the more difficult decision involvedmore changes of direction, but these changeshad the same frequency in both the easy andhard decisions. Thus, whether decision diffi-

culty increases oscillation depends on whetherone is using the total number of changes ortheir rate as the dependent measure.

Consistent with Hypotheses 5 and 6, indi-viduation produced more thoughts (r = .368,p < .01), and the number of thoughts was pos-itively correlated with the number of changesof direction (r = .411, p < .01). These resultsalso contained some surprises. First, the needfor cognition scale had a near zero correlationwith the number of thoughts and a surpris-ingly small correlation with the number ofchanges of direction (r = –.262, p < .05). Sec-ond, contrary to our expectations, distractionhad a positive correlation (r = .221, ns) withthe number of thoughts and a significant and apositive correlation (r = .420, p < .01) withthe number of changes in direction.

Thus, decisional conflict increases the ten-dency to change one’s mind, which apparentlymade the decision process take longer. Thisconflict did not, however, increase the rate ofthe oscillation. Contrary to the findings ofprevious studies (e.g., Petty et al., 1976), dis-traction did not reduce thought production.Rather, it made the thinking process takelonger.

McGreevy’s (1996) study (N = 102) used asimilar methodology to Wang’s (1993) studyand examined the effect of both decision diffi-culty and distraction. In the difficult decision,both college applicants were similar in thatboth were appropriate for admission into col-lege. In the easy decision, only one candidatewas appropriate for admission into college.The difficulty manipulation in this study wassuccessful.

The results generally replicated those justreported. For cognitive processing after read-ing the message, participants again showed sig-nificantly more oscillation for the difficultdecision than for the easy one. They also tooksignificantly more time in the condition inwhich they were distracted. (As explained




later, McGreevy, 1996, also measured the tra-jectory as the participants read the message.)

NEED FOR CLOSUREAND DECISION PHASE

Kruglanski’s (1989, 1990) theory of layepistemics suggests that people differ in theirneed for closure. Need for closure is defined as“the desire for a definite answer on sometopic, any answer as opposed to confusionand ambiguity” (Kruglanski, 1989, p. 14).On the other hand, need to avoid closure oc-curs in situations “where judgmental non-commitment is valued or desired” (p. 18).Kruglanski (1989, 1990) claimed that needfor closure can result in an “epistemic freez-ing” (Kruglanski, 1989, p. 14), in which par-ticipants are not motivated to process infor-mation and have a strong desire to come to aquick conclusion. We hypothesize that indi-viduals who experience a high need for closureare unwilling to expend the cognitive effortrequired to make a decision. Therefore, wehave the following hypothesis:

Hypothesis 9: Need for closure correlates neg-atively with (a) the time to make a decisionand (b) the number of changes of direction.

There is evidence that different kinds ofcognitive processing may occur during differ-ent phases of the decision-making process (seeBassili, 1989; Hastie & Park, 1986; Hastie &Pennington, 1989). Hastie and Pennington(1989) have found differences in cognitiveprocessing between social inference tasks thatwere made online (“during the process of per-ception, when the other person is present tothe senses”) and social inference tasks thatwere memory based (“when we think about aperson in their absence”) (p. 1).

Research on online cognition suggests that agreat deal of cognitive processing can occur

while an individual receives a message. Thiscognitive processing may be different from thetype of processing that occurs once the mes-sage has been received and while an individualthinks about the information contained in themessage in order to make a decision. To ex-plore this possibility, we divided the attitudetrajectory into two phases: (a) the messagereceipt phase, which occurs as an individual isreceiving the attitude message; and (b) thepost-message phase, which occurs after themessage has been received and while the indi-vidual is considering the information in themessage.

In addition to examining the effect of deci-sion difficulty and distraction, McGreevy’s(1996) study examined the effect of need forclosure and decision phase on the attitude tra-jectory. Need for closure was manipulated byvarying environmental noise (Kruglanski &Webster, 1994). In the high need for closurecondition, a loud humming noise was pipedinto the experimental room. In the low needfor closure condition, participants werewarned that the noise might occur; however,no noise was actually used. There was also oneindividual difference variable, trait need forclosure, which was measured by Webster andKruglanski’s (1994) need for closure scale.

Manipulation checks showed that individu-als who heard the noise reported the environ-ment to be significantly more distracting andalso reported a significantly greater motiva-tion to complete the task quickly than didthose who did not hear the noise. Thus, thismanipulation both increased the participants’need for closure and made them feel more dis-tracted. They did not, however, report thattheir cognitive capacity was affected by thenoise.

This study measured the attitude trajectoryusing the same computer mouse techniquedescribed earlier, with one important change.The previous studies had participants use themouse only after reading the message. In this

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study, participants started indicating theirinstantaneous preferences with the mousewhile they read the information about the can-didates. Participants were further instructedto push the left mouse button when they fin-ished reading the information. Then, as in pre-vious studies, they were to continue to movethe mouse as they thought about the issue untilthey made a final choice as to whom they pre-ferred. At this point, they were to push the leftmouse button a second time. This procedureallowed each participant’s decision trajectoryto be divided into two parts: (a) the messagereceipt phase (i.e., while the participant wasreceiving the message) and (b) the post-mes-sage phase (i.e., while the participant wasthinking about the message and deciding be-tween the candidates).

Overall Trajectory

Those with a high need for closure wereexpected to take less time on the decision-making process (Hypothesis 9a) and havedecision trajectories that exhibit fewer oscilla-tions (i.e., fewer changes in direction) (Hy-pothesis 9b) than those with low need for clo-sure. We first examine these results for theoverall trajectory over two decision-makingphases and then examine the phases sepa-rately.

As expected, participants with a difficult de-cision took significantly more time to decidebetween the candidates (p = .001) than didthose with an easy decision. But contrary toHypothesis 6, the number of changes of direc-tion exhibited by the mouse had no significantrelation to the difficulty of the decision. How-ever, a self-report measure of changes in cogni-tive direction produced results consistent withHypothesis 6. In what follows, we examinethis finding.

A statistically significant interaction be-tween manipulated need for closure and the

candidates’ similarity (decision difficulty) ondecision time was also found. Consistent withHypothesis 9a, when participants faced themore difficult decision, the higher the needfor closure, the less time participants took tomake their decision. But when participantsdealt with the easy decision, contrary to Hy-pothesis 9a, the greater the manipulated needfor closure, the more time the participantstook.

We found a somewhat similar interactioneffect when the number of changes of direc-tion was our dependent variable. Consistentwith Hypothesis 9b, when the decision wasrated as difficult by the participants, those inthe high need for closure condition had fewerchanges in direction than did those in the lowneed for closure condition. However, whenthe decision was rated as less difficult, those inthe high need for closure condition exhibitedmore changes in direction than those in thelow need for closure condition.

The results that are contrary to Hypothesis9a or 9b can be better understood when weremember that the need for closure manipula-tion was a distraction. Wang (1993) found thatthose who experienced a distraction took lon-ger to come to a final decision than did thosewho did not experience a distraction. And itis also possible that the distraction not onlyincreased the time spent but also caused peo-ple to reconsider their decision, resulting inadditional oscillations. However, the reasonthat this effect was found only in the easy deci-sion scenario is not clear.

Separate Decision Phases

In the post-message phase, we found mixedresults for both hypotheses. Consistent withHypothesis 9b, the need for closure scale hada significantly negative linear correlation withthe number of changes in direction. But con-trary to Hypothesis 9a, it had a near zero




linear correlation with the decision time. Con-sistent with Hypothesis 9a, manipulated needfor closure had a negative (but nonsignificant)linear correlation with decision time. Butcontrary to Hypothesis 9b, it had a near zerolinear correlation with number of changes indirection.

Examination of trajectories showed that theindependent variables had different relationsto the trajectories in the two different phases.As indicated previously, for the post-messagephase, those with a difficult decision showedmore changes in direction than did thoseasked to choose between different candidates.For the message receipt phase, however, theresults were in the opposite direction and theinteraction was significant (see Figure 2.1).

We also found a significant interaction be-tween decision phase and measured (trait)need for closure (see Figure 2.2). As indicatedpreviously, the post-message phase shows theexpected results. Those measuring high inneed for closure exhibited fewer oscillations

than did those measuring low in need for clo-sure. For the message receipt phase, however,the results were in the opposite direction.

These results suggest that different kinds ofcognitive processing occur at different pointsin the attitude change process. Those with ahigh need for closure do most of their oscil-lating (and perhaps most of their cognitiveprocessing) while receiving the message. Evi-dence of oscillation while receiving a messageis consistent with current research about on-line cognition (Bassili, 1989). But consistentwith Kruglanski (1989), those with low needfor closure are more likely to oscillate after themessage has been received.

Let us now return to the findings relatingnumber of changes of direction to difficulty ofdecision (similarity of candidates). We havefound that (a) the overall trajectory showsno significant effect of difficulty, (b) there isa significant effect of difficulty on the self-reported oscillations, and (c) the effect of deci-sion difficulty on the number of observed

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Figure 2.2. Mean Number of Changes in Direction, by Phase and by Measured Need for Closure



changes is as predicted in the post-messagephase but is in the opposite direction in themessage receipt phase. Taken together, thesefindings may suggest that the observed trajec-tory is a more accurate reflection of the cogni-tive process in the post-message phase than inthe message receipt phase. In the messagereceipt phase, participants were asked to readthe message and record their preferences asthey were having them. In this phase, it is pos-sible that when they were asked to choose be-tween two similar candidates, they were con-centrating so hard that they forgot to move thecursor in conjunction with their thoughts.When asked to recall the number of times theychanged their minds between candidates,however, they were able to recall changingtheir minds more often for the difficult deci-sion scenarios. Further research is needed toclarify this issue.

DEGREE OFRANDOMNESS AND CHAOS

As indicated previously, we started with amodel that predicted periodic trajectories.We found this prediction to be disconfirmed.Furthermore, we proposed that cognitive re-sponses create trajectories that are chaotic.Indeed, such chaos is suggested by the Deweyquote that begins this chapter.

The (most positive) Lyapunov exponent is astatistic that permits us to examine the degreeof pattern in a trajectory. This statistic is “ameasure of the rate at which nearby trajec-tories in a phase space diverge” (Sprott &Rowlands, 1992, p. 19; see also Casti &Karlqvist, 1991). Periodic orbits have Lyap-unov exponents that are near zero, chaoticorbits have at least one positive Lyapunovexponent, and random orbits have still largerLyapunov exponents. In other words, thehigher the Lyapunov exponent, the more un-

predictable the future trajectory is based on itspast values.

We find that in McGreevy’s (1996) study,out of 102 trajectories, only 1 has a negativeLyapunov exponent and 1 more has a valueless than 0.10. Fully 75% of the trajectorieshave Lyapunov exponents that are 0.24 orgreater. The median value for the Lyapunovexponents of these trajectories is 0.30 (range:–0.10 to 1.66). This result suggests that thetrajectories are chaotic.

A reexamination of the attitude trajectoriesin Wang’s experiment (see Fink, Kaplowitz, &Wang, 1994) showed that whereas greateroscillation occurred when the decision wasdifficult than when the decision was easy,those in the difficult decision conditionsexhibited attitude trajectories that were lesspatterned (having higher Lyapunov expo-nents) than the attitude trajectories of those inthe easy decision conditions.

The results from the McGreevy (1996)experiment were different. These resultsshowed no significant effects of any of our in-dependent variables on the Lyapunov expo-nents of the attitude trajectories. However,when we enter the participants’ assessments ofhow careful they were as a covariate and alsohave it interact with our independent vari-ables, several highly significant (p < .01)effects are found. The trajectories of thosewith high manipulated need for closure havehigher Lyapunov exponents than do thosewith low manipulated need for closure. Thereis a significant interaction between decisiondifficulty and manipulated need for closure,such that the trajectories of those with an easydecision but low manipulated need for closurehave relatively low Lyapunov exponents,whereas those with an easy decision but highmanipulated need for closure have relativelyhigh Lyapunov exponents. There are also sev-eral significant interactions that are not easilyinterpreted.




CONTINUOUS VERSUSDICHOTOMOUS DECISIONS

Some decisions require a choice between twoopposing alternatives (e.g., which of twocandidates to choose), whereas others allowfor the possibility of a compromise betweenthem. Some decisions, in fact, allow for anearly continuous range of possible outcomes(e.g., the amount of money to contribute to anorganization). This distinction, the discrete-ness of the decision outcome, may affect oscil-lations.

Suppose that the balance of attitudinalforces causes the decider to be uncomfortablewith either end point of the set of decisionalchoice alternatives and to prefer some com-promise. If the decision is continuous, thisequilibrium location is a viable decision.However, if the decision is dichotomous, anysuch compromise is an impossibility. Thus,with dichotomous decisions, for oscillationsto die down, it is not sufficient that the indi-vidual settle down at the position where thecognitive forces balance. It may also be neces-sary that the strength of these forces be alteredso that one decisional end point can becomethe equilibrium location. The preceding dis-cussion suggests the following hypothesis:

Hypothesis 10: Difficult dichotomous deci-sions are likely to sustain more oscillationsand take longer than are continuousdecisions.

This prediction may be investigated by em-ploying the data summarized in Table 2.1. Wehave identified two independent variables thatshould affect oscillation. One is the impor-tance of the decision to the respondent; theother is the difficulty of the decision. Amongall of the oscillation studies, the one in whichthe decision is probably most important to therespondents is the tuition study. This issue af-fects the respondents in a way that none of the

others affects them. On the other hand, themost difficult decisions were probably thoseadmissions decisions that were designed to bedifficult. In these decisions, the respondentstruly were pulled in both directions. The tui-tion study allows a continuous outcome,whereas the admission decisions requires a di-chotomous choice.

In Table 2.1, we see that the continuousdecisions have a smaller mean time of decisionand fewer changes than do the difficult dichot-omous ones. But we also see that the continu-ous decisions and the easy dichotomous onesdo not differ in the number of oscillations.The two easy dichotomous decisions, how-ever, took less time than the continuous ones.Moreover, because the discreteness of thedecisions is confounded with decision diffi-culty, we cannot reach any conclusions aboutwhether continuous decisions produce feweroscillations than dichotomous ones.

LENGTH OF DECISIONAND RELIABILITY

At the beginning of this chapter, we said thatstudying oscillations might tell us how longwe need to wait for the attitude to reach equi-librium. At equilibrium, an attitude should bestable and its measurement should be reliable.Table 2.1 provides some useful informationon this issue. Looking at decision time, acrossall studies it seems that even in the easiest de-cision, if we want at least 75% of the respon-dents to reach a decision that they considercomplete, we need to wait at least 36 seconds.This time period is a slight overestimate ofhow long the participants oscillate becauseparticipants usually waited several secondsafter reaching their final position before de-claring themselves done. However, it indi-cates that when people are creating an atti-tude response online (rather than retrieving arating stored in memory), it takes more time

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to do so than an attitude survey typicallyallows.

CONCLUSION ANDFUTURE RESEARCH

Clearly, oscillation occurs (especially for dif-ficult decisions) and exhibits a systematic re-lation to theoretically relevant independentand dependent variables. Evidence indicatesthat attitude trajectories are not simple sinu-soids. This finding suggests that we need tosupplement our oscillation model with theorybased on consideration of conscious cogni-tion. Results also suggest that the attitudechange process is more complex than currentmodels imply.

Conclusions from our online investigationsare based on two assumptions. First, themotion of the computer mouse representstrue cognitive motion (i.e., attitude or beliefchange). Second, the attitudinal position indi-cated by the mouse is the position the respon-dent would take if required to make a finaldecision at that moment.

We have seen evidence that the first assump-tion is not always met. Trajectories sometimescontain vibrations and spikes that look likerandom motion. However, we have correctedfor this apparent noise by not counting thesemotions as true change. We also have seen thatour independent variables have a differenteffect on the trajectories created while peopleare reading a message as compared to theirpost-reading trajectories. We suggest that peo-ple may sometimes forget to move the mousewhile they are reading. If so, the trajectory ofmouse movement that is created while readingdoes not fully reflect the cognitive changes.This point merits further research.

At first glance, it might appear that if thefirst assumption (i.e., that the recordedmotion of the mouse is true change) is valid,then the second one (i.e., that the position at

any instant represents the decision at thatinstant) must also be valid. However, ratherthan being what the participant would chooseif forced to decide, the mouse motion may bethe cognitive equivalent of “trying on” a posi-tion or decision to see whether it “fits.”

To resolve this question, we propose the fol-lowing experiment. One could, at a predeter-mined time, interrupt the participants whilethey are thinking and moving the mouse. (Par-ticipants would be randomly assigned to dif-ferent interruption times.) One could thenask for a paper-and-pencil response, allowingthe participants different amounts of time tothink before responding. A finding that thecorrelation between the final mouse positionand the paper-and-pencil rating is muchhigher when participants are required torespond immediately than when they are isgiven more time to think would support ourassumption that the mouse position is, in fact,the choice the participant would make at thatpoint.

Future research should also focus on adeeper understanding of the relationshipamong the many variables responsible foroscillation in attitudes and beliefs. In addition,we want to resolve some confusing findingsregarding distraction. Distraction sometimesslows cognitive processing, and at other timesit apparently creates a need to finish morequickly, speeding up the decision process andreducing oscillation. Future research shouldfurther examine the relationship among vari-ables such as decision time, the number ofthoughts, the number of changes in direction,and the amplitude of the oscillation. Resultsfrom our research provide exciting evidenceregarding differences in the types of cognitiveprocessing that occur (a) while individualsreceive a message and (b) while individualsconsider the information contained in themessage. A closer examination of these sub-processes, including how the different types ofprocessing affect the outcome of persuasive




messages, will lead to a clearer understandingof the entire attitude change process.

A second set of issues relates to interactionsinvolving the message receipt phase of cogni-tive processing. McGreevy (1996) found thatin the post-message phase, those faced with adifficult decision oscillated more than didthose faced with an easy decision. She alsofound that those with a low need for closureoscillated more than did those with a highneed for closure. Neither of those findings wassurprising. What was surprising, however, wasthat while reading the message, both of thesefindings were reversed. We have suggestedthat perhaps those dealing with the difficultdecision were so absorbed in reading that theyforgot to move the mouse. But why did theyshow this effect only in the message-readingphase and not in the post-message phase? Re-search and theory are needed to investigatethis question.

Furthermore, why does need for closureplay such a different role in the two phases?Recall that during the message receipt phase,individuals with a high need for closure havegreater oscillation. What is the link betweenneed for closure, speed of message processing,and oscillation? Do those with a high need forclosure process messages more thoroughly?What are the characteristics of the messageon which oscillation and speed of processingdepend?

The Lyapunov exponent indicates that atti-tude trajectories that we observed are ratherchaotic, suggesting that Dewey (1991) may becorrect. We found some very interesting inter-actions involving the Lyapunov exponents.But although several experimental variablesclearly have a substantial effect on these expo-nents, we currently lack a theory that canmake sense of these results.

We should be engaged in theory buildingfrom several directions. First, it appears thatthe process of decision making and attitudechange may be best described by the mathe-

matics of nonlinear dynamics and chaos.Understanding this mathematics offers thepossibility of making explicit the links be-tween the psychological forces and the attitu-dinal trajectory.

Second, we should improve our under-standing of how various features of the trajec-tory lead to higher versus lower Lyapunovexponents. Does the total number of changesof directions have an effect? Does the speed atwhich the changes in direction take placemake a difference? How do changes in theamplitude and frequency affect the Lyapunovexponent?

Once we investigate these issues, we may bebetter able to understand how various psycho-logical and communication variables influ-ence the decision trajectory. If we can use thisinformation to predict the effects of certaintheoretically relevant independent variables,we will be better able to understand and ex-plain the cognitive processes at work.

NOTES

1. The equilibrium predictions of this modelare isomorphic with those of an information inte-gration model we have used (see Fink, Kaplowitz,& Bauer, 1983; Kaplowitz, Fink, Armstrong, &Bauer, 1986; Kaplowitz & Fink, 1991). Thesemodels, in turn, have been based on earlier onesproposed by Anderson (1981), Anderson andHovland (1957), and Saltiel and Woelfel (1975). Inthe Information Integration Model, the weight ofthe initial attitude is analogous to the anchoringlinkage, and the weight of the message position isanalogous to the message linkage. Equation (2) isactually a special case of a more general equationproposed by Kaplowitz and Fink (1992, p. 353).

2. An alternative would be to consider the am-plitude to be zero in those cases without anychanges in direction. However, if this were done,the Pearson correlation between amplitude and thenumber of changes would exceed .80, and it would

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then not be possible to disentangle the effects ofour predictors on amplitude and frequency.

3. Subsequent analysis of the data suggeststhat distraction led to thoughts that were moreconcrete and sequential.

4. Statistical analysis within the linear modelrequires that residuals be normal and homoscedas-tic. Although these methods are robust with respectto modest violations of these assumptions, in manycases our data indicated gross violations (e.g., largepositive skews). Where this was the case, the de-pendent variable was logarithmically transformedprior to analysis.

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