expectancy-value models of health behaviour: an analysis by conjoint measurement

European Journal of Social Psychology, Vol. 23,167-183 (1993)

Expectancy-value models of health behaviour: An analysis by conjoint

measurement

KLAUS JONAS Ps ychologisches Institut, Universitat Tubingen, Germany

Abstract

Various studies in the health area consistently rejected the multiplicative combination between severity andprobability of threat which is predicted by expectancy-value ( E V ) theories. It is hypothesized here, that this negative evidence may be due to an overly demanding assumption underlying the multiplicative combination, namely, the assumption that people are able to performs trade-offs between expectancies and valences. This hypothesis is tested in two studies in which subjects judged hypothetical health threats. Results from a nonparametric analysis (conjoint measurement) of individual data (Study I ) and an experimental study of trade-offjudgments (Study 2 ) are mostly consistent with the prediction. Unexpectedly, however, an A N 0 VA of the aggregate data of Study I yielded a small, but significant effect consistent with the multiplicative assumption. Whereas this latter result can be interpreted as evidencing an attempt to perform trade-oJs, the overall results show as predicted that trade-off judgments are associated with a systematic error component due to the inherent dificulty of this type ofjudgment.

INTRODUCTION

Among researchers of health behaviour, expectancy-value (EV) models are popular. EV-based health models assume that preventive health intentions are mediated by individuals’ cognitions regarding probability and negative valence of the respective threat. Two prominent EV models of health behaviour are Rogers’ protection motivation theory (Rogers, 1983; Self and Rogers, 1990) and the SEU model of Eiser and Sutton (e.g. Sutton and Eiser, 1984; Sutton and Hallett, 1988).

Both theories share the assumption that health-related behavioural intentions are a function of (1) the appraised severity of the threat (e.g. infection), (2) its perceived

I thank Regina Eder-Jonas, Alice Eagly, Margaret Stroebe, and Wolfgang Stroebe for their comments on earlier versions of the manuscript.

Correspondence concerning this article should be addressed to Klaus Jonas, Psychologisches Institut, Universitat Tubingen, Friedrichstr. 21,7400 Tiibingen, Germany.

0046-2772/93/020167-17$13.50 0 1993 by John Wiley & Sons, Ltd.

Received 6 August 1991 Accepted 17 May 1992

168 K. Jonas

likelihood, and (3) the perceived effectiveness of a recommendation to avert the threat (e.g. vaccination). Results from a considerable number of studies provided evidence that each of the three variables influences health-related intentions (e.g. Chu, 1966; Maddux and Rogers, 1983; Rogers, 1985; Rogers and Mewborn, 1976). These studies were not equally successful, however, in clarifying how these variables combine to affect intentions. Thus, whereas Rogers (1975; Rogers and Mewborn, 1976) and Sutton and Eiser (1984) assumed protective intentions to be multiplicative functions of probability and valence, most of the pertinent studies found no evidence for a multiplicative combination (e.g. Maddux and Rogers, 1983; Sutton and Eiser, 1984; Sutton and Hallett, 1988).

The present investigation aims at finding an explanation for this lack of evidence for the multiplicative combination. It seems worthwhile to clarify this combinatorial issue since the above-mentioned separate effects of the EV variables testify to the general explanatory and predictive power of the EV approach. To simplify the presentation, the present investigation will focus on protection motivation theory (PMT) although the issue that is addressed is relevant to other theories that assume a multiplicative relation between subjective probability and valence (see Sutton’s (1982) comparison of PMT and SEU theory).

Originally, PMT was formulated as a theory of fear appeals (Rogers, 1975), but its reformulation (Rogers, 1983) represents a general theory of health behaviour. Although Rogers (1975) did not present PMT in a quantitative form, the original version of his theory can be expressed by equation 1 (cf. Rogers, 1975; Rogers and Mewborn, 1976, p. 56).

Measure of protective intention = f[severity x probability x efficacy] (1)

Equation 1 assumes a strictly multiplicative combination of the three factors; the f describes the response function which relates the combination of the factor levels to measures of protective intention. Assuming that the response function is linear, in a three-factorial design an ANOVA should yield significance for each of the main effects as well as for each of the possible interactions (Rogers, 1975). With only a few exceptions (Rogers, 1985; Rogers and Mewborn, 1976, Experiment 3), none of the pertinent studies, however, obtained evidence for the ordinal interaction effects predicted by the multiplicative assumption (see Rogers (1983) for a review).

Interestingly, whereas the negative evidence for the assumed multiplicative combination stems from across-subjects analyses, in a study employing a within-subjects design (Rogers, 1985), at least two of the predicted ordinal interactions were found to be significant (efficacy x severity, efficacy X probability). This result may be due to the higher statistical power provided by within-subjects designs. However, because of the preponderance of negative evidence regarding the multiplicative combination, Rogers (1983, 1985) reformulated his theory. Besides incorporating self- efficacy (Bandura, 1986) into the theory, he substituted the assumption of an additive link between the three variables for the multiplicative hypothesis (Rogers, 1985). Thus, the reformulation omits the original prediction by which the effect of a factor is magnified by alterations in the levels of other factors.

In testing the predicted interactions, Rogers and his coworkers employed factorial designs which were analysed by ANOVAs. ANOVA results may not be definitely conclusive, however, because ANOVA presupposes, rather than tests, the linearity

Expectancy-value models of health behaviour 169

of the response function (cf. Birnbaum, 1982; Krantz and Tversky, 1971). Research from related areas of psychology shows that it may be safe only to assume a monotonic instead of a linear response function (e.g. Birnbaum, 1982; Krantz and Tversky, 1971). Thus, theoretically, the absence of an interaction may merely be due to a negatively accelerated response function (cf. Birnbaum, 1982).

Equation 1 assumes (1) that individuals merge the different dimensions into a common overall value determining protective intention (i.e. the severity of a given threat is integrated with its probability and with the efficacy of a recommendation) and (2) that individuals are able to perform trade-offs between different dimensions. This trade-off assumption implies that low levels of one dimension can compensate for high levels of another dimension and vice versa. For example, an individual may have a weak intention to protect against a strong threat because its probability is perceived as being low.

That the above assumptions are implicit in equation 1 can be seen by studying Figure 1, which depicts its predictions (ignoring the lower case letters for the moment). The comparison of, for example, a high severity/low probability- and a low severity/ high probability threat, shows that perceivers can specify the relative danger of at least some of the threats only by performing trade-offs. Such trade-offs require that perceivers map the different dimensions into subjective scales with more than ordinal properties (Montgomery and Svenson, 1976).

C 0

C a! C

.- c

c

-

0 High Probabil i ty 0 High Probab i l i t y

0 Low Probabil i ty Low Probabi l i ty

1 1 I I I

High Low High Low Sever i t y Severi t y Sever i t y Sever i ty

Low Ef f i cacy High Eff icacy

Figure 1. Intention as hypothetical multiplicative function of severity, probability, and efficacy. (To facilitate illustration of conjoint measurement axioms, threats underlying the intentions are designated by combinations of lowercase letters)

In contrast, only ordinal scales are necessary to compare, for instance, a high severity/low probability- and a low severity/low probability threat. Such judgments can be made by relying on the dominance principle (Montgomery and Svenson, 1976). According to this principle, a threat is more dangerous than another if it is more dangerous than the other with regard to at least one dimension, and at least equally dangerous with regard to the remaining dimensions. Regarding the ordinal relations between non-trade-off situations, the dominance principle and the multiplicative rule make the same predictions. In contrast, however, the multiplicative rule does allow

170 K. Jonas

coping with trade-off situations. As is obvious, however, it requires somewhat demanding cognitive capabilities, that is, to represent the different factors on subjective scales with more than ordinal properties as well as to convert them onto a common scale.

Figure 2 shows the predictions specified by an additive combination of severity, probability, and efficacy, which is assumed by Rogers’ (1985) reformulation of his PMT. It is evident that at least some of the comparisons implied by the additive combination likewise require that perceivers perform trade-offs. Thus, in this respect this type of combination cannot be regarded as cognitively less demanding than the multiplicative. (Trade-offs are also implied by various other combinatorial rules; c$ Krantz and Tversky, 1971; Montgomery and Svenson, 1976.)

The significant main effects for severity and probability which, as mentioned above, were reported in several studies, do not contradict the hypothesis that trade-offs may be too demanding. Respondents in these studies may have applied decision rules not requiring trade-offs. For instance, main effects should be obtained if respon-

0 High Probabil i ty

0 Low Probabll t ty [ a,q,u I

I

High Low Severity Sever i t y

Low Ef f i cacy

0

High Low Sever i t y Severity

High Ef f icacy

Figure 2. Intention as hypothetical additive function of severity, probability, and efficacy. (To facilitate illustration of conjoint measurement axioms, threats underlying the intentions are designated by combinations of lowercase letters)

dents simply count the number of components which make a recommendation appear desirable and ‘adjust’ their intention ratings correspondingly. For example, if both severity and probability take on high values, a stronger adjustment is made than if only one or none of the dimensions assume high values.

Neither Rogers nor Sutton and Eiser directly tested the trade-off assumptions. Rather, according to Sutton, Marsh, and Matheson (1987) ‘it is not suggested that in making decisions people consciously perform the multiplication . . . implied by the [SEU] model, but only that they behave as if they do these calculations’ (p. 36).

However, even if the EV approach is taken only as an attempt to describe the outcomes of cognitive processes, rather than the processes themselves, the lack of evidence for the multiplicative combination raises doubts whether the approach can be considered as an adequate description of the outcomes. Furthermore, it is question-


able that a cognitive process whose results are to be described by a strictly multiplicative formula can operate by circumventing the critical aspects of this formula. Thus, at least implicitly the multiplicative formula makes assumptions about the underlying cognitive process.

Of course, EV models containing the multiplicative assumption are also common in various other areas in psychology, for example in models of the relation between attitudes and beliefs (e.g. Ajzen, 1988). Empirically, the question concerning the combination of expectancies and values has most stringently been addressed by researchers guided by the information-integration approach (e.g. Lynch and Cohen, 1978; Shanteau, 1974; Shanteau and Nagy, 1979). Although these investigators' studies on helping, betting, and dating-behaviour generally found evidence for the predicted interactions, the ANOVA tests they invoked are not definitive because ANOVA presupposes rather than tests the linearity of the response function (cJ Birnbaum, 1982).

In sum, it is assumed here that respondents have difficulties in performing trade-offs between the diverse EV dimensions and that these difficulties may explain the negative evidence for the multiplicative assumption. This hypothesis was tested in two studies. Study 1 was conducted to find out whether the elusive multiplicative combination could be obtained under extremely facilitating experimental conditions, that is, under conditions which placed minimal demands upon concentration and memory. To insure optimal statistical power, a within-subjects design was employed in Study 1. To avoid the assumption of a linear response function, a method was used which does without this assumption - conjoint measurement (CM). Study 2 is intended as a stringent test of the trade-off assumption implicit in equation 1.

Preceding the description of the empirical studies, an introduction to CM will be given. Applications of this method are certainly less frequent than applications of ANOVA, and so far there has been no application of CM to the present topic. For a more extended exposition readers are referred to Krantz and Tversky (1971) and Nickerson and McClelland (1988).

Conjoint measurement

Axiomatic conjoint measurement analyses multidimensional attributes, that is, attributes that are composed of two or more components (factors, independent variables). The method allows the identification of the combinatorial rule which underlies the combination of these components (cf: Krantz and Tversky, 1971; Dawes and Smith, 1 98 5). '

For each of several possible combinatorial rules, CM theorists have elaborated its empirically testable properties, so-called axioms. In testing these axioms CM uses only the ordinal relations between the levels of the dependent variable. This approach is an advantage over ANOVA in cases where the response function is either unknown or nonlinear but can be assumed to be strictly monotonic. Thus, whereas monotonic transformations may render a significant interaction in an ANOVA nonsignificant, such transformations do not change the results of tests of CM axioms. The necessary CM axioms are also practically sufficient for the various

' Axiomatic conjoint measurement should be distinguished from conjoint analysis, a numerical scaling technique which tries to fit data to certain composition rules instead of analysing violations of axioms (e.g. Umesh and Mishra, 1990).

172 K. Jonas

combinatorial rules. Cases where the conditions are satisfied, but the respective rule does not hold, are empirically rare (Krantz and Tversky, 1971). As implied in the term conjoint measurement, simultaneously with testing for combinatorial rules, CM diagnoses the measurement level of the dependent and independent variables. This measurement issue will not be dealt with here (but see Luce, Krantz, Suppes and Tversky, 1990).

In the following exposition, the two axioms which are central to the multiplicative and the additive composition rule in the three-factor case will be described. As will be demonstrated, these axioms lend themselves to a psychological interpretation in accordance with the present hypothesis. They make it possible to determine whether violations of the predicted combination rule are due to difficulties in performing trade-offs or to respondents’ lack of concentration or motivation.

Following Krantz and Tversky (1971), the three independent variables will be designated by the capital letters A , P , U. Lower case letters taken correspondingly from the beginning (e.g. a, b), middle (e.g. p , q), and end (e.g. u, v ) of the alphabet designate different levels of these independent variables. To simplify matters, the positive case is assumed, that is, that all scale values have the same sign and none of the levels of any factor assumes a zero value.

Component A is independent of P and U, if the following equation holds for all a, b in A ; p , q in P, and u, v in U:

(a,p,u) >=(b,p,u)ifandonlyif(a,q,v) >=(b,q,v).

Stated less formally, this axiom is satisfied if the ordering of the levels of component A does not in any way depend on the levels of the remaining components. Both the additive and the multiplicative rule satisfy independence. Consider Figure 2: Components A and P may be exemplified by severity and probability of threat, and U by efficacy. As can be seen, the ordering of the dependent variable according to levels of severity is not affected by alterations in the levels of probability and/or efficacy. As is evident, the axiom does not imply demanding cognitive capabilities. Thus, provided that subjects are given enough time to answer carefully, violations of independence in judgmental tasks should be due to a lack of motivation or concentration, rather than to cognitive limitations.

A and P are jointly independent of U if the following equation holds for all a, b in A ; p , q in P; and u, v in U:

(a,p,u) > = (b,q,u)ifandonlyif(a,p,v) > = (b,q,v). (3)

The multiplicative combination may serve as an example: Since the two pairs in equation 3 differ only with respect to the level of component U, this difference should not affect the relative order of the (a,p)- and (b,q)-combinations. Figure 1 helps to elucidate the axiom. Consider a respondent who is requested to judge the relative danger of combinations of severity x probability X efficacy. If this respondent is asked to judge the relative extent of danger presented by the situations (a,p,u) - (b,q,u) and by the situations (a,p,v) - (b,q,v), inconsistencies in his judgments cannot be precluded. Thus, he may judge (a,p,u) as more dangerous than (b,q,u) but (a,p,v) as less dangerous than (b,q,v) or vice versa. If the pairs have to be judged independently, such inconsistencies are difficult to avoid, since the respondent may not really be able to perform a trade-off between A and P. Thus, the joint indepen-


dence-axiom is sensitive to the trade-off problem. Note however, that not all of the logically possible tests of the axiom involve trade-offs. For example, the axiom also implies that (a,q,v) > = (b,p,v) if (a,q,u) > = (b,p,u). It is obvious that the relative extent of danger in situations like these can be determined by the dominance principle.

In cases where the respondents’ task is to produce a rank order instead of making pairwise comparisons, with three factors and given the positive cases, the only necessary axiom to be tested for the additive, as well as the multiplicative rule is joint independence (cf. Krantz, Luce, Suppes and Tversky, 1971, p. 340). Joint independence for all pairs of factors implies single independence with respect to each individual factor (cf. Krantz and Tversky, 1971).

In the positive case CM cannot distinguish between the additive and the multiplicative rule (cf. Krantz and Tversky, 1971). This is not considered as a severe disadvan- tage here, since the present investigation examines an assumption common to both types of composition rule - that respondents can perform trade-offs.

CM, as of yet, lacks a satisfactory general foundation for testing the statistical significance of axiom-violations (cf. Nickerson and McClelland, 1988). Attempts to establish a statistical error theory for CM were only partially successful (e.g. McClelland, 1977). Due to the lack of appropriate statistical tests for rejecting a certain combinatorial rule, CM researchers often employ the strategy to allow a small number of errors before rejecting the respective rule (cf. Nickerson and McClel- land, 1988). This strategy is also employed in the study reported below.

STUDY 1

In order to test the multiplicative combinatorial rule proposed by Rogers (1975), subjects were provided with materials consisting of hypothetical situations which differed systematically with respect to severity of threat, probability of a dangerous event, and efficacy of recommendation. Certainly, these hypothetical situations differ from actual health threats which also may evoke affective reactions (i.e. fear). Yet this limitation is not consequential for testing EV formulations like Rogers’ (1 975) because they take only the cognitive aspects of threats into account. In addition, such scenarios allow control of interfering irrelevant variables and thus, should facilitate the accomplishment of the cognitive processes required by equation 1.

In an additional attempt to increase respondents’ ability to perform trade-offs, the perceived danger implied by a certain situation was chosen as the dependent measure instead of intentions to engage in protective action (as in PMT). Research on the attitude-intention relationship (e.g. Ajzen, 1988) suggests that perceived danger of a situation may be only one of several determinants of an intention. Due to their greater number of determinants, intentions should be less completely determined by the model’s independent variables than are perceptions of danger.

Thus, it is predicted that due to the difficulty of performing trade-offs a high percentage of the subjects will violate joint independence, that joint independence will be violated more frequently than independence, and that at least some of the subjects will employ noncompensatory decision rules (i.e. rules which do not imply trade-offs). Due to the lack of an adequate statistical error theory of CM, Study 1 should be seen as an exploratory study which will be supplemented by a study in which subjects’ data are submitted to a traditional test of significance (Study 2).

174 K. Jonas

Method

Subjects

Among the 40 first- or second-year psychology students from the University of Tub- ingen who served as subjects, 24 were female (median age: 25 years), and 16 were male (median age: 24 years). Although most students participated as part of a study requirement, a few subjects were unpaid volunteers.

Materials

The topic of tetanus infections was chosen to operationalize the health threat. First, subjects were presented with some brief written information concerning the origin, symptoms, and development of tetanus infections (taken from Alexander and Raettig, 1981). Subsequently, they were given written descriptions of 18 types of vacations in Mediterranean countries. Each of the descriptions corresponded to a cell of a 3(probability) x 3(efficacy) X 2(severity)-design.

Probability of dangerous event was manipulated by distinguishing three types of vacation: ‘Lodging in a hotel’, ‘staying at a camping ground’ or ‘working as a farmhand in a vineyard’. The information stated that these three types of vacations imply an increasing risk of infection: While working as a farmhand, the probability of infection by pollution of wounds is higher than that during a stay at a camping ground, which in turn implies a higher risk than during a stay in a hotel.

Participants were informed that in the case of an infected wound, the risk of getting manifest tetanus increases with the period of time since the last vaccination. This information allowed the eficacy of recommendation to vary at three levels: ‘Never vaccinated’, ‘last vaccination 10 years ago’ or ‘last vaccination 3-4 years ago’.

The material also informed participants that the severity of manifest tetanus increases the longer the subject goes without medical care. Accordingly, severity of threat was manipulated at two levels by varying the temporal distance between the vacation site and the next institution providing medical care: ‘Medical institution at the vacation site’ or ‘medical institution 6 7 hours away’.

Each situation was presented on a 10.5 X7.4 cm card containing keywords which indicated type of vacation, period of time since last vaccination, and distance of medical institution. The 18 cards were presented simultaneously.

Manipulation checks

Before answering the dependent measure, the participants judged on scales from 0 (minimal) to 100 (maximal) (a) the probability of an infection for each of the three types of vacation, (b) the probability of getting acute tetanus for each of the three conditions of efficacy, and (c) the severity of acute tetanus in each of the two severity-conditions. The main function of these manipulation checks was to identify subjects whose ratings of the various factor levels were not related by strictly monotonic increasing functions to the ‘objective’ extent of danger according to the medical information given to them. Subjects whose manipulation checks reveal that they do not perceive the levels of the factors as different do not constitute negative


evidence against the predicted rule. Instead, the range of levels may not have been sufficiently wide enough for them to discriminate between the levels.

Dependent measure and instruction

Subjects were requested to take the role of the vacationer in each of the described situations and indicate on a scale from 0 (not at all dangerous to health) to 100 (maximally dangerous to health) the extent of danger involved in staying in the described situation. The instruction explicitly required that participants’ ratings should not only express the relative extent of danger in the different situations but also reflect differences and ratios of extent of danger existing between the situations. To facilitate this task, participants were instructed first to rank order the 18 situations according to their extent of danger, and only thereafter to give their exact rating.

Procedure

Subjects were tested in individual sessions lasting from 1 hour to 1% hours. At the beginning of a session it was pointed out that the task did not have a time limit. Subjects were not permitted to take written notes because this activity was regarded as being ‘ecologically invalid’.

Diagnosis of composition rules

The data were analysed by PCJM (Ullrich and Cumins , 1973), a computer program that allows for the analysis of each of the CM axioms in the positive case. The assumption of the positive case seems justified in the present study because obviously none of the factors changes its sign; that is, all the levels of the three factors are associated with various levels of disutility (danger) rather than utility. The additive/ multiplicative rule was tested by the examination of joint independence. In the present 3 X 3 X 2 design, the axiom requires 36 tests for efficacy X probability, 45 tests for efficacy x severity, and 45 tests for probability X severity (cf. Ullrich and Cummins, 1973). The data were analysed separately for each individual subject.

Results

Manipulation checks

The success of the manipulation of the three factors was tested for each individual subject. Thirty-nine subjects satisfied the criterion of strictly monotonic increasing order with respect to each of the three components. One subject left the pertinent questions unanswered; it was assumed that this had happened accidentally. Thus, the strict monotonicity of the three dimensions, which is a necessary precondition for a sensitive test of the multiplicative rule, holds for all of the subjects.

CM results

The judgments of 10 subjects satisfied the additive/multiplicative rule perfectly; that is, the responses of each of these subjects passed the 126 tests of joint independence

176 K. Jonas

without failure. Interestingly, however, seven of these additive/multiplicative subjects could be classified equally well as having employed a judgmental rule, which is designated as ‘lexicographic order’ in decision research (e.g. Montgomery and Sven- son, 1976) because it implies a sorting of the situations and does not require trade-offs: In the judgments of these subjects, the three factors showed a clear gradation of importance. One of the factors served as the primary criterion for rating the extent of danger. The second (third) factor was invoked only if two or more situations had the same level with respect to the first (first and second, respectively) factor. Finally, 30 subjects showed at least one violation of joint independence, whereas only 11 subjects had one or more independence violations.

Since some of the axiom-violations may be due to random errors, the criteria for assigning subjects to the additive/multiplicative rule were relaxed: A factor pair was regarded as jointly independent if maximally one inversion in the ranking would have been necessary to establish perfect joint independence. This modification follows the precedent CM study of Ullrich and Painter (1974) which also employed a three- factor design with the same number of levels as the present study. As in the Ullrich and Painter (1974) study, one inversion for each of the factors was conceded in tests of independence.

As a consequence of relaxing the criteria for the assignment, the number of subjects classified as additive/multiplicative increased to 2 1 (including the seven lexicographic subjects). All of the remaining 19 subjects violated joint independence, whereas only four of them showed violations of independence. It is unlikely that these remaining 19 subjects had employed compensatory composition rules other than the additive/ multiplicative because 14 of the 19 subjects showed patterns ofjudgments not compat- ible with any of the compensatory composition rules which are distinguished by Krantz and Tversky (1 97 1).

A N 0 VA results

An analysis of variance yielded main effects for severity (F,,39 = 72.2, p < 0.0001, R2 = 0.08), for probability (F2,78 = 114.7, p < 0.0001, R2 = 0.21), and for efficacy (F2,78 = 122.9, p < 0.0001, R2 = 0.26). As is obvious from Figure 3, the direction of these effects is in accordance with the predictions of the protection motivation theory. In addition to the main effects, each of the three possible two-way interactions became significant: severity X probability (F2,78= 11.7, p < 0.0001, R2 = 0.002), severity x efficacy (F2,78 = 9.4, p < 0.001, R2 = 0.002), and probability x efficacy (F4,1s6 = 22.4, p < 0.0001, R2 = 0.01). Though the amount ofvariance explained by these interactions is very small, their direction is consistent with equation 1: For each pair of independent variables, the danger difference between the highest and the lowest level of the first variable was higher for the highest rather than the lowest level of the second variable (see Figure 3).

No significance was obtained for the three-way interaction (F4,,56 < 1). This result is inconsistent with the strictly multiplicative combination assumed in equation 1.

Discussion

Several results of this study are consistent with the predictions: Whether the criteria for axiom-violations were relaxed or not, a considerable percentage of the subjects


loor

~

(medical ~nstitutionl

" 6-7 " a t hours,, vaca\!on a w q s i te

" nwer vacc i nat e d "

loor

t I

(medical institution)

" 6 - 7 "a t hour!, vcca!!ut away s i t e

"last vaccination 10 years ago"

0 "farmhand"

)c "camping"

0 "hotel"

1 % imedical inrtitut~on)

'' 6 -7 " a t hour!, vaccq!ion away sit c

" last vacc i nation 3-Lyears ago"

Figure 3. Results of Study 1: Mean danger ratings as a function of the independent variables

violated joint independence, the axiom sensitive to the trade-off assumption. Consis- tent with predictions, the majority of errors concerned joint independence rather than independence. Admittedly, since CM lacks a method of testing for the significance of violations of one axiom over the other, this result cannot be regarded as conclusive.

As expected, the findings also suggest that several subjects circumvented trade-offs by employing a decision rule which does not involve trade-offs (lexicographic order). Nonetheless, it cannot be proven that these subjects employed a lexicographic order. Theoretically, they may have followed the additive/multiplicative rule but perceived some of the factors as less important such that not even their highest level could compensate for the lowest level of a more important factor.

To turn to the ANOVA results, significance for each of the two-factor interactions was obtained. This result can be regarded as support for the original version of the protection motivation theory, ifa linear response function for the danger ratings is assumed. This assumption, however, cannot be decided positively or negatively for the present data.

In contrast, CM has the advantage of assuming only a monotonic response function. It is noteworthy then, that even with this method, discrepant with the original predictions, 14 subjects were classified as additive/multiplicative. Thus, obviously, the scepticism toward the trade-off assumption has to be qualified. Several subjects appear to have combined components additively or multiplicatively. On the other hand, only three subjects satisfied joint independence perfectly. Thus, nearly all of the subjects violated this axiom to a greater or lesser extent. Finally, the observed individual differences regarding axiom-violations should not be taken as evidence for stable interindividual differences in performing trade-offs since no retest measure on the stability of these differences is available.

As the results show, the efficacy-main effect explained a higher proportion of

178 K. Jonas

variance than the main effects of severity and probability. It cannot be precluded that the features of the present scenario and the choice of the dependent variable (danger ratings) contributed to the obtained rank order of the three variables regarding proportion of explained variance. On the other hand, efficacy might have explained even more variance if behavioural intentions had been the dependent variable since efficacy of preventive action arguably may be more relevant to intentions than to ratings of danger.

STUDY 2

Several aspects of the results of Study 1 are consistent with the assumption that performing trade-offs between the independent variables of PMT poses cognitive difficulties. Due to the statistical limitations of Study 1, however, the evidence is somewhat indirect. Therefore, Study 2 is designed to test the hypothesis more directly: In this study subjects were forced to perform trade-offs under controlled conditions, and their respective performance was compared with their error frequency regarding judgments not requiring trade-offs.

The rationale and methodology were as follows: Subjects were presented with several pairs of hypothetical dangerous situations. For each pair they were requested to determine which of the two situations was more dangerous. Half of the pairs required a trade-off between the different components that contributed to the overall extent of danger, the other half of pairs allowed subjects to apply the dominance principle. Each pair was presented twice, thus making it possible to assess the reliability of the respective judgment as reflected by the frequency of judgment reversals. Degree of reliability served as an indicator of cognitive effort: Since pairs requiring a trade-off between components are cognitively more demanding, compared to pairs with a dominant alternative, more reversals of judgment are to be expected for trade- off pairs.

Method

Subjects

Subjects were 40 first-year psychology students at the University of Tubingen. Twenty-seven subjects were female (median age: 22 years) and 13 were male (median age: 24 years). Subjects participated as part of their study requirements. None of the subjects had participated in Study 1.

Materials

As in Study 1, the health topic was tetanus infections during vacations in Mediterra- nean countries. Likewise, for each of the situations information concerning severity of threat, probability of infection, and efficacy of the recommendation was given. Subjects were presented with 80 pairs of situations. For each pair they had to indicate which of the two situations appeared to them to be more dangerous to their health. The subset of pairs 1 4 0 was identical with the subset 41-80. That is, each pair from the first subset was repeated in the second subset, and in the repeated pair


the order of the two situations was reversed. Separately in each of the two subsets the order of presentation of the pairs was randomly determined for each individual subject.

The situations were taken from a 3(efficacy) X 2(severity) X 2(probability) design of hypothetical situations. The operationalizations were similar to those in Study 1. The levels of the factors were ‘never vaccinated’, ‘last vaccination 10 years ago’ and ‘last vaccination four years ago’ (efficacy); ‘medical institution at the vacational site’ versus ‘medical institution six hours away’ (severity); ‘vacation in a hotel’ versus ‘vacation at a camping ground’ (probability). The total number of painvise comparisons possible within this design is 66. To avoid fatigue and loss of motivation, a subset of 40 of the 66 pairs of situations was chosen, 20 requiring a trade-off, 20 requiring no trade-off. The pairs were selected such as to allow varying each of the three factors at least several times.

The 80 pairs of situations were compiled in a booklet that presented the pairs in serial order. Each page contained one pair. Information on the two situations was presented by keywords referring to the levels of the three factors. The keywords were arranged in two columns (situations) by three rows (factors).

Manipulation checks

Following the comparisons, a manipulation check for each of the three components was conducted (as described in Study 1).

Dependent measures and instructions

After receiving their individual booklet, subjects had to indicate for each pair which of the two situations they perceived as more dangerous or that they perceived the two situations as equally dangerous. They were requested not to go back to previously answered pairs.

In addition, subjects had to rate each of the 12 situations on a scale from 0 (not at all dangerous to health) to 100 (maximally dangerous to health). Instructions for these danger ratings were identical with the instructions for the ratings in Study 1. To facilitate the ratings, the 12 situations were presented simultaneously. Ratings were made after the manipulation checks.

Procedure

Subjects were tested simultaneously in a classroom. It was made clear that the task did not have a time limit. The task lasted from % to 1 Yi hours.

Results

Manipulation checks

Manipulations were tested for each individual subject. Manipulation of a component was considered successful if the ratings of its levels and their objective order were related to each other by a strictly monotonic increasing function. Only the 37 of

180 K. Jonas

the 40 subjects who satisfied this criterion with respect to each of the three components were included in the following analysis.

Reliability of judgments

Pairs of situations were treated as the units of analysis and their pertinent number of reversals constituted the dependent variable. This one-way design consisting of two cells (trade-off pairs versus dominant-alternative pairs) was analysed by means of an ANCOVA that introduced the difference in perceived danger as a covariate. An ANCOVA is appropriate because the frequency of reversal may be confounded with differences between the alternatives in relation to perceived danger: Trade-off pairs tend to have smaller differences than pairs not requiring a trade-off (dominant- alternative pairs). To control for differences in perceived danger, each subject’s danger ratings were used to calculate the difference between the two situations of each pair with respect to perceived extent of danger. For each pair the resulting 37 individual differences were averaged. These averages constituted the covariate.

The effect of the type of pair (trade-off versus dominant-alternative) was assessed after assessing the effect of the covariate. As expected, the covariate explained a significant proportion of the variance of the number of reversals; F,,37 = 29.7, p < 0.001. Frequency of reversal increased with increasing similarity with respect to extent of danger.

As predicted, however, even after adjusting for the effect of the covariate, type of pair (trade-off versus dominant-alternative) explained a significant proportion of variance of the number of reversals; F1,37 = 20.8, p < 0.001. As predicted, reversals occurred more frequently with trade-off pairs (unadjusted mean = 4.95) than with dominant-alternative pairs (unadjusted mean = 0.70).

To obtain additional information on the covariate in the above analysis, the correlation between difference in perceived danger and frequency of reversal is of interest. A significant r = -0.53 ( 1 per cent-level, one-tailed) was obtained for trade-off pairs and a nonsignificant r = -0.07 for pairs with a dominant alternative.*

Discussion

As predicted, the reliability for judgments of trade-off pairs was lower than for judgments of dominant-alternative pairs. This result confirms the assumption that performing trade-offs poses cognitive difficulties. An additional result of the study, however, may make a qualification of the original hypothesis necessary. As reported, a significant negative correlation between difference in perceived danger and frequency of reversal was obtained for trade-off pairs. This correlation may be interpreted as suggesting that subjects tried to make trade-offs and were increasingly successful with decreasing similarity of the situations with respect to perceived danger- ousness.

The above-reported F- and r-values refer to changes of judgment from ‘more’ to ‘less dangerous’ or vice versa, excluding judgmental changes from ‘more’ to ‘equally dangerous’ or vice versa. When the latter type of change was included in the analysis, the F-values for the covariate and type of pair stayed significant. Similarly, only slight numerical changes were obtained regarding the reported correlations, when these additional changes in judgments were included.

Expectancy-value models of health behaviour 18 1

GENERAL DISCUSSION

The results of the two studies provide support for the hypothesis developed in the Introduction but the original hypothesis has to be qualified. In line with the hypothesis, (1) more subjects violated an axiom which requires trade-offs than an axiom which does not, (2) evidence for subjects using noncompensatory rules was found, and (3) the reliability of judgments requiring trade-offs was lower than that of judgments which do not.

On the other hand, contrary to predictions, several of the subjects in Study 1 passed the necessary CM conditions for the additiveimultiplicative rule. Furthermore, as the correlational results from Study 2 suggest, apparently subjects tried to make trade-offs and managed to do this if the two situations were not too similar with respect to perceived extent of danger. The ANOVA (Study 1) also yielded indications for some of the ordinal interactions which are predicted by the original version of PMT. This latter result is consistent with the multiplicative assumption $a linear response function is assumed.

These seemingly conflicting results can be integrated by the assumption that (some) subjects try to perform trade-offs, but this attempt indeed seems to be prone to errors which are not unsystematic but related to the inherent difficulty of this type of judgment. This conclusion can be drawn even if the ANOVA results are not accepted because of the uncertainty regarding the linearity of the response function.

On the other hand, it has to be pointed to the fact that the ANOVA interactions - though explaining only a minimal proportion of the variance - assumed the form predicted by the original version of PMT. Thus, it seems possible that the multiplicative formula is adequate in that it describes a tendency according to which the effect of a factor is magnified by alterations in the levels of other factors. This conclusion would be consistent with the results of Rogers’ (1985) study and the above-mentioned information-integration studies which also obtained significant ordinal interactions in within-subjects designs. Thus, assuming linear response functions in these studies, the lack of evidence for the hypothesized multiplicative combination in previous work on fear appeals could be due to the fact that most of these studies employed a between-subjects methodology which may lack the statistical power necessary to detect effects having effect sizes as small as those of the interactions in the present study. Even when combined, the three two-way interactions explain less than two percent of the total variance. For practical applications, thus, the predictions from a multiplicative rule are nearly tantamount to those from an additive combination.

Admittedly, the violations of the assumptions underlying equation 1 seem to be less severe than expected at the outset. Even if a critic does not accept the ANOVA results on account of the linearity of the response function being not proven, it should not be ignored that a considerable number of subjects were classified as additive/multiplicative in CM. Thus, the doubts concerning the assumptions underlying the additive/multiplicative rule have to be qualified. On the other hand, the facilitating conditions of Study 1 have to be taken into account: (a) The task had no time-limit; (b) the information on the cards was restricted to the three components, thereby excluding distraction by any further aspects; (c) the simultaneous presentation of stimulus cards placed minimal demands upon concentration and memory, and may have helped to avoid inconsistencies; (d) the fact that the manipulation checks

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were conducted before subjects gave their ratings should have increased the chance that subjects took the information carefully into account.

In sum, it was shown that trade-off judgments are error prone to a certain extent. This error proneness together with the small effect size of the multiplicative combination may have contributed to the lack of evidence for the multiplicative rule in previous studies. Since the present study was conducted under highly facilitating conditions it can be speculated that the multiplicative combination would be even more elusive under more realistic conditions (e.g. higher informational complexity, higher demand upon concentration).

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