MATHEMATICAL MODELS OF COMMUNICATION AND < : BELIEF CHANGE PROPORTIONAL CHANCE} ‘2 13;“;2 ' ACCUMULATED INFORMATION, AND BELIEECERTAINTY :g- ’ . Dissertation for theDegree of FIND; -' ’ MICHIGAN STATE UNIVERSITY » JEFFREY E DANES ‘ . 1976 Rena-”Walt! 9.33:; W I; if" 8 l2: R Y Michigan State University E. This is to certify that the thesis entitled ‘ MATHEMATICAL MODELS OF COMMUNICATION AND BELIEF CHANGE: PROPORTIONAL CHANGE, ACCUMUIATED INFORMATION, AND BELIEF CERTAINTY presented by Jeffrey E. Danes has been accepted towards fulfillment of the requirements for Ph-D- degree in _Comrmmica_tion \ l ’ \. , N. \a’v ' ‘h I («J r 4.» BN( ./ . I V \\__ Major professor I Date July 29, 1976 0-7639 ABSTRACT MATHEMATICAL MODELS OF COMMUNICATION AND BELIEF CHANGE: PROPORTIONAL CHANGE, ACCUMULATED INFORMATION, AND BELIEF CERTAINTY BY Jeffrey B. Danes Three models of communication and belief change were proposed and tested. The proportional change model stated that receivers change their beliefs in the direction of the message with the resulting belief change being proportional to the amount of change requested. The accumulated infor- mation model was based upon the same logic; however, it stated that belief change would be inhibited by the degree to which information has been accumulated into the belief. It was hypothesized that accumulated information and belief certainty would be positively correlated; hence, a belief certainty model was also proposed and tested. The three models were tested with two sets of data, and the results obtained showed clear support for the accu— mulated information model. The belief certainty model was the most inferior of the three. Although a positive corre- lation was found between accumulated information and belief certainty, the "informed neutrals" were almost nonexistent; while "uninformed resolutes" prevailed. Regardless of Jeffrey E. Danes initial belief, the "uninformed" were the most affected by the belief-change messages. MATHEMATICAL MODELS OF COMMUNICATION AND BELIEF CHANGE: PROPORTIONAL CHANGE, ACCUMULATED INFORMATION, AND BELIEF CERTAINTY BY Jeffrey E: Danes A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Communication 1976 Accepted by the faculty of the Department of Communication, College of Communication Arts, Michigan State University, in partial fulfillment of the require- ments for the Doctor of Philosophy degree. €4.le Diiéctor of Dissertation Guidance Committee: ‘>§§11LLCMQ'1 , Chairman LL /\ ( b(,_1_// l((( ~\ Q [1% a L (:74 // - Fr L’V'N. All of this work and more is dedicated to the three most important people in my life: Katherine, Nathan, and Eric Danes. ii ACKNOWLEDGMENTS I would like to express my thanks and appreciation to the two persons who were most influential during my gradu- ate training in Communication: Dr. Joseph Woelfel and Dr. John Hunter. I thank Dr. Woelfel for the many stimula- ting conversations and the many hours put into this disser- tation. His help was deeply appreciated. I thank Dr. Hunter, for without his help, this dissertation might never have been completed. His assistance in math modeling and in the analysis of model data was very much appreciated. My appreciation also goes to Drs. Bettinghaus, Atkin, and Ebel. Dr. Bettinghaus provided many useful and perceptive comments on earlier drafts of this dissertation. Both Drs. Atkin and Ebel also did much to bring the dissertation into a clearer focus. Dr. Atkin gets a special word of thanks for allowing me time to write when I was suppose to be in the classroom. My thanks and gratitude are also given to many of my colleagues and students: I express my thanks to Nick Stoyanoff for the many hours spent listening and criticizing the ideas presented in this dissertation. Nick also de- serves thanks for his help during data collection. Patti Kluck and Donna Borris who also helped collect the data are iii also thanked for their efforts. Paul Taperek and Helen Short gave continual support and overall encouragement; for this, I express my thanks and appreciation to them. Lastly and most importantly, I would like to thank my family: Katherine, Nathan, and Eric, for their patience and love while I spent three years working toward the Ph.D. in Communication. iv Chapter I II III IV TABLE OF CONTENTS INTRODUCTION . . . . Introduction to the Problem The Proportional Change Model Accumulated Information . The Accumulated Informational Model Belief Certainty . . The Belief Certainty Model METHOD . . . . . Pilot Study . . . . Accumulated Information Belief Topic and Message Selection . . . . Testing the Models: Main Study Experimental Design . Procedures . . Measurement . . . PRELIMINARY ANALYSES . . Scale Construction, and Reliability . Message Effect Manipulation Check RESULTS . . . . Testing the Models Accumulated Information and Belief Certainty Evaluation, Page wNKDQAbUJ HF4 16 16 17 18 18 20 22 22 24 27 27 32 Chapter V DISCUSSION . . . . . . . . APPENDICES . . . . . . . . . . A. Belief topics and standard deviations REFERENCES for the belief certainty and accumulated information measures used in the pilot study . . . . . . . . The military message used in the ex- periment. The material was adapted from an actual news story presented in the March 8, 1976 issue of Time: "That Alarming Soviet Buildup." . . . The nuclear message used in the experi- ment. The material was adapted from an actual news story presented in the March 8, 1976 issue of Time: "The Struggle Over Nuclear Power." . . The pretest questionnaire. Adminis— tered on May 13, 1976 . . . . Posttest questionnaire. Administered May 13, 1976. . . . . . Delayed posttest. Administered May 20, 1976. . . . . . . Multiple groups, oblique cluster analysis (key to indicators). . vi Page 36 40 40 43 47 51 60 68 76 78 Table 1. 8a. 8b. 8c. LIST OF TABLES Reliability Estimates for the Pretest Measures of Belief and Accumulated Information Mean Pretest, Posttest, and Change Values and Standard Deviations for the Experimental and Control Situations . . . . . . ANOVA Regression Summary for Effects of Nuclear Message upon Nuclear Belief Change . ANOVA Regression Summary for Effects of Military Message upon Military Belief Change Correlations Between Ab and d for the Nuclear and Military Topics in Both the Experimental and Control Situations . . . . . . Belief Change Means and Sample Size for the Three Levels of Accumulated Information and the Three Levels of Belief for the Nuclear Message . . . . . . . . . . Belief Change Means and Sample Size for the Three Levels of Accumulated Information and the Three Levels of Belief for the Military Message . . . . . . . . . . Number of Subjects in Each of the Cells for the Three Levels of Belief and the Three Levels of Accumulated Information for the Nuclear Pretest Group . . . . . . Number of Subjects in Each of the Cells for the Three Levels of Belief and the Three Levels of Accumulated Information for the Military Pretest Group . . . . . . Number of Subjects in Each of the Belief- Accumulated Information Cells for Both the Nuclear and Military Topics . . . . . vii Page 24 24 25 26 27 30 31 33 34 34 Figure LIST OF FIGURES Parametric curves for the prOportional change model with a parameterized. The curves graphically represent predicted change as a function of the amount of change requested . . . . . . . Parametric curves for the accumulated information model with a held constant at one; and accumulated information (i ) controlled. The curves graphically represent predicted change as a function of the amount of change requested, in- hibited by prior information accumulation . Parametric curves for the belief certainty model with a controlled. The curves graphically represent predicted change as a function of the amount of change requested, inhibited by belief certainty . . . . . . . . . Regression curves of nuclear belief change on initial belief with accumulated information parameterized . . . . . Regression curves of military belief change on initial belief with accumulated information parameterized . . . . . viii Page 10 14 30 32 CHAPTER I INTRODUCTION In much of communication research, a major construct used for the assessment of communication effects is typi- cally "attitude" change. It is recognized by numerous com- munication scholars, however, that communication affects a multitude of other mental variables. That is, not only are "attitudes" possibly altered by the reception of messages, but "knowledge," "perception," "opinions," "meaning," be— lief," and a host of other constructs may change during the process of communicating. A current view adopted by many communication scholars is that communication has its primary effect upon the ways in which the human structures, maps, or organizes the sym— bolic environment so that it becomes understandable (Roberts, 1971). The structuring and restructuring of one's symbolic environment goes by many different terms; however, the term currently in vogue for much of communication re- search is Boulding's (1956) construct of the "image." Boulding (1956) has conceptualized the image to be what one believes to be Eruef-one's subjective knowledge of the various aspects of the physical, social, and symbolic world. By another name, the image construct has also been 1 2 referred to as belief; Bem (1970) has offered the following treatment of belief: If a man perceives some relationship between two things or between something and a char- acteristic of it, he is said to hold a belief. For example, he might suppose asteroids to be round, the dean of women to be square, God to be dead, men to love freedom, himself to dislike spinach, and Republicans to promote congress. Collectively, a man's beliefs compose his understanding of himself and his environment (pp. 4-5). The focus of this study is upon the change of beliefs using messages; the belief of concern is what Rokeach (1968) has termed the "authority" belief and Fishbein and Azjen (1975) "informational" beliefs. Many of our beliefs are formed neither on the basis of direct experience with the object of belief nor by way of some inference process. Instead, we often accept information about some object provided by an outside source. Such sources include newspapers, books, mag- azines, radio and television, lectures, friends, relatives, coworkers, etc. Beliefs formed by accepting the information provided by an out- side source may be termed informational beliefs (Fishbein & Ajzen, 1975, p. 133). For the present, belief is conceptualized as the con- ceived truth value of an assertion or statement. And as such, a belief exists when one thinks "true," "uncertain," or "false" to a given assertion or statement. Gradations of truth value may also be considered; thus, belief is viewed as continuum ranging from "true" to "false." Introduction to the Problem Currently there is an increased interest in the modeling of communication effects within the domain of "passive com- munication." Passive communication as opposed to active communication restricts the domain of inquiry to those situ- ations where a receiver decodes a message sent by a source, and the receiver ". . . is not asked to respond to the mes- sage in any active way (argue, give money, risk life, etc.) or openly commit himself to a position that might be contrary to that taken by his peers or reference groups" (Hunter and Cohen, 1972, pp. 4-5). This context for which to study com- munication effects is desirable in that it does represent many forms of symbol transmission actually applied to prac- tice: many forms of the mass communication of news and many forms of advertising fall within the domain of passive com- munication. Within the passive communication context, the simplest possible model for the effects of communication upon belief change is one that predicts changes that are equal to the amount of change advocated. Of the identical genre, a slightly more complex model would predict changes that are proportional to the amount of change advocated. The propor- tional change model is derived from the equal change model below. 4 The Proportional Change Model With the assumption that a message is perfectly effec- tive, a change in belief (Ab) as a result of receiving a belief—change message would result in maximum change; i.e., all of the change requested would be obtained. The perfect effects model is quantified below (for the purpose of quan- tification, true will be set to zero and false to 100): Ab = -b0 (1) where, Ab = the change in the original belief b0 = the original belief bO = the subjective probability for truth—value; totally true equals 0 and totally false equals 100. Consistent with the assumption, this model states that a perfectly effective message would produce a change equal to the negative of the original belief (b0); this would render the next belief (bl) to be zero (maximum truth): bl = b0 + Ab (2) b1 = bo ’ b0 (3) bl = o (4) This model, however, assumes that the message is per- fectly effective; as is well known among communication scholars, the impact of a message typically yields changes that are proportional to those recommended. The proportional change model was first suggested by French (1956) and has since been elaborated by a variety of authors (Hovland and Pritzker, 1957; Anderson and Hovland, 5 1957; Anderson, 1959; Anderson, 1965; Hunter and Cohen, 1972; Anderson, 1971; Whittaker, 1967). This model asserts that the change in a belief is proportional to the discrep- ancy between the belief and the message. If bO is the initial belief and the message asserts the truth of the statement, then this model becomes (see Figure 1.): Ab = -abo (5) where, a = a parameter for measured message effectiveness a = Oidil lA — i> b0 d = 1/4 Vb d = 1/2 a = l Figure l. Parametric curves for the proportional change modelMdiiuxparameterized. The curves graphically represent predicted change as a function of the amount of change requested. If it were absolutely true that the amount of belief change obtained was proportional to the amount of change commanded, then once a was measured, the future states of b (i.e., bn) could be clearly and unambiguously predicted 0 by the calculation of the prediction equation latent within 6 this difference model. The change in b (Ab) may also be 0 written as: Ab = bl - b0 (6) where, bl = the next belief b0 = the original belief Adding b0 to both sides of equation (6) gives: Ab + b0 = b1 (7) = + b1 b0 Ab (8) Equation (5), however, specifies that Ab is equal to -db0; thus: bl = b0 - abo (9) b = (l - d)b0 (10) As such, the model predicts that after one exposure to a belief-change message, the next belief ((bl) will be (1 - a) times the original (last) belief (b0). Thus, the general predictive equation for n repeated exposures to a change message becomes: 11 b = (1 - a) b n 0 (11) The resulting predictive equation for n message repetitions of one change message results in an exponentially declining sequence, indicating that as n grows large, the acceptance of the truth claim increases; that is as n_+ w, bn + 0. As such, it is clear that even with relatively minute changes, the accumulative effects of message repetition may be rather dramatic. There are a number of communication variables that are believed to be related to the accuracy of predicting belief change. Given the initial assumption that belief change will be proportional to the amount of change commanded, in- creased accuracy of prediction would be enhanced if one in- corporated those communication variables that impede, enhance, and interact with the amount of change commanded. That is, if one knew the values for the credibility of source, message sidedness, message distraction, evidence, topic relevance, topic interest, the entertainment value of the message, ac— cumulated information, belief certainty, etc. then one might be in a better position to accurately predict the amount of change expected. This dissertation focused upon the follow- ing variables: Accumulated information and belief certainty. Accumulated Information For some years we have known that "established" atti- tudes are more difficult to change than are "de novo" atti- tudes (Hovland, 1959). Anderson (1959, 1965) and Rosenberg (1968) suggested that this effect could be accounted for within the context of the discrepancy model if the parameter a were to decrease as a function of accumulated information. This model was specialized by Saltiel and Woelfel (1975) who asserted that the parameter a is n n (12) 8 where n is the number of messages ever received on the topic. If a were to decline in this manner, then the belief after 3 messages would simply be the arithmetic mean of those mes- sage values. Using the average number of times an individual has com- municated with his or her significant others about a partic- ular topic (a composite of American values) as a measure of accumulated information, Saltiel and Woelfel (1975) have provided path analytic support for this hypothesized rela- tionship. Saltiel and Woelfel (1975), however, failed to present a conceptual definition for "information" or for "accumulated information"; nonetheless, they do assert that messages carry information and that the reception of messages causes information to internally accumulate within the re- ceiver. On the definition of information for human commun- ication, Lin (1973) has argued that information exists only when a receiver is familiar with the symbols of a message: unfamiliar symbols convey little to no information. Further, Lin (1973) has argued that information may be ". . . defined as a set of symbols which both the source and receiver are familiar" (p. 23). As such, accumulated information may be defined as the mental aggregation (stor— age) of a set of familiar symbols sent from a source to a receiver. Accumulated information is seen to differ from "knowledge" in that knowledge implies "correctness"; where- as the notion of accumulated information makes no such -implication. The relationship of accumulated information to belief change messages may be interpreted in the following way: when a receiver decodes a message advocating belief change, the receiver according to the proportional change model, makes a mental comparison between his or her initial be- lief and the proposed belief, and then yields proportionately. Likewise, other mental comparisons are likely; the accumu- lated information hypothesis implies that a receiver not only makes belief comparisons but also assesses the degree to which he or she is "informed" about the belief topic. If one is ngt_informed; that is, if one cannot retrieve prior message content (pro or con) then this new information compared to the old (none) takes precedent and consequently alter the initial belief. Further, if one has accumulated much information, then during the comparison process this information might be retrieved and used in defense of the initial belief, resulting in little to no belief change. A model which incorporates the accumulated information hypothesis into the proportional change model is presented below. The Accumulated Informational Model According to the accumulated information hypothesis, the amount of information that one has accumulated into a belief will be inversely related to that belief's suscepti- bility to change. In the model presented below, the 10 accumulated information hypothesis is compactly incorporated into the proportional change model (see Figure 2): _ _ 1 Ab - Odm) b0 (13) 0 b0 Ab = “0(i—fi) (l4) 0 where, i0 = the amount of information that has been accumulated into the original belief (b0). 1\ > be Ab io= 2 10: l 10: 1/2 i0= 0 Figure 2. Parametric curves for the accumulated information model with a held constant at one; and accumulated information (i0) controlled. The curves graphically represent predicted change as a function of the amount of change requested, in- hibited by prior information accumulation. To derive the predictive form of the above change equation, it is first noted that a change in belief may also be written as: Ab ll 0‘ 1 O‘ (15) 11 Adding b to both sides of the equation gives: 0 Ab + b0 = b1 (16) bl = Ab + b0 (17) bl = b0 + Ab (18) Substituting the identity given in (13) above yields: .39., io+l b = b - d( 1 o (19) Factoring gives: a bl — [1 — (1+i0)] b0 (20) The value for 10 after the reception of one belief message may or may not change. If accumulated information does not change, then the model presented below is appro- priate for predicting the number of messages necessary to change the belief to a desired value: n __ _ OI bn ‘ L (1+1 )] b0 (21) 0 If, however, accumulated information does change as a re- sult of message repetition, then the succeeding beliefs may be predicted by the following equations: _ r _ a b = F1 - (—9‘——)- - ( 0‘ ) b (23) 2 l+il 1+1O 0 _ H _ d 102 ‘ b0 k=0 [1 (1+1 )] (24) 12 As such, belief after the nth message repetition is: n-l _ H -___L 25 bn _ b0 k=0 [1 (1+ik)] ( ) Belief Certainty The forthcoming argument makes the following claim: accumulated information and belief certainty are positively correlated. In ordinary English "don't know" and "uncertain" sometimes mean the same thing. If one does not "know" or is not informed about a given belief issue, then it might be presumptious for that person to assume an extreme belief stance. On the other hand, if one does assume an extreme belief stance, then it is likely that one is also informed about the topic of concern, an assumption implied by the work of Patterson and McClue (1976). However, if the relationship between accumulated infor- mation to belief certainty were perfect then there would be no people of the following kind: those who are well informed about a given belief topic but refuse for one reason or another to take an extreme stance (the "informed neutrals"), and those who are not informed but yet adopt an extreme be— lief stance (the "uniformed resolutes"). For many years investigators have believed that people with extreme beliefs are more resistant to change than those with more neutral beliefs (Brim, 1955). This principle was dubbed the "polarity" principle by Osgood and Tannenbaum (1955) when they incorporated it into their congruity theory. 13 The polarity principle was used in conjunction with discrep- ancy theory in a version of "information processing" theory by Hunter and Cohen (1972) and the model below is adapted from theirs. The Belief Certainty Model Like that of accumulated information, it was hypothe- sized above that the certainty of a belief should also be inversely related to change; as such, the model for belief certainty is: _ _ 1 Ab _ (17%;) b0 ‘26) b0 Ab = " (Titer) ‘27) 0 Where, c0 = the certainty to which the belief is held B = a scaling parameter Belief is operationalized as a response to a subjective probability scale such that 0 represents totally "true" and 100 represents totally "false." The uncertain or uncom- mitted position is represented by a score of 50. As the be- lief departs from the uncertain (50) position, then Bc may 0 be defined as: BC0 = 2 b0 - 50 (28) And, the parametric curves for the belief certainty model are presented in Figure 3. l4 Ab Figure 3. Parametric curves for the belief certainty model with a controlled. The curves graph— ically represent predicted change as a function of the amount of change requested, inhibited by belief certainty. The predictive form of this model is: k=0 k The validity of the predictive equations for the pro— n-l ~ u bn = 130 H [1 " (TIE—Ff] (29) portional change, accumulated information, and the belief certainty models have their foundations upon the validity of the following change equations: Ab = - abo (the proportional change model) b Ab = - a(ifT—J (the accumulated information +1 0 model) b0 Ab = — a