Credibility and the Statistical Interaction Variable:

Speaking Up for Multiplication as a Source of Understanding

Davis Foulger

Presented at the 1979 Annual Conference of the Speech Communication Association
San Antonio, TX

Human interaction, it is argued in the interpersonal perception model of relationships (Laing, Phillipson, and Lee, 1966), occurs in the context of the perspectives, direct, meta, and meta-meta, of the interactants. The perspectives may or may not agree. The perspective of one interactant may or may not be understood by the other. The understanding (or lack) of one may not be realized by the other. When, as communication researchers, we try to assess these agreements, understandings, and realizations, we construct statistical interaction variables. There are a variety of logically equivalent ways of constructing these interaction variables. The simplest, both in demonstration and execution, is multiplication.

Statistical interaction terms are routinely generated and assessed for significance in most N-way Analysis of Variance (ANOVA) algorithms, but recent movement away from simple experimental designs and toward archival studies, field studies, and more complex experimental designs (with control variables, lagged variables, continuous, rather than categorical, independent measures, and the explicit modeling of expected outcomes) has been accompanied by a movement toward more complex methods of analysis. These methods, which include multiple regression, discriminant analysis, and multivariate analysis of variance (MANOVA), vastly increase the researchers control of, and flexibility in performing, the data analysis while increasing the information value of the main effects, but do not generate nor assess interaction effects. It is the intent of this paper to show how this seeming loss can be turned to gain.

The interaction variable is constructed by multiplying, for each case, the values of two or more component variables (main effects (1)). As the product of two or more variables, the interaction is clearly related to those component variables, but this relationship implies neither causation nor correlation. The interaction comes into being when its components come into being. The occur contemporaneously. Thus the interaction cannot be said to be caused by its components. The causes of the interaction are the causes of the component variables. Neither this causality or the relationship to the component variables may be observable. The statistical interaction variable can be entirely uncorrelated with any or all of the variables from which it was constructed (In ANOVA this orthogonality is assumed). By implication, the interaction variable may be entirely uncorrelated with its causes.(2)

An Example from the Literature of Source Credibility

Sternthal, Phillips, and Dholakis (1978), after reviewing the literature of source credibility, make the following statements (which can be viewed as propositions):

  1. The highly credible source has a substantial immediate persuasive effect which decays with the passage of time.
  2. It appears that a high credibility source is typically more influential than a low credibility source when identification is made before the appeal. When it follows the message, source credibility appears to have no systematic effect on social influence. Further, deferring the identification of the low credibility source until after the message has been consistently shown to facilitate persuasion, ... in some cases delaying identification of a credible source reduces influence ...
  3. The data suggest that credibility is likely to have a systematic effect on persuasion only when an appeal is highly discrepant from the message recipient's initial opinion, ... but not extreme, and there is less of a credibility effect or no systematic effect when the discrepancy is relatively low.
  4. Increased physical or social threat enhances persuasion when the communicator is highly credible. When source credibility is low, individuals are relatively unpersuaded regardless of the level of threat induced. Furthermore, it appears that a credible source is particularly likely to enhance social influence when physical or social thread is relatively extreme. When low levels of threat are induced, the highly credible source exhibits greater persuasive power than a low credibility source, though the magnitude of this difference is often less than obtained in highly threatening messages.
  5. A two sided message induces more persuasion than a one-sided appeal provided that the unfavorable side (1) is presented first, (2) is refuted in a compelling manner, and (3) cites only those arguments that are already known to the audience.
  6. Low credibility sources may increase their persuasiveness either by assuming an incongruous position or by including evidence to support their assertion. However, once one of these credibility enhancement devices is used, the inclusion of the other will apparently not further enhance persuasion.
  7. Locus of control ... Externals were more influenced than internals. Furthermore, the highly credible source was more persuasive for externals than was a low credibility source, whereas internals were equally persuaded by high and low credibility communicators.
  8. Highly authoritarian individuals are strongly influenced by source credibility cues, whereas less authoritarian people make greater use of message cues in determining their attitudes.
  9. When an audience is favorably disposed toward an advocacy, a low credibility source will induce greater persuasion, whereas when an audience is negatively disposed, a high credibility source will be more influential.
  10. A low credibility source induced greater influence when individuals perceived their compliance with the request to be voluntary. ... when compliance was perceived to be involuntary, no source effect was observed. It was also found that the highly credible source was more influential than the low credibility source when no compliance was asked for.

All of these propositions imply the existence of interaction variables which will be explored during the course of this paper.

A Typology of Interaction Variables

Interaction variables can take several forms, only one of which is the familiar ANOVA interaction term. The ANOVA term can be referred to as a reversing interaction, but other forms of interaction include what can be called constraining interactions, logarithmic interactions, and various combinations of these forms. The differences between these forms of interaction term result from coding component variables in different ways before their multiplication into interaction variables.

The coding of these component variables can vary in two ways. First, variables can be coded either categorically or continuously. Second, they can be represented using different sets of values. These coding differences don't change the component variable as long as the proportional intervals between the values are maintained. Differences in the coding of the component variable will, however, change the form of any interaction variables produced.

The distinction between categorical and continuous coding of the component variable is primarily a distinction between levels of measurement. Nominal and ordinal measures would normally, in parametric designs, be represented by a (series of) two value categorical variable(s). Interval and ration level measures would normally be represented by a continuous range of values. From the standpoint of interaction variables, however, the distinction takes on some additional importance. The categorical case is generally more rigid in its adherence to a typological category. As a result, it is often easier to code.

The only differences of importance in selecting the values of component variables for interaction are, first, the occurrence of negative values, and , second, the occurrence of factional values and, more importantly, zero.

The Reversing Interaction

The reversing interaction variable is constructed from component variables which have been coded with both negative and positive values. The negative component values allow the variable to, in its multiplication to form an interaction variable, reverse the values of other component variables. In the categorical case, the coding necessary to the construction of a reversing interaction variable is effect coding (Kerlinger and Pedhauser, 1973). Effect coding assigns categories the values of 1 and -1. Agreement, understanding, and realization, in the interpersonal perception model, are reversing interactions. Figure One demonstrates the interaction of effect coded component variables taken from proposition nine (stated earlier in the paper). The interaction variable appears in the cells and is he product of multiplying the two effect coded component variables. One should note that if the number of subjects in each 'cell' were equal, the interaction variable would be totally uncorrelated (orthogonal) with both component variables.

Figure One: The categorical reversing interaction of source credibility and audience predisposition toward the advocacy. Audience Predisposition Towards the Advocacy
Favorable Unfavorable
-1 1
Source Credibility High 1 -1 1
Low -1 1 -1

Coded as in figure one, the reversing interaction interaction of source credibility and audience predisposition toward the advocacy should be positively related to persuasion if proposition nine is correct. Speakers low in source credibility should enjoy more success with favorable audience predispositions. Speakers high in source credibility should enjoy more success with unfavorable audience predispositions.

In the continuous case of the reversing interaction variable, one uses bipolar coding of he component variables. If we visualize the variables of proposition nine as continuous rather than categorical, we arrive at a variable like that shown in Figure Two.

Figure Two: The continuous reversing interaction of source credibility and audience predisposition toward the advocacy. Audience Predisposition Towards the Advocacy
-3 -1 1 3
Source Credibility




3 -9 -3 3 9
1 -3 -1 1 3
-1 3 1 -1 -3
-3 9 3 -3 -9

The major difference between this variable and the categorical interaction of Figure One is the assumption of continuity. An assumption of continuity may increase the effectiveness of a the interaction variable by assessing degree as well as direction, but may prove untenable if the relationship is not close to linear.

The coding of component variables for reversing interaction is not always straightforward. In the categorical case, the job is relatively simple. One simply assigns values to categories.(3) But in the continuous case, the task can be complicated by the need to to locate a value as zero and decide on an appropriate metric. The mean and standard deviation can provide easy answers, but may not accurately represent the distribution of the reversals or result in a linearly unified interaction variable metric. Incorrectly locating the zero point will result in the occurrence of reversals which should not occur and/or the nonoccurrence of reversals that should. An inappropriate metric in one of the component variables will result in dual metrics within the interaction variable. Use of standardized codings in constructing reversing interactions is often somewhat more forgiving of errors, but where information is available on how component variables are best coded for interaction, it should be used to advantage.

The Constraining Interaction

The constraining interaction differs from the reversing interaction both in both construction and intent. The intent of the reversing interaction is to explore a set of effects which cannot be directly examined by its components and may be entirely uncorrelated with the components. The intent of the constraining interaction is to explore effects which cannot be completely examined by its components, but which are somewhat correlated to each of the components. The constraining interaction variable represents a subset of its components: the intersection of component values.

The construction of the constraining interaction entails coding one end of a range of values as zero. The occurrence of this zero constrains any value against which it is multiplied to a value of zero within the interaction. This has the effect of identifying those cases which are non-zero in all of the component variables from which the interaction is constructed.

The occurrence of zero and near-zero values within the continuous case of the reversing interaction gives standardized component values their forgiving qualities. Values near zero will constrain values against which they are multiplied to the area near zero. Larger numbers may reverse larger numbers from one extreme to the other, but small values will constrain values to the center of the distribution.

In the categorical case, the constraining interaction is built by dummy coding (Kerlinger and Pedhauser, 1973) the component variables using the values 0 and 1 (or -1). This produces, in the intersection, the equivalent of a simple or nested effect. Figure Three shows a constraining interaction taken from proposition six. Here source credibility is multiplied against inclusion of evidence. If proposition six is accurate, the resulting interaction should be positively related to persuasion.

Figure Three: The categorical constraining interaction of source credibility and inclusion of evidence. Source Credibility
High Low
0 1
Inclusion of Evidence Yes 1 0 1
No 0 0 0

There are four forms of categorical constraining interaction. 'And' and 'nor' interactions occur when all of the interacting component variables must equal particular values if an effect is to occur. 'And' occurs when all variables must equal a particular value. 'Nor' occurs when no variables obtain for the given value. 'Or' and 'nand' interactions occur when the occurrence of a value in any of a set of interacting variables can realize an effect. The interaction shown in figure three is 'and' if persuasion occurs when credibility = low and evidence = yes, but 'nand' if persuasion does not occur if credibility = high or evidence = no. Both are true within the interaction, but it is the 'and' relationship which is of interest. An 'or' relationship can be seen in the proposition six relationship between incongruity and evidence. An effect occurs in the presence of either, but nothing is added by the occurrence of both.

In the continuous case, the constraining interaction is constructed from components coded with values including and ranging upward from zero. The dominant feature of the continuous constraining interaction is a range of constraints from maximum constraint (at zero) to minimum constraint (at the maximum coded value). The probability distribution, with its range from 0 (full constraint) to 1 (no constraint) is a good example of the continuous constraining interaction variable. Probability variables are used to advantage by Fishbein and Ajzen (1975) and Wyer (1974).

An example of a continuous constraining interaction (Figure Four) is taken from proposition one. This interaction is constructed in the multiplication of source credibility and the inverse of the amount of time elapsed since he message. It implies that the effect of source credibility declines with time to the point where it has no systematic effect.

Figure Four: The continuous constraining interaction of source credibility and time. Source Credibility
0 1 2 3




1 0 1 2 3
.66 0 .66 1.33 2
.33 0 .33 .66 1
.00 0 0 0 0

The coding of the constraining variable should not be considered as restricted to positive numbers. As long as there is a zero point, component variables can be coded for constraint with either, but not both, positive and negative numbers. Indeed, it will later prove useful to code decision freedom (perception of compliance as being voluntary or involuntary) of proposition ten with a negative value. Such coding can be especially useful, moreover, when one is trying to recreate negative serial autocorrelation within a time series analysis.

Relating Constraining and Reversing Interactions

Although differing in structure and intent, the reversing and constraining interaction are related to one another. A two component reversing interaction can be reproduced by adding two constraining interactions. A three component reversing interaction can be reproduced by using four constraining interactions. Indeed, any N-component reversing interaction can be exactly duplicated by adding 2N/2 constraining interactions; where N is the number of variables

Constraining interactions are linearly reproduced using both component variables and interactions. A constraining variable constructed from two components is reconstructed by both components and their reversing interaction. A three component constraining interaction is duplicated from the three component variables and their four reversing interactions. Ultimate, any constraining interaction is reproduced with the N component variables from which it was constructed and their 2N - N - 1 reversing interactions.

The fact that a reversing interaction can be entirely reproduced by constraining interactions; that a constraining interaction can be entirely reproduced by component variables and reversing interactions; does not argue that either reversing or constraining interactions can be brushed aside as expendable. The exploration of all possible constraining interactions within a data set should tap all the relationships possible within that data set. The exploration of all the effects of all component variables and all possible reversing interactions should achieve the same end. But the testing of all possible interactions using either form is undesirable. The practice capitalizes heavily on chance. With five component variables, twenty-six reversing interactions are generated, at least one of which will be significant by chance at the .05 level.(4) A tremendous amount of power is lost, moreover, if the wrong set of interactions are tested.(5) Finally, a choice of the wrong form of interaction may result in a Type IV error (Marascuilo and Levin, 1970), the misinterpretation of the interactions meaning.

Both reversing and constraining interactions may prove predictive of a dependent variable, even when there are only two component variables.(6) Each form of interaction and the component variables attacks different characteristics which may be present within a data set. The most effective prediction may not be obtained unless both are considered.

The Logarithmic Interaction Variable

A third form of interaction is obtained by coding the component variables with non-zero positive values. Such coding should have no categorical case, as it implies data characteristics (notably continuity) which should not be applicable to categorical data and may distort any results obtained. The continuous case of such coding results, in interaction, in what might be called a logarithmic interaction variable. This form of interaction takes its name from the fact that the result of multiplying non-zero positive values can be duplicated by adding the logarithm of each component variable. This the logarithmic interaction actually does little that is not already accomplished by the component variables. Such transformations (Huck and Sutton, 1975) can be particularly useful when curvilinear relationships (say power functions) exist within the data, but the logarithmic interaction, although easily constructed, will rarely add to the data analysis.

Mixed Mode Interactions

The way in which a component variable is coded is essentially meaningless. Thus, beyond avoiding the appearance of continuity in categorical data, the coding of component variables for interaction should be viewed flexibly. I may be desirable to preserve the coding used in measurement for component variables, but the construction of interactions will require recoding those component variables, perhaps in several different ways. It may also be desirable to multiply component variables which have been coded in different ways in constructing interactions. One such interaction, taken from proposition ten, is shown in Figure Five. This interaction codes 'decision freedom' for constraint and 'source credibility' for reversal. The result might be called a constrained reversing interaction. If proposition ten is correct, it is positively related to persuasion.

Figure Five: The mixed mode (constrained reversing) interaction of source credibility and decision freedom (perception of compliance as being voluntary). Decision Freedom
High Low
-1 0
Source Credibility High 1 -1 0
Low -1 1 0

The constrained reversing interaction variable is a staple of expectancy-value theories. Such theories often assume that the importance of a given event to an individual is a function of the interaction of the value of the event and the probability of its occurrence. Steinfatt (1978) notes that although research with expectancy value theories, notably that of Fishbein and Ajzen (1975), has been inconsistent in the way component variables are coded for interaction, there is a test way to code components for the expectancy-value interaction. The expectancy variable should be coded as a continuous constraining component (perhaps as a probability). The value variable should be coded as a continuous reversing interaction. The result is a continuous version of the categorical constrained reversing interaction shown in Figure Five.

Modeling the Statistical Interaction Variable

The decision concerning what component variables should interact and how those interaction variables should be constructed rests with the researcher/data analyst. A variety of methods are available, including theory (as in the expectancy-value notion), previous research (the ten propositions outlined early in this paper), the testing of all possible interactions (which for all its faults, was probably largely responsible for those ten propositions), and personal intuition. Regardless of method, but ignoring all possible interactions if at all possible,(7) some decision should be made concerning what interaction variables will be tested.

These decisions can be aided by the explicit modeling of the interaction variables. Such modeling can be accomplished economically with a modified version of path modeling and analysis. Path analysis (see Cappella, 1976 for a review of the method) is not specifically designed to account for interaction terms, but if we make the legal gestalt switch from thinking of interactions as ANOVA cell patterns to thinking of them as distinct variables, introduce a set of reasoned restrictions on how interactions occur in the path model, and a convention for representing the interaction within the model, the technique of path modeling and analysis become as appropriate to the modeling and testing of interaction variables as they are to component variables.

The gestalt switch is probably the more difficult task. Experience with analysis of variance does not encourage viewing the interactions as variables. It presents the interaction as an arrangement of cells. The cell arrangements status as a discrete variable is not visible because we never handle it as a variable. Once this status does become visible, however, it becomes possible to name and/or model interaction variables.

The modeling of interaction variables can only be performed within a set of tight restrictions. These restrictions, which address issues of prediction and temporal ordering, assume that interaction variables, created in the multiplication of component variables, cannot be regarded as being causally related to their components, yet cannot be adequately predicted except with respect to those components. Given these assumptions, the following restrictions should be observed:

  1. An interaction variable should be temporally located at the same inclusion level(8) as the latest occurring component variable involved in constructing the interaction.
  2. Regardless of the inclusion level at which an interaction variable is entered into the analysis, it should be treated as exogenous(9) to all endogenous(10) variables at subsequent levels.
  3. Where the component and interaction variables present in a model are moderately to strongly correlated, and the correlated component remains in the model, the component variable should be covaried out of the interaction.

Locating the interaction variable at the inclusion level of its latest occurring component respects the existence of the interaction variable as a distinct variable that is determined contemporaneously with its components. Locating an interaction prior to any of its components would violate the temporal roots of the interaction's construction. Placement at an inclusion level which follows all the components would imply that the interaction came into being after its components. Although it may be inevitable, when components occur at different points in time, that some component variables occur before the interaction can occur, the practice of letting all component variables precede their interaction implies a causality that may not be justifiable. The interaction should, therefore, occur at the same point in time as the last component variable from which it is generated.

Treatment of interaction variables as exogenous involves the recognition that the only causes of an interaction variable are the causes of its component variables. The interaction is, in a sense, fully predicted in its creation. Thus any relationship between an interaction and temporally prior variables must be either spurious or due to shared causes which express themselves, in the interaction, through its parent main effects.(11)

The exogenous treatment of interaction variables is not without problems, however. Particularly serious are potential problems of correlated error terms. Two solutions exist for handling this problem. Fist , the entire inclusion level at which the interaction occurs can be treated as exogenous to all subsequent portions of the model. This solution essentially ignores the problem. The second solution controls the interaction variable for the effects of its components (covaries the effect of the components out of their interaction). This partialling out of effects eliminates the correlated error, but it may also distort the structure of the interaction in undesirable ways.

Given a set of restrictions on how interactions should be presented within a path model/analysis, a convention for presenting the interaction in the model is also necessary. The path model is generally presented with boxes (to represent variables), arrows, to represent the movement of effect from one variable to the next), and plus and minus signs (+/-) to represent the expected direction of effect). The additional convention necessary to incorporate the interaction into the path model is a multiplication sign (*). This symbol represents the multiplication of the component variable to form an interaction effect and signals that the accompanying arrow represents a multiplicative effect rather than a causal effect.

An additional useful convention is the notation, either on the model or in its variable key, of the coding uses. An example, taken from proposition three, demonstrates both of these conventions in Figure Six. It should explain itself.

Figure Six: A path model of the effect of source credibility and discrepancy of message on persuasion

A Model of the Effect of Source Credibility and Discrepancy of Message on Persuasion

Using the restrictions and conventions outlined above, it is possible to construct a model of the effect of source credibility on persuasion as outlined by Sternthal, Phillips and Dholakia (1979) and summarized in the ten propositions of this paper. This model is shown in Figure Seven. The model is an interpretation of the ten propositions outlined at the beginning of this paper. Other interpretations are undoubtedly possible. However, this model does have interesting characteristics, not he least of which is the dominance of interaction variables among the direct effects (9) on persuasion. Only one component variable in the model affects persuasion directly (locus of control). Every one of the fifteen other component variables expresses its effects on persuasion only through its interactions with other variables.

All of the variables in this model, except persuasion, can be assumed, despite the appearance of the model, to occur at the same inclusion level. Although sixteen component variables occur in the model, there are only eight direct effects on persuasion, indicating that there has been a considerable amount of data reduction over the course of the interactions. All of the direct effects should be positively related to persuasion if the model is correct. Seven of the direct effects are interactions. Of the seven interactions, four are constraining, two reversing, and one mixed mode. All of the variables are coded categorically except for time. Some are really more likely to be coded continuously in the course of real data analysis.

Figure 7: A Model of the Persuasive Effects of Source Credibility as Reviewed by Sternthal, Phillips, and Dholakia (1978)

The variables are coded flexibly. The intent has been to obtain meaningful interaction terms, not intuitively obvious codes.(3) Thus some variables code high as zero and low as one while others code high as one and low as zero. This may be confusing when one is reading the model, but leads to straightforward interpretations of the interactions which might not be possible otherwise.

The central interaction in the model does not directly affect persuasion by itself, but figures into the construction of six of the interactions that do. As this interaction is composed of source credibility, time, and message discrepancy, it would appear that all the interactions that directly affect persuasion are relatively complex. Indeed, none has less than four components. This interaction states propositions one and three and makes the rest of the model subject to those propositions. It should be noted that the results of this interaction are coded three different ways for use in subsequent multiplications.

The one interaction which does not contain the above central interaction is that derived from proposition five. In its construction, an 'and' interaction of "Unfavorable Side Presented First", "Compelling Refutation", and "Unfavorable Arguments Known" is first performed to establish the conditions under which two sided messages succeed. The results of this interaction are then recoded as an effect variable to construct a reversing interaction with the number of sides presented in the message.

Propositions six and ten supply the components of the next interaction. This interaction is concerned with the evidence circumstances under which speakers with low credibility can be effective. The interaction begins with a 'nor' interaction of "position supported by evidence" and "position incongruous with speaker". The coding of the resulting interaction is then reversed (Not) in its multiplication against the central interaction of source credibility, discrepancy of message, and time. Finally, the and interaction of decision freedom and explicit request complete the interaction.

The explicit request for compliance of proposition ten also interacts with the high source credibility coding of the central interaction to produce a variable that further tests the proposition. Multiplication of this interaction against threat provides an additional variable for testing proposition four.

A fourth constraining interaction tests propositions seven and eight. This interaction is constructed by first obtaining the "or" interaction of "Locus of Control" and "Authoritarianism" and then recoding it for an "and" interaction with the central interaction with source credibility, discrepancy of message, and time. It states that an auditors high authoritarianism or external locus of control will increase the effectiveness of a highly credible speaker on that auditor.

The model is completed by two reversing interactions, one pairing the "audience disposition to advocacy" with the central interaction with source credibility, discrepancy of message, and time (proposition nine) and another testing proposition two's hypothesis that credible speakers are best introduced at the beginning of a speech while non-credible speakers are best introduced at the end of a speech.

No part of the model is tested in its present form to the best of the author's knowledge. It is inevitable that it has left out causal relationships among the variables, overcomplicated some relationships, and oversimplified others. Yet, given the ten propositions presented at the onset of this paper, the model is a reasonable one. Further research, including reanalysis of existing data, the careful re-review of the existing literature, and the generation of new experimental tests specifically designed to this model can do a lot to clarify the true nature of source credibility effects on persuasion. The model should, therefore, be considered tentative and highly malleable.


Although the model of source credibility effects generated within this paper has value in and of itself for explaining the nature of source credibility effects, its most important role in this paper is to demonstrate the importance of dealing with interaction effects both in the analysis of research data and in the construction of theoretical models. This model, as it happens, was taken from attitude research, but it could equally well have come from the study of human interaction, mass media, small groups, intercultural communication, nonverbal communication or any one of dozens of areas of study. Statistical interactions happen in the real world in both the constraining and reversing forms. If we don't deal with either as we proceed to complex research and analysis, we'll be letting a deeper understanding of our world slip past. And if we don't deal with both, we may catch that world only to misinterpret it.


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