Statistical Dependence

Statistical analyses make assumptions about the distribution and association between resid­ual (error) terms. For example, significance test­ing of parameter estimates within ordinary least squares linear regression or ANOVA assumes that population errors are homoscedastic (i.e., have equal variance across the cells of the ANOVA or above and below the regression line at any point on the X-axis), nonautocorrelated (i.e., the order of the errors across time or space has no pattern or effect), and normal (i.e., have a normal distribution within each cell of the ANOVA or above and below the regression line at any point on the X-axis).

Many conflict situations are posed as two­sided situations: employer-employee, buyer­seller, hostage taker and hostage, aggressor nation and target nation, and violent domes­tic partner and violated domestic partner. Such dyadic interactions involve interdepen­dence between the parties. These samples have dependent (in the statistical sense) units, and the data analysis needs to account for this dependence. SEM is one way that statisti­cal dependence can be represented (see, e.g., Duncan, 1969; Duncan, Haller, & Portes, 1968).

Imagine pairs of variables such as hus­band’s level of anger and wife’s level of anger, and husband’s level of verbal aggression and wife’s level of verbal aggression. A model that has parallel sets of variables for each interac­tant can be created that takes into account the dependence among the variables due to the dependence among the interactants; if the wife’s verbal aggression rises because of the rise in her husband’s verbal aggression, and vice versa, this situation can be represented by including the appropriate variables and causal effects.

have a sample size that is 10 to 20 times the number of variables in the model (Mitchell, 1993; see Bentler & Chou, 1987, for other guidelines for setting SEM sample size). In other words, the sample size (i.e., the number of participants, not the number of dyads) for a model that includes interdependent par­ticipants will need to be greater than a sample that includes independent actors.

Kenny and Kashy (1991; see also Kashy & Kenny, 2000) described two types of interde­pendence that may exist in dyadic data sets: within-dyad interdependence and between- dyad interdependence. Within-dyad interde­pendence reflects systematic changes over time within a single dyad, such as the changes over time in uncertainty reduction within a dating couple. In this case, the errors in the equations will correlate over time if the causes of the time-based interdependence are not included in the model. B etween-dyad interdependence results from cross-sectional dependence in dyads at a single point in time due to an omit­ted factor that effects more than one depen­dent variable. In this case, we should expect that the errors in the equations will correlate across variables if the causes of the cross­sectional interdependence are omitted. Kenny, Kashy, and Cook’s (2006) book on this subject is an excellent source that shows the general strategies that may be used to analyze dyadic dependence in data.

If we have data with interdependence, analyses need to test for and take into account the interdependence. The two basic strategies, regardless of the specific analytical method employed, are to hypothesize the absence of these effects and examine how well the model fits under this constraint or to hypothesize the presence of these effects and to test the significance of the statistics that represent the interdependence (see, e.g., Hanushek & Jackson, 1977).

In studies of groups larger than dyads that use multilevel sampling, the same issues appear. For example, in studies in which families are sampled, and in which each fam­ily unit includes several family members, there is interdependence among the sampled units. Analytical methods that deal with multiple levels (with or without multiple time points within the data set) include hierarchical linear models (HLM); repeated-measures, multivari­ate, and other nested models in the ANOVA framework; and multiple group (or multi­sample) analysis in SEM. Of the three meth­ods mentioned above, HLM is probably used least by scholars studying communication and conflict, but there are several exemplary studies: Julien, Chartrand, Simard, Bouthillier, and Begin’s (2003) study of positive and nega­tive communication during conflict in hetero­sexual, gay, and lesbian couples (with partners nested within couples); Karney and Bradbury’s (1997) analysis of trajectories of marital sat­isfaction; Rhoades, Arnold, and Jay’s (2001) investigation of affective traits and mood on organizational conflict over time; Sanford’s (2003) investigation of “topic difficulty and communication behavior across multiple problem-solving conversations” among mar­ried couples (p. 99); and Smith and Zautra’s (2001) piece on the effect of spousal conflict, interpersonal sensitivity, and neuroticism on affect in a sample of older women.

Conflict communication research typically involves interdependent participants, and therefore scholars studying in this area need to be aware of the statistical problems—and, once understood, the statistical opportunities—that such data provide. Using a sophisticated ana­lytic method such as SEM or HLM encourages the researcher to think about the ways that units relate and to represent this interdepen­dence in the statistical models employed.