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Interaction Effect

An interaction effect is the simultaneous effect of two or more independent variables on at least one dependent variable in which their joint effect is significantly greater (or significantly less) than the sum of the parts. The presence of interaction effects in any kind of survey research is important because it tells researchers how two or more independent variables work together to impact the dependent variable. Including an interaction term effect in an analytic model provides the researcher with a better representation and understanding of the relationship between the dependent and independent variables. Further, it helps explain more of the variability in the dependent variable. An omitted interaction effect from a model where a nonnegligible interaction does in fact exist may result in a misrepresentation of the relationship between the independents and dependent variables. It could also lead to a bias in estimating model parameters.

As a goal of research, examination of the interaction between independent variables contributes substantially to the generalization of the results. Often a second independent variable is included in a research design, not because an interaction is expected, but because the absence of interaction provides an empirical basis for generalizing the effect of one independent variable to all levels of the second independent variable.

A two-way interaction represents a simultaneous effect of two independent variables on the dependent variable. It signifies the change in the effect of one of the two independent variables on the dependent variable across all the levels of the second independent variable. Higher-order interactions represent a simultaneous effect of more than two independent variables on the dependent variable. Interaction effects may occur between two or more categorical independent variables as in factorial analysis of variance designs. It may also occur between two or more continuous independent variables or between a combination of continuous and categorical independent variables as in multiple regression analysis. To illustrate these effects, the following sections start with the interpretation of an interaction effect between two categorical independent variables as in ANOVA, followed by the interpretation of an interaction effect between one categorical independent variable and one continuous independent variable, and finally the interpretation of an interaction effect between two continuous independent variables. Interpretation of three or more higher-order interaction terms effects follow the same logic of interpreting the two-way interaction effect.

Interaction Between Two Categorical Independent Variables

Consider a survey research study investigating the effectiveness of incentives and postal mailers on response rates in a mail survey. Incentive amount is the first categorical independent variable (A) with three groups; A1 is a control group who receives no incentive, A2 is a $1 incentive group, and A3 is a $5 incentive group. The second categorical independent variable (B) is type of mailer with Bi for First-Class Mail and B2 for Federal Express. Response rates to the mail survey in percentages (Y) are the dependent variable for the study. In this typical (3 x 2) ANOVA there is (a) a possible main effect for incentive amount on response rates, (b) mailer type as a possible main effect on response rates, plus (c) a possible interaction effect between incentive amount and mailer type on response rates. A significant interaction effect suggests that the differences in the effects of incentive amount on response rates depend on mailer type (and vice versa). That is, in this example, the average differences in incentive amount effect on response rates are different in magnitude and possibly in direction for First Class versus what they are for Federal Express. Conversely, one can say that the average difference (in magnitude and direction) for response rates between a First-Class envelope and a Federal Express envelope depends on the incentive amount a household receives. An insignificant (negligible) interaction effect between incentive amount and mailer type on response rates suggests that the differences in response rates across incentive amounts are essentially the same for First Class and Federal Express. One can also interpret an insignificant interaction effect between mailer type and incentive amounts by recognizing that the difference between First Class and Federal Express is basically the same (in magnitude and direction) across the three incentive amounts.

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