What combination of effects can a two-way factorial research design exhibit?

A two-way factorial research design allows researchers to examine the effects of two independent variables on a dependent variable simultaneously. One of the key characteristics of this type of design is that it can reveal different types of effects.

The primary reason the correct choice identifies that the design can yield both main effects and interaction effects is because main effects assess the impact of each independent variable on the dependent variable while ignoring the other variable. For instance, if one variable is treatment type and another is gender, a main effect of treatment type would indicate that the type of treatment has a separate, measurable impact regardless of gender.

Interaction effects, on the other hand, occur when the effect of one independent variable on the dependent variable differs depending on the level of the other independent variable. Continuing with the earlier example, an interaction effect would suggest that the effectiveness of a treatment might differ based on the gender of the participant, indicating that the two independent variables work together in influencing the dependent variable.

Given these definitions, it is clearly possible for a two-way factorial design to exhibit no notable effects if the variables do not significantly influence the outcome. Therefore, all proposed scenarios – the presence of only main effects, the presence of both main and interaction effects, or the absence of any effects at all –