True, False, Uncertain with Explanation(a) Including an interacti.pdf
- 1. True, False, Uncertain with Explanation: (a) Including an interaction term between two independent variables, X1 and X2, allows for the measurement of the effect of a unit increase in X1 and X2, above and beyond the sum of the individual effects of a unit increase in the two variables alone. Solution When an interaction is present, the lines in a graph of the means will not be parallel. Another way of describing the interaction is to say that the effects of one factor are not the same at all levels of the other factor.Also we woll say that “the simple effects are different,” because a simple effect looks at the effects of one factor at each level of the other factor. An interaction effect is a change in the simple main effect of one variable over levels of the second. An A X B or A BY B interaction is a change in the simple main effect of B over levels of A or the change in the simple main effect of A over levels of B.In either case the cell means cannot be modeled simply by knowing the size of the main effects. An additional set of parameters must be used to explain the differences between the cell means. These parameters are collectively called an interaction. If interaction is significant, determine whether interactions are important. If not, can examine main effects If interaction present & important, determine whether interaction is simple or complex. . For simple interactions, can still talk about the main effects of A at each level of B For complex interaction, must simply consider all pairs of levels as separate treatments. If interaction effects are very small compared to main effects or only apparent in a small number of treatments, then they are probably unimportant. We can proceed by keeping interaction in the model, but using marginal means for each significant main effect individually The interaction effect is so large and/or pervasive that main effects cannot be interpreted on their own. This is TRUE statement.