The correct answer is: a. There is one main effect and an interaction in the 2x2 design, as the observed changes in cell means indicate an interaction between the independent variables. Option a is the correct choice.
In a 2x2 design, where two independent variables each have two levels, the results are typically presented in a matrix. The given results, "20 40" and "40 80," likely represent the mean values of the dependent variable in each of the four conditions.
To determine the presence of main effects and interactions, we can compare the marginal means (means of each level of one independent variable across the levels of the other) and the cell means (means of each specific condition).
In this case, the cell means show a clear pattern of change, suggesting an interaction between the two independent variables. Specifically, the change from 20 to 40 in one condition is different from the change from 40 to 80 in the other condition.
Therefore, the correct answer is a. there is one main effect and an interaction.
Que. In a 2x2 design, the following results occur In a 2x2 design, the following results occur:
20 40
40 80
Which of the following is true?
a. there is one main effect and an interaction
b. there is an interaction but no main effects
c. there are two main effects but no interaction
d. there are two main effects and an interaction