which of the following is a possible statistically significant outcome from a 2x2 factorial design. A. The other three choices are all possible outcomes . B. Two main effects and an interaction . C. no main effect for either factor but an interaction D. two main effects and no interaction
To determine the possible statistically significant outcomes from a 2x2 factorial design, we should first understand the meaning of main effects and interactions.
In a factorial design, there are two or more independent variables, or factors, each with multiple levels. The main effects represent the effect of each factor independent of the other factor(s). An interaction occurs when the effect of one factor depends on the level of the other factor(s).
Now, let's analyze the given options:
A. "The other three choices are all possible outcomes."
This option is incorrect because it suggests that all other options (B, C, and D) are possible. In reality, not all of them may be statistically significant outcomes.
B. "Two main effects and an interaction."
This option is a possible outcome. It means that both factors individually have a significant effect, and there is also a significant interaction between the factors.
C. "No main effect for either factor but an interaction."
This option is also a possible outcome. It means that neither factor has a main effect, but there is a significant interaction between the factors.
D. "Two main effects and no interaction."
This option is a possible outcome. It means that both factors have individual main effects, but there is no significant interaction between the factors.
Based on these explanations, the correct answer is either option B (Two main effects and an interaction) or option C (No main effect for either factor but an interaction), as both of them represent possible statistically significant outcomes in a 2x2 factorial design.