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
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To determine which of the options is a possible statistically significant outcome from a 2x2 factorial design, we need to understand the concept of main effects and interactions in factorial designs.
In a 2x2 factorial design, we have two independent variables, each with two levels. Let's call the independent variables Factor A (with levels A1 and A2) and Factor B (with levels B1 and B2).
Main effects refer to the overall influence or impact of each factor on the dependent variable. An interaction occurs when the effect of one factor on the dependent variable differs depending on the level of the other factor.
Now, let's analyze each option:
A. The other three choices are all possible outcomes.
This option states that none of the other options are possible. However, we don't have enough information to determine if this is correct without analyzing the remaining options.
B. Two main effects and an interaction.
This option suggests that both factors have individual main effects on the dependent variable, and there is also an interaction between the two factors. This is a possible outcome in a 2x2 factorial design.
C. No main effect for either factor but an interaction.
This option states that there are no individual main effects for either factor, but an interaction exists. This is also a possible outcome in a 2x2 factorial design.
D. Two main effects and no interaction.
This option suggests that both factors have individual main effects on the dependent variable, but there is no interaction between the two factors. This is another possible outcome in a 2x2 factorial design.
Therefore, options B, C, and D are all possible statistically significant outcomes from a 2x2 factorial design.
In conclusion, the correct answer is A. The other three choices are all possible outcomes.