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Answer :
1) The factorial design with army rankings Private, Commander, General is denoted as a 3x3 design.
2) A two by four factorial design has four potential main effects.
3) The number of possible potential interaction effects differs between a 2x3 within groups design and a 2x3 factorial design.
In factorial design each independent variable is varied at different levels to examine their effects on the dependent variable. In this case, the independent variables are army rankings (Private, Commander, General).
To denote the factorial design, we need to determine the number of levels for each independent variable. Since there are three army rankings, the factorial design is denoted as a 3x3 design. Therefore, the answer to the first question is B) 3x3.
In a two by four factorial design, there are two independent variables with two and four levels, respectively. To calculate the number of potential main effects, we add the number of levels for each independent variable. So, in this case, there would be a total of six potential main effects. Therefore, the answer to the second question is D) 4.
A 2x3 within groups design and a 2x3 factorial design differ in terms of the number of possible potential interaction effects. The within groups design does not allow for interaction effects, as each participant experiences all conditions. However, the factorial design does allow for interaction effects, as different participants are assigned to different conditions. Therefore, the answer to the third question is C) Possible potential interaction effects.
Learn more about factorial design and potential main effects from the given link
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