Let's analyze the change from a 2 x 3 independent-groups factorial design to a 2 x 3 within-subjects factorial design in detail:
1. Number of Cells:
The number of cells (conditions) in our design is given by the product of the levels of two factors. Since we have a 2 x 3 design, we have [tex]\( 2 \times 3 = 6 \)[/tex] cells in both independent-groups and within-subjects designs. This does not change based on the type of design.
2. Number of Interactions:
In a factorial design, the number of interactions depends on how the factors interact with each other. Since we still have two factors, we will examine the interaction between these two factors, resulting in one interaction effect for both designs. This does not change.
3. Number of Main Effects:
Each factor has a main effect that needs to be examined. Since we have two factors, we will have two main effects to examine. This remains consistent regardless of whether it's an independent-groups or within-subjects design.
4. Number of Participants Needed:
This is the variable most affected by the type of design. In an independent-groups design, each participant experiences just one of the conditions, requiring a larger pool of participants to cover all 6 cells. In a within-subjects design, each participant is exposed to all conditions, meaning fewer participants are needed overall to gather the same amount of data.
To summarize:
- The number of cells does not change.
- The number of interactions that need to be examined does not change.
- The number of main effects that need to be examined does not change.
- The number of participants needed will change (generally decrease) when switching from an independent-groups design to a within-subjects design.
