You are designing a 2×3 factorial design and need 20 participants in each of 6 conditions.
1 How many participants in total would be needed for a 2×3 independent groups (between-subjects) design?
2 How many participants in total would be needed for a 2×3 repeated-measure groups (within-subjects) design?
3 How many participants in total would be needed for a 2×3 mixed factorial design?
The correct answer and explanation is :
1. Independent Groups (Between-Subjects) Design:
In an independent groups design, each participant is assigned to only one of the six conditions. Since you need 20 participants in each condition, and there are 6 conditions in total (2 levels of factor 1 × 3 levels of factor 2), the total number of participants can be calculated as:
[
\text{Total participants} = 20 \times 6 = 120
]
So, 120 participants would be needed for the 2×3 independent groups design.
2. Repeated-Measures (Within-Subjects) Design:
In a repeated-measures design, each participant is exposed to all conditions. This means that you don’t need separate participants for each condition. Since you need 20 participants for each of the 6 conditions, the total number of participants required will still be 20 (because each participant will experience every condition).
Thus, the total number of participants needed in a repeated-measures design is:
[
\text{Total participants} = 20
]
So, 20 participants would be needed for the 2×3 repeated-measures design.
3. Mixed Factorial Design:
A mixed factorial design involves a combination of both independent and repeated-measures designs. In this case, one factor is manipulated between-subjects, and the other factor is manipulated within-subjects.
For this design:
- The between-subjects factor requires 20 participants in each of the 2 levels (this means 20 participants for each level of the between-subjects factor).
- The within-subjects factor will involve all 20 participants experiencing the 3 conditions of the within-subjects factor.
Therefore, for the between-subjects factor (2 levels), the number of participants is:
[
\text{Participants for between-subjects factor} = 20 \times 2 = 40
]
Since the within-subjects factor involves the same 20 participants, no additional participants are needed for that factor.
Thus, for the mixed factorial design, the total number of participants required is:
[
\text{Total participants} = 40
]
So, 40 participants would be needed for the 2×3 mixed factorial design.
Explanation:
- Independent Groups Design: Each condition requires a unique set of participants, meaning you need as many participants as the total number of conditions.
- Repeated-Measures Design: Each participant is exposed to all conditions, so only one set of participants is required to experience all conditions.
- Mixed Factorial Design: The total number of participants needed is a combination of the between-subjects and within-subjects requirements, where participants for the within-subjects factor are the same across conditions, and only the between-subjects factor requires additional participants.
Summary:
- Independent Groups Design: 120 participants
- Repeated-Measures Design: 20 participants
- Mixed Factorial Design: 40 participants