I am currently in the design phase for an experiment on different packaging attributes and their effects on an actual purchasing choice. In this context, I am asking myself a possibly trivial question: Is the follwing design a true within-design or not?

Each participant chooses one out of 16 products (presented at the same time), which represent the combinations of 4 independent variables (IVs) with two levels each:

1. size: large or small
2. shape: bottle or box
3. material: recycled or not
4. brand: sustainable or not

In one sense, it is a 2x2x2x2 factorial design with the resulting 16 conditions/combinations.

I have understood that a within-design means, that each participant is tested under all conditions. Usually, this is done sequentially - in my research, I would present each participant with a choice between large or small, and then a choice between bottle or box, and then... etc. However, what if I present the participants with a choice out of all the 16 combinations at once? (as described above) Is this still a true within-design?

And what does it tell me regarding sample size and analysis tools? Do I need

• only 30 participants since each makes only one choice (which tells me a combination of the 4 IV they prefer)
• or do I need 30x4=120 participants (since I have four IVs)
• or do I actually need 30x16=480 participants (because of the 16 conditions/combinations)?

In this sense, I am also trying to figure out the sample size needed dependent on how many packaging attributes are included as independent variables and whether the experiment is set-up as within or between-subject design...

I have browsed different literature on experimental design and power analysis, but haven't come to a clear conclusion yet. Hence, I would be very grateful for your perspective on this.

Thanks and kind regards! Stef

I am currently in the design phase for an experiment on different packaging attributes and their effects on an actual purchasing choice. In this context, I am asking myself a possibly trivial question: Is the follwing design a true within-design or not?

Each participant chooses one out of 16 products (presented at the same time), which represent the combinations of 4 independent variables (IVs) with two levels each:

1. size: large or small
2. shape: bottle or box
3. material: recycled or not
4. brand: sustainable or not

In one sense, it is a 2x2x2x2 factorial design with the resulting 16 conditions/combinations.

I have understood that a within-design means, that each participant is tested under all conditions. Usually, this is done sequentially - in my research, I would present each participant with a choice between large or small, and then a choice between bottle or box, and then... etc. However, what if I present the participants with a choice out of all the 16 combinations at once? (as described above) 
Is this still a true within-design?

And what does it tell me regarding sample size and analysis tools? 
Do I need

• only 30 participants since each makes only one choice (which tells me a combination of the 4 IV they prefer)
• or do I need 30x4=120 participants (since I have four IVs)
• or do I actually need 30x16=480 participants (because of the 16 conditions/combinations)?

In this sense, I am also trying to figure out the sample size needed dependent on how many packaging attributes are included as independent variables and whether the experiment is set-up as within or between-subject design.

I have browsed literature on experimental design and power analysis, but haven't come to a clear conclusion yet. Hence, I would be very grateful for some perspective on this.