Using a repeated measures study design, I plan on carrying out a study to test the effects of 3 different factors on certain variables of interest. The factors can adopt 3, 2 and 2 characteristic values, making for a total of 12 experimental conditions. Since I cannot expect our participants to present on 12 occasions, I was wondering whether it was possible to randomly allocate each subject to only a certain number of all possible experimental conditions (e.g., 4), while controlling for known biasing factors (e.g., sex and age).
Ultimately, I was hoping to have 10 subjects tested under each experimental condition, yet still make do with a total of 30 (120/4) subjects. Any advice on whether this is feasible, how randomization to experimental conditions would have to be performed and where I could read up on the topic would be much appreciated.
Thanks, Robert
Dear Robert,
It is certainly possible to proceed this way. The general topic is "fractional factorial designs"; such designs are often built out of combinations of latin squares or graeco-latin squares. What is the price of this design? The worst issue is that you must assume that there are no interactions between the experimental factors or between the biasing factors and experimental factors. Included in this is that most research in the social sciences does not have adequate power. So think carefully what you might accomplish with 10 people per cell!
Building a randomization table is pretty easy. A simple algorithm is to build a table with the full representation you are planning (all 12 conditions) then a random vector. Sort on the random vector and you have random assignment.
Better systems use adaptive assignment to conditions - this will help you best distribute people to "control" the biasing factors.
Good luck.
Dear Bruce,
Many thanks for your most helpful reply. I am aware of statistical power being a big issue here and think that I might have to restrict myself to testing fewer experimental conditions (although we expect between-condition differences to be fairly large). That being said, I am still curious how the adaptive assignment to conditions you mentioned would work, so I'll try to read up on the topic.
Thanks again, Robert
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