What is the criteria for calculating the exact sample size for experimental and control group in a 2x2 factorial design?
There are four treatments in my experimental design and a fifth control group for their comparison. Please guide me, how many participants I must need for this experimental design for each group (e.g., four experimental groups and a treatment group) in a social science study.
Thank you
This depends upon the scale of measurement you are using for the dependent variable. Chi square is for small frequencies (>5) in each cell, so it could be used with a small sample slightly over 20 with a nominal scale of measure.
If your dependent variable is interval/ratio, I would recommend at least 30 in each cell.
If your data is normally distributed, you can even have a single replicate .
See for example many methods from
ANALYZING UNREPLICATED FACTORIAL EXPERIMENTS:
A REVIEW WITH SOME NEW PROPOSALS
M. Hamada and N. Balakrishnan, Statistica Sinica 8(1998), 1-41; and several others citing this article. If you have more resources, you can use as many as you can but equal number to all the four to maintain the orthogonality of the design.
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