I am applying an online experiment using a 3*2*2 between-subjects full factorial design (1 independent variable of 3 levels and the other 2 are moderating variables with 2 levels, each), yielding 12 conditions/groups in total and I need to know the minimum number of participants in each group in order to test causal effects with 95% confidence. If you could provide me with academic references for the sample requirements of experimental conditions, I would greatly appreciate it.

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