Scenario: 3 treatments (Solutions 1, 2 and 3) with 4 levels each (Red, green, orange and blue). This creates 12 Petri dishes, each with a different treatment. Numerator degrees of freedom (3-1)*(4-1) = 6. In each dish we are measuring how much dye is absorbed in wooden pellets. There are 50 small pellets in each Petri dish. Denominator degrees of freedom 50-1 = 49.

As it is, we may say we have numerator df = 6, denominator df = 49. Sample size n = 50. Total sample size (50 x 12) N = 600.

But if we were calculating for sample size, we may give significance 0.05, power 0.8, numerator df 6, denominator degrees of freedom 49. (and effect size if needed).

We want to replicate each combination 4 times. In detail similar to above, how would you treat the replicated plates in the numerator degrees of freedom?

Cheers G