Degrees of Freedom

#1
I hope you are all well. This question is about degrees of freedom for G*power ANOVA A priori and extends to calculating degrees of freedom for replicates of replicates (Replicated dishes).

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
 
#3
As I see it, your experimental unit it the petri dish and value is the average of the 50 pellets. You don't need to worry about the df of the pellets.
Thank you katxt yes good point, either the pellets (if individually measured) or Petri dishes could be the experimental unit, that is the denominator degrees of freedom. In the first case how many degrees of freedom would you give the numerator?
 
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#4
Perhaps we are talking at cross purposes, because I'm not familiar with G*power ANOVA. If this is any help, as I see it the final anova table would have solutions 2df, colors 3df, solutionXcolour 6df, these are the numerators. Dishes error36df. This is the denominator for the f tests for the main effects. The df for the pellets would not be used for testing the main effects.
 
#5
I see that, it's interesting isn't it. Now imagine the variation between the individual pellets is wanted, parametric pellet SD, not n=4 plate SD, but we'll perhaps model plates as a random effect
 
#6
You can include the pellets and include the extra df to see if the dish to dish variation is greater than can be explained by pellet to pellet variation but because pellets are nested in dishes, the main effects will still be calculated from the dishes.