I'm trying to learn how to operate JMP's dialog boxes for sample size for use in experimental design. I'd like to understand how to determine the number of replicates necessary in a factorial experiment. I'd like to know how many times to run each treatment combination.
Assume there is no measurement error, no need for blocking or centerpoints, the response variable is continuous and everything is exactly as needed to meet all the assumptions for classic calculation of sample size (random stationary homoskedastic normally distributed errors, etc.).
Suppose an experiment will have two factors at two levels, full factorial. Thus, there are four treatment combinations. I want to estimate the two main effects and the one interaction. What are the steps to determine the number of replications of each treatment combination?
The same question applies for fractional factorial. If I have 15 factors each at two levels and I want to run a fractional factorial of 16 treatment combinations, how do I determine the number of replicates of each treatment?
For the sake of sample data, let alpha = 0.05, beta = 0.05, sigma = 1, delta = 1.
I've used "Two Sample Means" dialog. There the static text says "Sample size is the total sample size; per group would be n/2". If I use this calculator for factorial design, what's the number of replicates per treatment combination for full or fractional factorial? Do I just divide the total sample size by the number of treatment combinations?
Now suppose I want a centerpoint in the 2^2 experiment. That's five treatment combinations. Assume I'll replicate all five treatments. To design an experiment to test the significance of the centerpoint effect, I'll assume that effect is equal to delta. How do I use the JMP dialogs to get the number of replicates per treatment? Do I divide the "Two Sample Means" sample size by five?
If I want replication only at the centerpoint and no replication of the corner points, I'll assume the standard deviation that is revealed at the centerpoint is constant throughout the inference space. The goal is still to estimate the significance of the main effects, the interaction and the centerpoint. Assuming the same delta, how do I use the dialogs to get the number of replicates of the centerpoint combination? Do I divide the "Two Sample Means" sample size by one?
I'm aware of the custom design platform and its power analysis and know how to operate it. I would like to use DOE > Design Diagnostics > Sample Size and Power. After all, those calculators are in the "DOE" menu, I'm trying to figure out how to use them for DoE.
