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I have been trying to understand one question from CQE Primer, and the solution is given, but I can not understand. If simple explanation is given, greatly appreciated.
Question:An experiment has 3 factors with 2 levels and 1 factor with 3 levels. What is the minimum number of trials necessary if all interactions are ignored?
Solution:
When experimenting, 1 degree of freedom is required to compute the overall mean, and n-1 degrees of freedom are required for each factor, where n is the number of levels for the factor. The degrees of freedom required for interactions are the product of the interactions for the factors involved in the interactions. This experiment has 1 degree of freedom for the overall mean, 3 factors with 2 levels, which require 1 degree of freedom each, and 1 factor with 3 levels, which requires 2 degrees of freedom. Thus, 6 degrees of freedom are required, so a minimum of 6 trials are required.
Question:An experiment has 3 factors with 2 levels and 1 factor with 3 levels. What is the minimum number of trials necessary if all interactions are ignored?
Solution:
When experimenting, 1 degree of freedom is required to compute the overall mean, and n-1 degrees of freedom are required for each factor, where n is the number of levels for the factor. The degrees of freedom required for interactions are the product of the interactions for the factors involved in the interactions. This experiment has 1 degree of freedom for the overall mean, 3 factors with 2 levels, which require 1 degree of freedom each, and 1 factor with 3 levels, which requires 2 degrees of freedom. Thus, 6 degrees of freedom are required, so a minimum of 6 trials are required.
