When should we include the "Replicate" in an ANOVA table for Factorial Design?

by WaveX   Last Updated November 08, 2018 23:19 PM

When I have been learning how to do Factorial Designs ($2^k$ mainly) the ANOVA table would usually include the main effects, all the interaction effects if necessary, and the error. However, on one of my exams it not only included the factors and their interactions, and the error, but it also included "replication".

First off, I was never taught that we could have replication as one of our sources of variation. So I don't know how that could effect the Sum of Squares of Error. I'm just guessing here, but I guess the degrees of freedom should be $n-1$ if we have $n$ replicates, but I am only guessing that because everything else appears to be of the form $\theta - 1$ for some parameter $\theta$.

Up to this point I have never included replication in my ANOVA table. Should replication be included and if it is included how does it affect the Sums of Squares?

The exact example we had was that we had a $3$ factor experiment with two replicates and it gave us part of the ANOVA table, and we had to fill in the rest. If it didn't include Replication, I would know exactly how to fill in the rest of the table, but I don't know exactly why Replication would need to be checked whether or not it is significant or not.

Any help on my confusion would be greatly appreciated!

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