Question

Suppose you have 4 factors to investigate. You have resource to do 2 replicates of a 2^4 design. But you can only conduct 8 runs every day. How would you set up the treatments for each day? What will be the degree of freedom for MSE in your ANOVA table?

Answer 1

 

Ans) We have 4 factors to investigate. We have resources to do 2 replicates of a 2 4 design.

       We can only conduct 8 runs every day.

       Replicates :- Not the same as repeated measurement.Repeated measurements is when you take multiple measurements on the sameunit.

Replication is when you repeat your design a 2nd, 3rd, 4th, etc. time.

For eg.Suppose,you have a 2^2design (2 factors, 4 runs) and want 3 replicates. Your experiment will have 3*2^2= 12 runs.

The 2^K designs are a special category of the factorial experiments where all the factors are at two levels. The fact that these designs contain factors at only two levels and are orthogonal greatly simplifies their analysis even when the number of factors is large. The use of 2^K designs in investigating a large number of factors calls for a revision of the notation used previously for the ANOVA models. The case for revised notation is made stronger by the fact that the ANOVA and multiple linear regression models are identical for 2^K designs because all factors are only at two levels. Therefore, the notation of the regression models is applied to the ANOVA models for these designs.

So, in the same way, 4 Factors , 8 runs & 2 Replicates means 4*3*2*1 = 24 runs.