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Level VI

## Balanced Block Designs Using Covariate Factors in Custom Design

A colleage recently asked me if JMP could create a balanced block design for the following situation:

There is one treatment effect for the study, and it has 4 levels (T1, T2, T3, T4).  The treatment factor is categorical.

There are 3 blocking factors:

• Block A has 4 levels (A1, A2, A3, A4)
• Block B has 2 levels (B1, B2)
• Block C has 2 levels (C1, C2)

Only two treatments can be used in each of the 16 blocks, so 32 experimental units are going to be used.  Some sort of balanced blocking is needed here.

The approach is to create a full factorial design in the treatment and blocking factors, and then to search for the optimal design with 32 runs that is a subset of the full factorial design.  I show the steps below.  Take a look at it and let me know what you think about this approach.   What I'm not sure about is how well this approach would work in general.  Have I overcomplicated this, or is there an easier way to do this?

Step 1:

Create the FF design:  DOE>Classical>Full Factorial Design.  Here is the setup with the factors and levels:

Click Continue, Make Table to create the FF design table.

Step 2:  With the full factorial DOE table in focus as the current data table, choose DOE > Custom Design from the menu.  Add the DOE factors (treatments and blocks) as covariate factors.

Use the default main effects model, and enter 32 for the number of runs.  Then click Make Design.

The resulting design is summarized here:

Tabulating the treatment pairs shows that 4 or the 6 treatments occur in two block each, and the other 2 treatment combinations occur 3 time each.

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