Blocking
In this example we assumed that a single experimenter performed all of the experimental runs. It is more likely that this work would be done in a team of people, each of whom might execute a share of the work. Suppose this experiment were being conducted by a four-member team, and we want to control for the possibility that different individuals could introduce an unintended factor into the mix.
We do this by blocking the experimental runs. A block is a group of runs that we expect to be relatively homogenous, but possibly different from other blocks. When we block, we eventually compare the results of each experimental condition within each block. In this case, it makes sense to block by person, enabling each experimenter to run several different formulations. We will randomly assign the runs to each experimenter such that each team member runs four different formulations.
Select DOE → Custom Design. This dialog box works much like the Full Factorial dialog box that we worked with earlier. As before, we'll specify that our response variable is Compressive Strength.
In the Factors panel, type 3 into the Add N Factors box and click Add Factor (see Figure 18.7); using the Continuous option add the three factors (coarse agg, water, and slag) for our experiment as you did earlier, again using the same factor levels.
Figure 18.7. Add Factor Options
Once you've entered the three factors, click Add Factor again and select Blocking → Other and specify 10 runs per block.
Initially, this blocking factor has 1 factor level, but that will change shortly. Then we can return and enter the names of the team members.
This is a full factorial experiment, so we want to be able to examine all interactions between the factors. Therefore, in the Model panel click the Interactions button and select 2nd.
Figure 18.8. Specifying Second-Order Interactions
You will see a warning that JMP does not support interactions involving blocks. Just click continue, and the model will include interactions for the three continuous factors.
Scroll back to the list of factors. The Team Member blocking factor now shows four cells. Enter these names: Jiao, Pranav, Daniel, and Li.
Click Make Design.
This time, we still have a full factorial design with four replicates and a total of 40 runs, but now see that the runs are grouped into four blocks. To compare your work to the author's, first set the random number seed once again.
Click the red triangle next to Custom Design and select Set Random Seed. Set the seed value to 5911.
Scroll to the bottom of the Custom Design window and select Make Table. In the new data table see (Figure 18.9) the random assignment of runs to team members is clear.
Figure 18.9. Portion of a Data Table with Blocked Design
In this blocked design, we still have 40 runs in all, with four replicates of the eight possible formulations, and each block (team member) has an assignment of 10 formulations to test in randomized sequence. The analysis of the strength data would proceed as before, with the blocks accounted for.