Plackett-Burman – main effects in a hurry!

There are a number of experimental designs available to us – including factorial designs to assess the effects of factors (see ______) and Box Behnken (see _______) which can be used to further investigate the effect of significant factors.  

The Plackett-Burman experimental design offers another option to factorial, used to screen the impact of effects. Plackett-Burman designs have a big advantage in that they can be used to screen a large number of effects, but their downside is that they only give information on main effects and can be confounded by two-way interactions. Be warned!!!!! 

The most important feature of Plackett-Burman designs is that they all involve 4n experiments, where n = 1, 2, 3, etc, so a total of 4, 8, 12, etc experiments. Additionally, the maximum number of factors that can be studied is 4n-1; so an 8-experiment Plackett-Burman design can study no more than 7 factors, a 12-experiment design will handle up to 11 factors, etc.  

For example, in the case that we want to study eight factors – eight experiments can only handle seven factors, so we need to do at least 12 experiments. Twelve experiments can accommodate up to 11 factors, so eight of those will be the ones we are interested in and the other three are dummy factors that have no meaning.  

Instead, these dummy factors are useful as their apparent effects can be used to estimate the measurement error and allows us to conduct the analysis to determine which factors are significant. The more dummy factors there are, the better the estimate of such errors, so it is not uncommon for experimenters to use a larger PB design than is strictly necessary, thus getting higher quality information on the significance of each “real” factor. 

Plackett-Burman designs utilise two levels for each factor, the higher level being denoted “+” and the lower “-”, as seen in other experimental designs.  

To create a Plackett-Burman design in R, the code is: 

• The term "require(“daewr”)” loads the appropriate package with the required function.  
• "PBDes(...)" instructs R to create a Plackett-Burman experimental design with the stated number of runs and factors: 
• The “nruns” is the number of runs/experiments to be included in the design. For this package nruns can only be 12, 20 or 24 (in this case it is 12). 
• The “nfactors” is the number of factors (real and dummy) to be incorporated – typically this is one less that the number of runs. In this case it is 11).  

When this is run, R will give an output something like the below, which can the be used to say the levels of each factor for each run. Just ignore the columns related to the dummy factors.  

Once you have completed the runs, you analyse the results using ANOVA (see Two-way ANOVA – Twice the Fun!).