Randomized vs. Split-plot

Randomized designs potentially change the levels of all the factors after every run. This is done to protect against a lurking variable effect as well as to ensure each run is exposed to the same sources of variation from resetting the factor levels.

Factors such as the temperature of a kiln are difficult to randomize. If one run is high temperature and the next run is low temperature, then the kiln will need to cool down before starting the next run. As most kilns are not designed to cool off rapidly, the extra time needed to randomize the temperature can make the experiment too time consuming. These types of variables are considered hard to change (HTC).

Split-plot designs are used to control the number of times a HTC factor must be changed. Making the design easier, and more cost effective to conduct. The analysis of split-plot design takes into account the restriction on randomization. HTC factors do still need to be changed (reset) a number of times if the effects are to be tested and a p-value produced.

There is a trade-off for making the design easier to run. The power to detect significant effects and precision of the model predictions is worse for HTC factors.

Compare the cost of randomizing a smaller design versus performing a large enough split-plot design capable of providing adequate power (> 80%) or precision (FDS > 0.80).