Best Bang for the Buck: Part 1 – The Size of Experiments Relative to Design Performance
There are many choices to make, when designing an experiment for a study, such as: what design factors to consider, which levels of the factors to use and which model to focus on. One aspect of design, however, is often left unquestioned: the size of the experiment. When learning about design of experiments, problems are often posed as "select a design for a particular objective with N runs." It’s tempting to consider the design size as a given constraint in the design-selection process. If you think of learning through designed experiments as a sequential process, however, strategically planning for the use of resources at different stages of data collection can be beneficial: Saving experimental runs for later is advantageous if you can efficiently learn with less in the early stages. Alternatively, if you’re too frugal in the early stages, you might not learn enough to proceed confidently with the next stages. Therefore, choosing the right-sized experiment is important—not too large or too small, but with a thoughtful balance to maximize the knowledge gained given the available resources. It can be a great advantage to think about the design size as flexible and include it as an aspect for comparisons. Sometimes you’re asked to provide a small design that is too ambitious for the goals of the study. Finally, if you can show quantitatively how the suggested design size might be inadequate or lead to problems during analysis—and also offer a formal comparison to some alternatives of different (likely larger) sizes—you may have a better chance to ask for additional resources to deliver statistically sound and satisfying results