When should I stop experimenting? Sample size considerations in I‐optimal designs

The average prediction variance for an I‐optimal design for a specified normal theory linear model decreases nonlinearly with respect to sample size. In this paper, we develop a prediction equation to explain the relationship between average prediction variance and sample size. We investigate methods for determining what sample size is efficient for a given experiment using the average prediction variance (APV) versus sample size curves. The sample size determination is studied assuming a variety of cost structures for the trials in each experiment. For example, in practice, the length of time before an experiment is complete may be considered an implicit cost of experimentation. We provide results for designs and models based on two to five factors. We also present a potential application of the methods using a military system experiment.