![]() ![]() It can incorporate a variety of constraints such as sample size restrictions (e.g., the lab has a limited supply of test tubes), awkward blocking structures (e.g., shelves have different capacities) or disallowed treatment combinations (e.g., certain combinations of factor levels may be infeasible or otherwise undesirable). Optimal design provides a principled approach to accommodating the entire range of concentrations and making full use of each shelf’s capacity. Classical designs, like full factorials or RCBDs, assume an ideal and simple experimental setup, which may be inappropriate for all experimental goals or untenable in the presence of constraints. However, because concentration is actually continuous, discrete levels unduly limit which concentrations are studied and reduce our ability to detect an effect and estimate the concentration that produces an optimal response. If concentration were a categorical factor, we could compare the mean response at nine concentrations-a traditional randomized complete block design (RCBD) 1. The experimental design question, then, is: What should be the drug concentration in each of the 36 tubes? Furthermore, each shelf can only hold nine test tubes. Since we don’t expect such systematic variation within a shelf, the order of tubes on a shelf can be randomized. The shelf would therefore be a natural block 1. To illustrate how constraints may influence our design, suppose that the shelves receive different amounts of light, which might lead to systematic variation between shelves. ![]() We will address both by finding designs that are optimal for regression parameter estimation as well as designs optimal for prediction precision. Our goal may be to determine whether the drug has an effect and precisely estimate the effect size or to identify the concentration at which the response is optimal. The cells will be grown with the drug in test tubes, arranged on a rack with four shelves. It can flexibly accommodate constraints, is connected to statistical quantities of interest and often mimics intuitive classical designs.įor example, suppose we wish to test the effects of a drug’s concentration in the range 0–100 ng/ml on the growth of cells. In these cases, we can use optimal design: a powerful, general-purpose tool that offers an attractive alternative to classical design and provides a framework within which to obtain high-quality, statistically grounded designs under nonstandard conditions. However, the presence of unique constraints may prevent mapping the experimental scenario onto a classical design. To maximize the chance for success in an experiment, good experimental design is needed. ![]()
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