A simple method for constructing exact tests for sequentially designed experiments

A particular method is given for constructing exact tests for sequentially designed experiments when the treatments for the experimental units may be chosen. A simple artificial example of the form of test is presented. This method is applied to inverse estimation in a simple linear model, to testing a simple linear hypothesis about a linear model and to finding the change-point when a response is described by two linear models. In all cases the designs and analysis are less than optimal. However, the potential gains for such sequential designs can outweigh the losses and justify the simple techniques, which may be easily implemented.