Abstract This article describes how to be sure that there is, or not, an outlier in a two-level experimental design (16 runs or more) with no replicates. It also describes how to discover an outlier if there is one, and how to estimate the true value of this outlier. The method is based on the use of a dynamic variable and the “small effects” of the Daniel's diagram. The theoretical relationship between the “small effects” and the dynamic variable is established in the case of a two-level factorial design. The method is applied to two examples to show how the following three problems can be solved: whether there is, or not, an aberrant response, to detect an outlier when there is one and to estimate the value of the outlier as if it had not been aberrant.