Outliers and experimental designs

Outliers are not always useless data which must be discarded. They are sometimes valuable signals of something new and unusual. They may contain a lot of information, and even lead to a new scientific discovery. The problem is how to evaluate the significance of outliers. If they are sometimes so important, we should perhaps look for them even when they are not apparent. Experimental designs are well suited to tracking one outlier in a set of results. This paper describes 3 methods for detecting a hidden outlier: The Daniel's diagram, analysis of residuals, and experimental design reconstruction. An example shows how the proposed theory works, how factors that were unknown at the beginning of the study can be discovered, and how they can help experimenters.