ADLERSHOFER KOLLOQUIUM Analytik: Where does all that noise come from? Design of Experiments for Deeply Nested Data Structure

In analytical chemistry, we often face situations where multiple confounders contribute noise or random uncertainty to the analytical result. The question is then: how to allocate experimental resources efficiently? As a rule of thumb, it is best to concentrate the experimental effort on the largest confounders. However, this means we need to know the size of each confounder or more
generally: influencing factor. In analytical chemistry, deeply nested (aka hierarchical) data structure is very common. Unfortunately, this makes measuring the confounders rather difficult.

We present sampling schemes for estimating the variance contributed by the various confounders which do not lead to exponentially growing sample numbers for nested data. These staggered and inverted nested designs have been known since the 1960s [1] but only nowadays the computational resources to analyze such data have become readily available.

As an example, we discuss the sampling plan and design of experiments for chemical reference analysis for calibration of NIR spectra in the context of quality control during cacao fermentation. The experimental design was set up primarily to allow estimation of the biochemical variation in the analyte content between cocoa beans of the same fermentation but also to monitor the random
error introduced by the various steps in the analytical process.