Inferences acquired by applying clustering analysis cannot be reliably assessed before data-originated errors are quantified, an exacting task that is often not performed. This invention presents a clustering method suited for this purpose. Designed for systems with normally distributed error, a common trait to many data systems, and built on a framework of agglomerative hierarchical clustering, this invention treats each observation as a Gaussian distribution function, uses an exact mathematical relation to track error, and gives results from which quantitative statistics are easily extracted.