Reducing the standard deviation in multiple-assay experiments where the variation matters but the absolute value does not

Abstract

You measure the value of a quantity x for a number of systems (cells, molecules, people, chunks of metal, DNA vectors, etc.). You repeat the whole set of measures in different occasions or assays, which you try to design as equal to one another as possible. Despite the effort, you find that the results are too different from one assay to another. As a consequence, some systems' averages present standard deviations that are too large to render the results statistically significant. In this work, we present a novel correction method of very low mathematical and numerical complexity that can reduce the standard deviation in your results and increase their statistical significance as long as two conditions are met: inter-system variations of x matter to you but its absolute value does not, and the different assays display a similar tendency in the values of x; in other words, the results corresponding to different assays present high linear correlation. We demonstrate the improvement that this method brings about on a real cell biology experiment, but the method can be applied to any problem that conforms to the described structure and requirements, in any quantitative scientific field that has to deal with data subject to uncertainty.