Statistical Analysis of Physical Chemistry Data: Errors Are Not Mistakes

T goal of a physical chemistry experiment is to measure an interesting property. This property could be the lifetime of an excited electronic state, the exciton diffusion length within a solar cell, or the coupling strength between two optical transitions. In reporting the results of experiments it is extremely important to quantify the accuracy of the measurements. Errors are inevitable in experiments; however, they can be hard to work out. This is especially true when complex fitting functions are used to analyze the data, or when the data are compared to simulations. Nevertheless, a good analysis of errors can elevate the quality of your paper and help convince readers that the data have been carefully analyzed and are reliable. The goal of this editorial is to provide a basic practical guide for reporting errors in physical chemistry experiments. Unlike experiments in biological sciences which involve controls and sometimes complex hypothesis testing, errors in physical chemistry are relatively straightforward. There are two common situations: (i) the case where a series of experimental measurements are averaged together to determine an expectation value and (ii) curve fitting where experimental data are fit to a function. In both cases the goal is to provide a best estimate for the quantity being measured, as well as an estimate of the range of possible values. This discussion will assume that we are only dealing with random errors; that is, that there are no systematic errors in the measurements. Averages and Standard Deviations. When a series of nominally identical measurements have been performed, the best estimate of the true value of the quantity being measured is the sample mean x̅, and the range of the values obtained from the experiments is characterized by the standard deviation σx: