Comparing two samples about corresponding parameters of their respective populations is an old and classical statistical problem. In this paper, we present a simple yet effective tool to compare two samples through their medians. We calculate the confidence of the statement “the median of the first population is strictly smaller (larger) than the median of the second.” We analyze two real data sets and empirically demonstrate the quality of the confidence for such a statement. This confidence in the order of the medians is to be seen as a pre-analysis tool that can provide useful insights for comparing two or more populations. The method is entirely based on their exact distribution with no need for asymptotic considerations. We also provide the Quor statistical software, an R package that implements the ideas discussed in this work.
Pereira, C. A. D. B., & Polpo, A. (2020). Using Confidence Statements to Ordering Medians: A Simple Microarray Nonparametric Analysis. Open Journal of Statistics, 10(01), 154-162. https://doi.org/10.4236/ojs.2020.101012