Basic Concepts
To determine whether there is a significant difference between the effect on two groups (e.g. a treatment group and a control group), we normally randomly select a sample from the population being studied and then randomly assign subjects in the sample to the two groups. This is called an experimental study.
Sometimes it is impossible or unethical to randomly assign subjects to the two groups. For example, when studying the effects of smoking, we can’t assign non-smokers to the smoking group, and so there is no random assignment. The goal of experimental design is to reduce the chances that confounding variables will influence the outcome of the study. This is achieved since the random assignment of the sample groups tends to eliminate the effects of confounding variables.
When there is no random assignment of the sample into groups, then we have an observational study. We now need to take confounding variables explicitly into account. Two approaches for doing this are coarsened exact matching (CEM) and propensity score matching (PSM), in which we identify all important confounding variables, and then determine matching subjects from the sample based on similar confounding variable values, pruning non-matching pairs.
Topics
References
Ho, D., Imai, K., King, G., Stuart, E., Whitworth, A., Greifer, N. (2024) Matching methods
https://cran.r-project.org/web/packages/MatchIt/vignettes/matching-methods.html#mahalanobis-distance-matching-mahvars.
Nguyen, M. (2020) Matching methods. A guide on data analysis. Bookdown.
https://bookdown.org/mike/data_analysis/matching-methods.html
Wikipedia (2025) Matching (statistics)
https://en.wikipedia.org/wiki/Matching_(statistics)