Matching is a statistical technique which is used to evaluate the effect of a treatment by comparing the treated and the non-treated in non experimental design (when the treatment is not randomly assigned). People use this technique with observational data (ie non experimental data). The idea is to find for any treated unit a similar non treated unit with similar observable characteristics. By matching them and looking at their average difference, one can evaluate under some conditions the pure effect of being treated. This is one way to identify the Rubin Potential Outcome

Rubin Causal Model

The Rubin Causal Model is an approach to the statistical analysis of cause and effect based on the framework of potential outcomes. RCM is named after Donald Rubin, Professor of Statistics at Harvard University...

 model if there is selection on observable characteristics in the treatment.

Matching has been promoted by Donald Rubin

Donald Rubin

Donald Bruce Rubin is the John L. Loeb Professor of Statistics at Harvard University. He was hired by Harvard in 1984, and served as chair of the department from 1985-1994....

. It has been discredited by LaLonde in 1986. In this article LaLonde compares experimental estimates with matching methods and show that matching methods are biased in this case.
Dehejia and Wahba reevalutes LaLonde's critique and show that matching is a good solution.

Analysis

Paired difference test

Paired difference test

In statistics, a paired difference test is a type of location test that is used when comparing two sets of measurements to assess whether their population means differ...

s can be applied to analyze such matched studies. Forming matched pairs for paired difference testing is an example of a general approach for using matching to reduce the effects of confounding when making comparisons.

Overmatching

Overmatching is matching for an apparent confounder that actually is a result of the exposure. True confounders are associated with both the exposure and the disease, but if the exposure itself leads to the confounder, or has equal status with it, then stratifying by that confounder will also partly stratify by the exposure, resulting in an obscured relation of the exposure to the disease. Overmatching thus causes statistical bias.

For example, matching the control group by gestation length and/or the number of multiple birth

Multiple birth

A multiple birth occurs when more than one fetus is carried to term in a single pregnancy. Different names for multiple births are used, depending on the number of offspring. Common multiples are two and three, known as twins and triplets...

s when estimating perinatal mortality and birthweight after in vitro fertilization (IVF) is overmatching, since IVF itself increases the risk of premature birth and multiple birth.

It may be regarded as a sampling bias in decreasing the external validity

External validity

External validity is the validity of generalized inferences in scientific studies, usually based on experiments as experimental validity....

of a study, because the controls become more similar to the cases in regard to exposure than the general population.