If we assume unconfoundedness, then for these two people, there should be no other variables that have an effect on both the treatment and the outcome. So, by subtracting their outcomes, we should be able to estimate the causal effect of the job training program for this particular (specifically, 28-year old, unmarried, Black, non-Hispanic people without high school diplomas who've completed 8 years of schooling). If we do this for every possible set of values for the confounders , then we can take all of them and compute the expectation (weighting each by the probability of seeing that corresponding value of ). Empirically, this corresponds to just taking the average of all the data points. Here is the matching algorithm in English: For each treated row: Find all untreated rows that have the exact same values of all confounders. Take those untreated rows and average their outcome Subtract the average above from the treated row's outcome For each untreated row: Find all treated rows that have the exact same values of all confounders. Take those treated rows and average their outcome Subtract the untreated row's outcome from the average above Average all the results from steps 1 and 2