I have developed a recent interest in propensity scores. I have been using the SPSS tool created by Dr. F. Thoemmes to calculate propensity scores using bivariate "treatment" variables (e.g., depression) and several covariates (e.g., age, sex, persons in household). I am then given a resulting propensity score, but am left wondering what to do with it.
I have read that what is typical would be to match two individuals who have nearly identical propensity scores (e.g., two people get group number "17") but who actually differ on your treatment variable (e.g., depression), and then do a paired t-test based on group number and dependent variables (e.g., household income). In this example, we would see how two individuals with all of the same propensities (e.g., age, sex, persons in household) but differing on your treatment variable actually differ on your dependent.
This idea makes sense to me, but the software actually does not do matching based on propensity scores, and I don't know how to match them using SPSS or Excel, and I don't want to currently bother to learn how to do so in another program/language (e.g, R). This laziness, lets call it, has forced me to do more research.
Two authors state: "After the matching is completed, the matched samples may be compared by an unpaired t-test. (“Matching” erroneously suggests that the resulting data should be analyzed as if they were matched pairs. The treated and untreated samples should be regarded as independent, however, because there is no reason to believe that the outcomes of matched individuals are correlated in any way)." (Schafer & hang, 2008). Other research seems to suggest people often input propensity scores in logistic regressions next to their independent variable of interest, and see how the independent variable predicts while "propensity" is controlled for.
Although this line of research is interesting, I must admit I am slightly lost regarding what methods are possible/best in terms of conducting quantitative analyses AFTER propensity score calculations. Any guidance on this matter would be appreciated. I will likely have follow-up questions, too!
EDIT: I want to highlight that I am concerned about what types of inferential analyses to do AFTER I get the propensity scores calculated for each individual. For instance, perhaps I could calculate propensity score of being depressed (yes,no) based on covariates (age, number of people in household, smoking, sex, state). The program calculates a propensity score as a new variable for each individual. AFTER this, I am interested in seeing if depression is associated with household income while "controlling for"/"considering"/"matching" (Chose word based on what method you suggest, perhaps) the effect associated with propensity.