The study by douglas carroll and his colleagues (1994) examined the link between socioeconomic status and health using grave markers. which type of research was this?

That would be Correlational Research.
In correlational research, researchers look for well, correlation between the two variables in an attempt to assess the statistical relationship between those two variables. This is done in order to see which or if any variables are in correlation to one another. Correlational research like the one conducted by Douglas Carroll look at the variables that seem to intersect with one another.

The used coins.. .