Correlation versus ex-post facto designs
These are very similar quasi-analytic designs and it is possible to convert one to the other [e.g., assign dummy coding to the categorical (nominal) variable (if there is one and it has 2 levels) and calculate a point-biserial correlation coefficient instead of doing a between groups t-test]
Interpretation problems are not related to the choice of statistical analysis, rather they are due to the nature of these designs
Remember that unlike true analytic experiments: 1) subjects are not randomly assigned, 2) there is no attempt (in correlational designs) to control variables, and 3) different levels of the IV are not contrasted while concurrently holding all other variables constant.
Drawing conclusions from correlational designs -- we have all the same concerns as with experiments (valid, reliable measures, etc.) but in addition, have concerns with directionality, and there are usually many potential confounds (uncontrolled extraneous variables in correlational designs - the 3rd variable problem).
Although causality can not be inferred from a single correlational design, correlational designs can be used to discover relations, to solve ethical and practical problems, and to provide greater external/ecological validity (by being more easily applicable outside laboratory settings)
Causation is not a simple concept.To infer it from correlational studies, we want to have:
1) an association between variables that recurs in different contexts (replication, convergent evidence),
2) have a plausible explanation showing how the predictor variable could cause the criterion variable, and
3) have no equally plausible 3rd variable that could cause the variance in the criterion variable.
While correlation doesn't imply causation, causation does imply correlation