The case of no relationship would be X changes but Y remains constant.
A research design would require a minimum of two cases, and can have many more. We would need a case of X=0 and of X=1, or X low and of X high. For each of these, we will set out to find out the values of Y which we expect to be related to X.
In a case-study design, we have information on X and Y from two or more cases.
In a large-N design, we have many more – say, more than 50.
A medium-N design would be something in-between.
In a large-N design, we may take advantage of statistical techniques, to demonstrate that X and Y are related.