I mostly come from a scientific rather than a philosophical perspective, but here goes.

Frame challenge: I feel like this question is backwards.  One doesn't propose a theory and then ask, "What data could this apply to?"  It's the other way around: You start with observations (data), then proposed a hypothesis to explain them.

This is hard to see, for example, with Russell's five-minute hypothesis.  But only because his starting point is so broad.  He is starting with all human experience.  (And then proposing—for the sake of argument—the five-minute hypothesis as an idea to be disproven.)

Taking the Russell example further (or "When choosing between competing metaphysical theories"): Theories are made to explain.  If some data can be explained by a hypothesis, it's relevant. Alternatively, if some data could disprove a hypothesis, it's relevant.