Do my homework

[jmermin]

So a colleague in math ed has a hypothesis and does two experiments ("fall" and "spring") which each produce evidence in its favor

Comments

[eve_prime]

For a "theory of composite experiments," see "meta-analysis." It's used very frequently in health, for example, to combine evidence from numerous studies so they can make stronger claims. I haven't been involved in any meta-analyses, though, so I can't advise on methods.