In a study on caffeine, the researcher predicts that caffeine should improve learning and memory?

Thesis - a proposition stated or put forward for consideration, especially one to be discussed and proved or to be maintained against objections. Greek "hypo" means under. A hypothesis is a proposition thrown under a subject to define a study of it. The scientific method is based on an observation and a hypothesis that might or might not explain the observation. So the researcher's hypothesis in this case is "Caffeine improves memory and learning." (May or may not be based on an observation.)

Statistical - Based on counting things.

I'm fairly smart, and I have never heard those other terms. If somebody wants to use them, ok, but it's up to them to explain what they mean.