A premise is essentially an assumption or proven fact/phenomenon. Its the building block of truth upon which we try and build. The phrase; "GI3 claims that that no DIR diver has died" is a premise. It is also a false premise as his assertion has been that no WKPP diver has ever died under his direction.
A hypothesis however, is a guess or prediction, and it usually is predicated on an assumption or three. It is the leap of faith using deductive reasoning and grounded in the truth of the premise. Consider the phrase; "If DIR is as "All That" safety wise as GI3 claims, THEN we should find a lower incidence of deaths among DIR divers. This is a hypothesis that is used to test a premise. Clear as mud yet???
Now, here are some obvious non-controllable variables as you embark on this noble cause...
Diving hours/death
Difficulty of dives
Fitness level of the various divers
Mean age of the various divers
Diving environment
Support of divers (surface and sub-surface)
Wet suit/drysuit
AND I haven't really gotten started yet. I am sure that this list would EASILY quadruple if we put our minds to it. So many complain as to why insurance agencies/cert agencies/Dan don't give us numbers... thats why. It's too darned confusing and too dang easy to arrive at an erroneous conclusion. Realistically, we would probably find that in %100 of all cave diving deaths, that the deceased was wearing fins. Hmmnnnnnnnnnn... anyone want to give up their fins? Determining the mitigating/contributing factors and then the ultimate cause of death is tough and some accidents are simply indeterminate. We may never understand the mechanisms of many accidents. The only ones who really know for sure in any accident are God and the poor diver. Neither of them are particularly glib about this.
Don't get me wrong, I am not trying to dissuade you from this discovery. I just think you should know how daunting the journey will be.