Unless you just want to guess, you DO need demoninators. That's what gives us the rate/liklihood/chance etc. Otherwise, all you've got is a raw number.
Ken, "statistics" come in two different flavors, confirmatory statistics, which is what you are looking for and exploratory data analysis, which is my forte. If you are concerned about the probability of a given rate per unit something, then you are correct. If, on the other hand, all you want to do is make a comparison list of different activities, there are any number of techniques (one of which I sketched earlier) that may be applied. It is my view that accidents per number of dive statistics are complete and utter claptrap. For such statistics to be meanigful, at least in the way you are attempting to use them, the dependent variable (e.g., survived or did not survive dive) must be the result of a random event that does no vary with any of independent variables. Yet, it is clearly obvious that the probability of death is not just a function of the number of dives an individual makes per unit time but is also a function of the hours of traning received, the number of previous dives made, the number of previous dives made under similar conditions, the diver's age, etc. If you plug all this into an Analysis of Varience (ANOVA) I think that you would find that the number of dives is, rather than causal, inversely proportional and that other factors will, in point of fact, stuff the variance due to the total number of dives, down into the error term. What you are really looking for is a kinda common sense way to evaluate total risk, that is to say, is the average diver at more or less risk than the average driver, or the average recreational baseball player, or the average skiier, etc. That you can do, as I demonstated, without a denominator, but not without opening other questions ... like: "what is the population?"
Personally, I think that number may be high, when you talk about ACTIVE divers. But the number DEMA uses is 2-2.5 million active divers. I was at a presentation by Drew Richardson, PADI prez, and I think he was extrapolating the number of active divers to be closer to 3 million. Or you could trake the financial size of the dive industry (around $700 million annually - but that may not include travel booked but not through a shop or club), figure out what the "average" diver spends a year ($2000 ???) divide that into the total and you'd have an active population of 350,000. Using that as a demoninator instead of 1,000,000 basically triples the chances of dying.
So yes, the denominator matters.
Drew is just repeating the number that McAniff admitted to having pulled out of thin air back in the 1990s. Rather meaningless then, totally bogus today. As to the financial size, I hear numbers from 300 million all the way up to a billion, with the "usual" number being as you describe it. But I can never seem to pin down what that includes. What I want to know is how many tanks are filled, how many certifications are issued to unique individuals, how many regulators are sold, how many BCs, etc. I could likely construct a pretty good model with that kind of data, but we don't have it and are not likely to. That leaves us with exploratory data analysis (may I recommend Tukey's book of that title?).
And then you have to define what "ACTIVE" really is. We may be able to say what the number of basic certs issued over a given period has been. But we have NO idea how many of those people keep doiving and we have NO idea of how many dives they do annually. The thought is that most divers do an average of 10-12 dives/year because they do one vacation dive a year, 2 dives per day for 5-6 days. So that gives you a universe of 4.2 million dives producing an average of (using last 4 yrs avg of 80/yr) 80 fatalities a year or 1 fatality per 52,500 dives. Still pretty good odds.
Or you could take Richardson's number of 3 million active divers, assume they do an average of 20 dives/year, giving you a universe of 60 million dives peroducing 80 fatalities per year or 1 fatality per 750,000 dives. REALLY good odds . . . unless you're that one dive.
So again, yes the denominator matters, as do the assumptions you make to arrive at a given conclusion. And therein lies the rub: We have to rely on too many assumptions and if the underlying premise (assumption) is wrong, then the result won't represent an accurate picture of the situation.
- Ken
As I described, activity level doesn't really matter, unless you are trying to calculate the risk per dive. In fact, the obvious existance of a huge interactive term between risk and the number of recent dives, is something that nothing except a rather robust ANOVA will deal with.
