The normal curve is probably not appropriate for an analysis of survival probablities. One assumption is that the observations are independent, meaning that one person contributes one data point, not several data points. Another assumption is that your "scores" are continuous, either interval or ratio measurement scales. I don't think "chance of arriving alive" is a continuous scale. Another assumption (there are many) is that the continous data actually fit a bell shape. Percentage chance of X vs Y outcome rarely fit a bell shape (if they ever do).
What I suspect is needed is some math modeling procedures, perhaps one called "survival analysis." This uses live or die as the dependent variable (the observed outcome) and then allows various other input variables (e.g., cubic feet of gas, distance traveled per 100 psi, etc.) and uses those input variables to generate a prediction model and thus the probablities of survival under the variable conditions.
I've never conducted a survival analysis and only know that it is a statistical procedure, so I can't say for sure that it would do what you want to do. However, it was created to analyze surgical practices to discover those that produce the greatest chance of surviving the surgery! It's also been used in a variety of situations in which the outcome of complex procedures is dichotomous (this or that).
Older versions of SPSS (statistical package for the social sciences) and SAS (another software package) included this procedure under the same name: survival analysis. I don't know if newer versions of those software packages use the same name, include the procedure, etc., but it might be worth a look and be more productive than spending time with the bell curve (which I'm pretty sure is not appropriate).
-skip
"Learning the techniques of others does not interfere with the discovery of techniques of one's own." B.F. Skinner, 1970.
Here in Tennessee, our caves are no flow or low flow. If you can detect a flow you are more sensitive to it than I am. I have often gone to thirds, which I've since learned is not wise, and in all cases have returned with more than 1/3 left. So if you go in to X psi and it takes X-300psi to exit, even in no flow, then that tells me that I'd always make it out on half of the starting total. Unless something bad happened.
This idea that in no flow caves we consume more gas on exit than on entrance is not supported in my experience. Even when totally tired from a long swim in, and still not at thirds, but just too tired to continue on, somehow the exit takes less gas. And I'm talking no flow.
I suspect there's a psychological difference in going in and coming out. When it's time to go home, we tend to speed up, don't stop and look as much, already been there, so now we take a more direct route out? I suspect the variation in the route is less on exit than on entrance. I suspect the speed of entry is slower than it is on exit too, even in no flow systems.
I'm not saying dive halves! That's insane. But given that nothing bad happens on the way out I think we all use less gas on exit even in no flow systems. I've even dove minor syphons in which the work to exit was harder than the entry/penetration and still used less gas.
It makes me think that psychology is at play here. That on the way in we know we have plenty of gas, but on the way out, we concentrate more on getting out and our minds and bodies adjust. All I've ever read is that panic increases gas consumption and it makes intuitive sense, but what if one is not in a panic state, what if one is dedicated to getting out on remaining gas? Perhaps the mind and body work together to reduce oxygen need while increasing work load? Ok, i may be getting a bit too Zen here....
-skip
"Learning the techniques of others does not interfere with the discovery of techniques of one's own." B.F. Skinner, 1970.
Skip,
Low flow doesn't mean no flow. It only requires a minimal amount (that one cannot really feel) to make a large difference in time and gas consumed. For example, generally most people consider Peacock to be a no flow cave, but actually it's low flow. For example, if you're swimming from Peacock to Challenge, you are usually swimming against the flow, and even if your SAC rate is identical on the way in and the way out, you will find that your return time is quite a bit less than on your way in, and therefore the gas consumed on the way out will be less than on the way in. If, however, you swim the Grand Traverse, there and back, starting at Orange Grove you will find that you will consume significantly more gas on the return leg (Peacock to Orange Grove). That's because from Peacock to the point approximately half way between Challenge and Orange Grove (approximately where the distance tunnel begins) you will be swimming against the flow.
Marius
When I said low flow I really meant low flow, not the high flow you get in peacock. Think a ribbon of water trickling out of hole 1/10 the size of peacock. With a five gallon bucket you can bail faster than the flow.
-skip
"Learning the techniques of others does not interfere with the discovery of techniques of one's own." B.F. Skinner, 1970.
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