One of the reasons people have a hard time learning science is that it demands that one upside-down.
One item in particular is one I got to thinking about during all the medical news of the past month. It has to do with statistical probabilities and "rejection regions".
Suppose you're running a hospital, and you have a number of patients. Some of them will be very obviously alive and functioning. You can hold a conversation with them, for example. Or they'll hit the call button for the nurse and ask for something every now and then. Even if you happened to wander in while they were asleep, you wouldn't classify them as brain dead or in any other way "out of it".
There are patients whose hearts have just quit working. All other metabolic processes have stopped. They're well beyond the "pining for the fjords" stage. They're very obviously dead.
Then there are those somewhere in the middle. Maybe you have a patient – call her Sheri Tiavo, to use a thoroughly fictitious name – who is somewhere in the middle. She's never responsive enough that you can hold a conversation with her on any level, but she's just responsive enough that you can't declare her brain-dead.
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There's a line between "effectively alive" – there's someone home, and if we let the body die, we're killing a person – and "effectively dead". Sheri may be on one side of the line, or she may be on the other. We don't have a single test that will tell us, with 100% certainty, which side of the line she's on. The best we can get is assessments of the probability that she's on one side or the other.
Medical tests usually don't return a result of "normal" and "diseased" or even "normal" and "abnormal". Usually, you get some number, corresponding to a level of something measurable, and you compare it with textbook values tha define a normal range. Anything within the range is considered normal, and anything outside the range is abnormal.
Take temperature, for example. "Normal" is 98.6 degrees F. You can show up with a temperature lower or higher than that number, and still be OK. If it's too high, you officially have a fever. If it's too low, you officially have other problems. But in both cases, someone has to decide just how far away from the textbook figure you can get before you have a problem.
The same thing happens with drug testing. Generally, if you're tested for drugs, there will be some small background measurement, even if you're completely clean. If you've used drugs, there will be a large measurement. Somewhere in between, there has to be a cut-off below which any reading has to be considered part of the noise. Make it too high, and you miss some people who actually used drugs; make it too low, and you will classify innocent people as druggies based on a reading that is actually noise in the test procedure.
Science uses a statistical model to address this problem. Most of the time, for example, if you measure the temperature of a healthy person, you'll get a number close to the textbook average. Once in a great while, you'll get a number far away from that average. If you plot all these readings, you'll find they fall in a bell-curve around the average value.
The bell curve, or the Gaussian curve, is well-characterized. Once we know the standard deviation, we know how likely we are to see any number any distance away from the average value. A value here may occur by chance one time in twenty. A value over there may occur one time in a hundred. We'll see a value way out here one time in a million.
If we're lucky, the distance between "normal" and "sick" is several standard deviations. If a normal person breathes, say, ten times per minute, a person who breathes fewer than once per hour is well below the normal and can safely be called "dead".
But what if that person's on a respirator? What if without the respirator, he normally breathes only once per minute? Once every ten minutes? At some point, we have to decide on a number that means the brain's just not running the lungs any more.
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