You are stranded in the wilderness, hungry and exhausted. You haven’t eaten for days. As you focus on surviving, you also manage to admire the nature that surrounds you. At one point, you notice a four legged animal dwelling in the far distance. What is it?
You know there are occasional wandering goats in the area, but you are also aware of vicious dingo gangs.
Is it a dingo or a goat?
You look more carefully into the distance, but it isn’t clear, the animal is about one kilometer away (0.62 of a mile). You notice that it is shorter than the surrounding bushes and is moving around on four legs, but you can't tell exactly what it is.
You think: “If I make my way to the animal and it is a dingo, I’ll be in big trouble. The dingo may notice me and try to chase me down.”
“But if it is a goat, things can be much better. I haven’t eaten for days. I want goat. I’m hungry!”
You need to make a decision. Should you get closer or walk away. What do you do?
At this point your brain reverts to decision theory, hypothesis testing, clinical trials, specificity, sensitivity and similar concepts. These ideas from various fields of science, mathematics, statistics, economics and engineering play a key role in drawing conclusions and making decisions in view of inexact information.
Everyone has to do this automatically as part of life. Some automated systems do it as well. For example radars in air control systems continuously classify incoming signals as "aircrafts" vs. "clouds".
But you are stranded in nature without any machinery and tools. You don’t have a computer at hand, or even pen and paper to write on. Why are you thinking about all this mathematical stuff. Is it really needed now?
The thoughts continue and they are somehow beyond your control. You are reminded about the basic trade-offs that occur with medical diagnostics. You recently viewed this neat Healthcare Triage video. Specifically the first two minutes define false positives and false negatives very well.
A few months before that, you underwent medical testing for a specific disease. In that case, a “positive” is actually a bad thing. As you discussed with your doctor, you asked "what is the chance of error?". In response she explained that there are actually two types of errors to consider, each with a potentially different chance: “false positive” and “false negative”. What is the difference?
When a false positive occurs, the medical system tells you that you have the disease, even though you actually don’t. The implication of this type of error is that you undergo unnecessary treatment.
A false negative is often much worse. It means that the disease was not caught by the testing procedure even though you have it. Here the consequences may be truely bad.
In an ideal world, the chances of both false positives and false negatives are kept at a minimum. However, in practice, medical testing exhibits both types of errors.
Back from medical testing to nature, how do these terms map to dingos and goats?
A false positive means thinking it is a dingo while it is actually a goat.
A false negative means thinking it is a goat while it is actually a dingo.
Understanding the possibilities you consider your options. What do you do?
As you return from the wilderness, we suggest that you enjoy exploring such scenarios, discussing with your students or loved ones. Try to think of other situations where false positives and false negatives may arise. Do you have any examples to suggest?