## Confidence Intervals

This afternoon I got a text message from one of my roommates saying that there would be six inches of snow tomorrow and that they had firewood. Then, as I was on my way home, I got a message from one of my other roommates asking me to pick up some more firewood. Both of these matters are areas where one would want a confidence interval. What are the odds, for example, that there will be six inches of snow tomorrow and what are the odds that there will be only one inch or perhaps even none? What is the range between which we are 90% or 95% confident? Perhaps it is the fact that I am a math nerd of sorts that leads me to wonder such things, because the weathermen speak about the chance of rain, but not the confidence intervals of temperature and precipitation, which is far more useful than a number alone. Yet there appears to be a reluctance to show just how uncertain such numbers are, perhaps because it would reduce confidence in those guesses and predictions [1].

Yet when we are making decisions, we need to know confidence intervals because the range of reasonably likely or conceivable outcomes or repercussions of an event is far more important than merely knowing the most likely or average outcome. We are generally at least somewhat decent in guessing measures of central tendency (mean, median, and mode) for example. We are less skilled, though, at recognizing the full range of possibilities and then behaving accordingly. Given the same mode (most likely occurrence) in a given situation, our behavior would be very different if we knew that in one case the chance of nothing happening would be high but there would be a possible (but rare) positive outcome as opposed to the reverse situation, where there was the potential for total disaster. Yet we do not tend to think in terms of confidence intervals, which give us that range of possibilities, and let us know how reliable a given judgment is, which can give us a bit more information to give us either encouragement to act or to behave with restraint.

What is the goal of a confidence interval, and why is it important for us to consider it? For one, we need to know how much we can trust our own guesses and those of others. Of course, we may not always be good at conceiving the likely or possible repercussions of an act, or else we would probably act far differently than we do. We tend to be risk adverse in situations where courage is beneficial and delusionally optimistic in occasions where restraint and caution would be beneficial. How do we become better at recognizing the full range of possibilities in life, and in being wise enough and understanding enough to act thoughtfully and reasonably in light of that knowledge? I suppose that is part of the mystery of life, in that we have a great and difficult task to live our lives as best as possible, and yet we do not always know what means will best achieve those ends we seek. Nor do we always know just how sure we are that something will happen. Is it not better at least to have some way of showing the reasonable scope of our doubts and fears and at least having some boundaries beyond which we keep our imagination from wandering, for our own sakes, even as we deal with this deeply uncertain world around us.

[1] See, for example:

https://edgeinducedcohesion.wordpress.com/2011/08/09/the-confidence-game/

https://edgeinducedcohesion.wordpress.com/2014/10/24/lord-of-the-data/