We can’t know the objective world perfectly. We usually get it largely right, but whether we’re using our own senses or measuring it indirectly using instruments, our representations of alpha reality – i.e., our beliefs – are often a little off. Statisticians use confidence intervals to account for this error by describing the range within which we’re pretty sure the true value of whatever we’re measuring falls.
Hurricane path projections are visual examples of confidence intervals. The widening of the cone over time indicates that the more days ahead the prediction is made, the less sure forecasters are of where it will be.
Hurricane predictions are about the future, but confidence intervals are used most to qualify things we think we know right now. One that most people are familiar with is the margin of error that’s reported along with opinion poll results. Today’s Rasmussen Reports daily Presidential Tracking Poll, for example, finds that 31% of voters “strongly approve” of the way Barack Obama is performing his role as President. The poll has a margin of error of plus-or-minus 3%, which means the actual approval rating for the population the sample is supposed to represent (all U.S. voters) is somewhere between 28% and 34%.
Confidence intervals are expressed as a minimum and maximum number within parentheses. In this case, we would say, “The percentage of voters nationally who strongly approve of how President Obama is doing his job is 31% (28%, 34%).” We use confidence intervals only for numeric estimates, but the principle behind them is applicable to all our beliefs, which all have some error associated with them. What would it look like if we qualified our everyday beliefs with confidence intervals that captured the lower and upper limits of our beliefs’ “truth zones?” It would look something like this:
Darn, I can’t believe I was stopped for speeding – I was only going 32 (23, 41) in that 35 mph zone. I have about $120 in my bank account ($50 overdrawn, $300), which should be enough to cover the fine. I should have taken the bus anyway; it’s better for global warming (cooling, much warming). Things I need to remember to do:
- Push Jimmy to practice those reading exercises the learning center gave him; they’ll improve (have no effect on, double) his comprehension.
- Take my ginkgo supplement at bedtime; it helps me stay mentally sharp (is the source of my headaches, prevents depression).
- Pick up a gift tomorrow for my girlfriend’s birthday; she’s quite fond of (about to break up with, head over heels for) me.
