It’s not fun to waste precious mental resources on problems that don’t demand them, which is why the situation I’m about to describe is so irritating.
You’re discussing a topic on which you and your friend disagree. Your friend makes a compelling statement, and you begin to assess it to see how it might factor in to your own view of the issue and whether it might even prompt you to change your view somehow. Initial inspection of the idea also makes you wonder why your friend thinks this – if there’s good evidence behind it, the way it factors into your own thinking changes. Your friend’s idea carries more weight if it’s supported well.
The friend pauses to let you think the idea over. You glance up to let him continue, and he describes his reasoning: his uncle has experience in the matter, and this informs your friend’s opinion. You let that sink in. That’s it? That’s the basis for your friend’s general belief, a single personal experience? One data point? Continue reading “One Data Point”
Fellow college blogger and real-life friend David Postic recently wrote an excellent post about statistical improbability as it relates to specific lives, which got me thinking. David pointed out how unlikely each of our lives are, and how unique the simple power of probability makes us. What’s cool about this to me is that despite the unlikely circumstances that comprise each of our lives, we can reliably count on the fact that each of us will be improbably unique.
Here’s a clarifying analogy: the chance of drawing any four specific cards out of a 52-card deck is one in 6,497,400. Drawing all four aces, for example, happens once every 6,497,400 tries, on average. However, the chance of drawing some combination of four cards that you have a 1 in 6,497,400 chance of drawing is 100%. That is, each time you draw four cards, drawing that specific combination is ridiculously unlikely, but you can be totally sure that whatever combination you draw will be nearly irreplicable. The uniqueness of each combination is a certainty, despite the incredibly unlikely makeup of the combination.
You, I, and everyone we meet are far more unlikely than drawing four aces in a row. But precisely because of our unlikelihood, we can be positive that each of us is unique. Statistically, to be rare is a certainty. And that’s pretty cool: the assurance that everybody is an anomaly.
We usually don’t think about this actively, but generally the way people decide when to leave in order to get somewhere on time is (Desired Arrival Time)-(Transit Time). Easy enough, if I need to show up at the dentist at 8 and it takes 15 minutes to drive there, I leave at 7:45.
However, most people do an awfully careless job of estimating “Transit Time.” As any statistician knows, the expected value of anything is the sum of (relative frequency)*(possible outcomes). In this case, possible outcomes (in time, since we want the answer to be in time as well) include anything that could go wrong on the trip, and obviously the relative frequency is the likelihood that it will go wrong on any given trip. So a good way to estimate transit time would be:
Continue reading “A statistical explanation for punctuality”