![]() It doesn’t really matter for our purposes how this measurement is done, just that we can take a measure. Take the conversation that spawned this post as an example: someone said that a subculture had grown “less distinct” over time, but for a subculture to be less or more distinct means we must be able to measure it in terms of distinctness. Being able to use regression to the mean as an explanation is one such opportunity. I might not go as far as Jacob Falkovich in my desire to put numbers to things, but a lot of opportunities open up if you think of the world as measurable, even when it seems totally impossible to take measurements. After all, regression to the mean applies to variance too.īut you probably don’t care much about how tall people are, so I hope you are asking yourself “what else can I use this for?”. For example, if a person is only 1 inch taller than average but the variance in height is 6 inches, the next person is more likely to be more than 1 inch shorter/taller than average than the last person and thus farther away from the mean. The distinction is important because for observations close to the mean the opposite - that the next person is farther away from the mean than the previous person - is more likely to be true because of variance. Note though that regression to the mean does not imply that the next person to walk by will likely be closer to the mean, just more likely to be in the direction of it relative to the last sample. You know the heights of the people you’ve seen in the park, so if you charted a histogram of their height measurements you’d get a picture that looked approximately like this: ![]() There are several ways to understand why this works, but I think the most straightforward is to think in terms of sampling from a distribution. So if a short person walks by, you tell your friend the next person is likely to be taller and vice versa, and most of the time you will be right! Whatever the distribution of the heights of the park goers, each person who walks by, lacking any other information to inform your decision, is likely to be in the direction of the mean within the height distribution relative to the previous person. Regression to the mean tells you how to answer this. After some time a friend joins you on the bench and, hearing about what you’ve been doing, ask you if the next person to walk by is likely to be taller or shorter than the last person who did. You notice the height of each person that passes you and develop a sense for how the height of people at the park is distributed. Suppose you are sitting on a park bench, watching people walk by. So to atone for my sin of neglecting the most likely reason anything ever happens, I present to you my penance - an introduction to regression to the mean.
0 Comments
Leave a Reply. |