Here’s an excerpt from a lovely little book by John D. Barrow called One Hundred Essential Things You Didn’t Know You Didn’t Know; Math Explains the World. This selection has a great lesson about statistical inference. The chapter is entitled, “Why does the other queue always move faster?”
You will have noticed that when you join a queue at the airport or the post office, the other queues always seem to move faster. When the traffic is heavy on the motorway, the other lanes always seem to move faster than the one you choose. Even if you change to one of the others, it still goes slower. In fact, the reason you so often seem to be in the slow queue may not be an illusion. It is a consequence of the fact that on the average you are usually in the slow queue.
The reason is simple. On the average, the slow lines and lanes are the ones that have more people and vehicles in them. So, you are more likely to be in those, rather than in the faster moving ones where fewer people are.
The proviso “on the average” is important here. You won’t invariably be in the slowest line, but on the average, when you consider all the lines that you join, you will be more likely to be on the more crowded lines where most people are.
This type of self-selection is a type of bias that can have far-reaching consequences in science and for the analysis of data, especially if it is unnoticed. Suppose you want to determine if people who attend church regularly are healthier than those who do not. There is a pitfall that you have to avoid. The most unhealthy people will not be able to get to church and so just counting heads in the congregation and noting their state of health will give a spurious result.
When we do science or are confronted with data, the most important question to ask about the results is always whether some bias is present that leads us preferentially to draw one conclusion rather than another from the evidence.
Paul Levy is the former President and CEO of Beth Israel Deaconess Medical Center in Boston and blogs at Not Running a Hospital. He is the author of Goal Play!: Leadership Lessons from the Soccer Field and How a Blog Held Off the Most Powerful Union in America.