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Life Outside the Normal Distribution
Humans like regularity. Our brains drive us to seek out that which is predictable. If we could have our way, then everything would fall into neat categories. Unfortunately, the universe does not work this way. Nature is chaotic and scattered. Scientists must constantly work with randomness and try to extract the order. In our desire for consistency, humans often find patterns that are not there.
(Note: Friend and fellow science writer Harlan Brothers and I have started a new publication called “Science Spectrum” here on Medium where we will now be publishing our content. Please consider following our new pub to support our efforts!)
During the Scientific Revolution, many people studying nature became aware of its inherent uncertainty. This led to the development of probability theory and eventually modern statistics. However, uncertainty is almost always harder to deal with than we think. Despite making considerable progress in dealing with the unknown, we still tend to gravitate toward methods that provide clean and straightforward solutions.
In this article, I am going to talk about the most common technique for dealing with randomness: the normal distribution. While the normal distribution certainly has its uses, it has become far more widespread than its accuracy warrants. I am also going to give multiple examples of where this method goes wrong and provide some alternatives.
The Normal Distribution
If you ever took a statistics course, then you’ve certainly heard of the normal distribution. It is the ideal probability distribution for beginners since it can be described so simply. You only need the know the mean (μ) and standard deviation (σ). The mean tells us the average measurement or the peak of the curve, and the standard deviation tells us how “spread out” the data are.
If you’ve never seen a probability distribution before, it can be a little confusing. The x-axis just tells us the thing being measured, like human height, and the y-axis is the chance of that height occurring. The total area under the curve, otherwise known as the integral…
