A Statistical Odyssey

Selection bias occurs when the participants chosen for a study or survey do not represent the whole group. For example, suppose you want to know what percentage of the population likes chocolate, and you conduct your survey at a chocolate factory. In that case, your survey results will be skewed by selection bias.

If a variable is unusually high or low on one occasion, it will likely be closer to the average on the next occasion. This phenomenon is called regression to the mean. For example, if an athlete performs exceptionally well one day, chances are they will have a closer to average performance the next day.

Imagine a coach praises athletes whenever they do well and notices that they tend to perform worse the next day. If he assumes that the poorer performance is caused by the praise, he ignores the more likely explanation that it is the result of regression to the mean.

Correlation means two variables move together. Causation indicates one variable directly affects the other. A correlation between two things can exist with or without causation. For instance, ice cream sales and drowning incidents are correlated because both increase in summer. However, eating ice cream doesn't cause drowning. Assuming that correlation always means indicates can lead to false conclusions.

If you look at a collection of randomly generated points on a map, you will likely see some clusters of points. This is because randomly spaced points are not necessarily evenly spaced.

Similarly, if you flip a coin 100 times, you will likely see a streak of heads somewhere in there—this is just what randomness looks like.

When we see meaning or patterns in clusters or streaks that are simply random, we fall for the clustering illusion.

Adaptive bias is the concept that the human brain prioritizes keeping us safe over making rational decisions. For example, people have a tendency to judge familiar things more favourably than unfamiliar things. Biases that kept us safe in the past may still influence our thinking even when they no longer apply.

The gambler's fallacy is the mistaken belief that, in a series of independent events, past outcomes influence future ones.

Example: Someone flips a coin and gets heads 5 times and thinks that tails is more likely on the next flip.

The base rate fallacy, also called base rate neglect, is the tendency to rely too heavily on specific details while ignoring general statistical information.

Example: “50% of milk food poisoning cases in the US are from pasteurized milk, so pasteurized milk is no safer than raw milk.” This neglects to consider that over 99% of milk consumed in the US is pasteurized.

This is the mistake of overlooking people or things that didn't make it past a selection process because they are less visible.

Example: You decide to implement strategies used a by a high percentage of successful businesses without considering whether an even higher percentage of failed businesses used these same strategies.

Simpson's paradox is a statistical phenomenon in which a trend disappears or reverses when you combine or split a group of data.

Example: A university has an overall lower acceptance rate of women than men, but women have higher acceptance rates in each department. (It turns out that women applied to more competitive departments.)

Yes! Check out A Statistical Odyssey for the Classroom for a short explanation of how to utilize this course in a school setting.