# Clustering Illusion: See the Bigger Picture

#### Problem

During World War II, German forces laid siege on Britain with a string of bombings in central London. A handful of neighborhoods were particularly hard hit by the attacks, while others saw less damage. Many citizens deemed the heavily bombed areas more dangerous than the others and speculated that the Germans specifically targeted these places. However, a statistical analysis of the bombing locations revealed that there was no correlation in their locations. In fact, the bombings were completely random. So why did many Londoners assume there were designated targets, when in reality, there were not?

#### Explanation

Thomas Gilovich, the psychologist who ran the statistical analysis of the bombing locations, credited the Londoners’ sense of being targeted to the clustering illusion. The clustering illusion occurs when similar data points within a random sample appear to be in clusters, seemingly indicating a correlation. It is not uncommon for data points to aggregate in certain areas, but a single cluster is not necessarily indicative of a pattern across an entire data set. These false patterns become misleading when making assessments of the sample data.

#### Clustering Illusion Definition

The clustering illusion is a cognitive bias that leads people to falsely detect non-random patterns or clusters in randomly distributed data samples.

#### How It Works

Two preeminent scholars on the clustering illusion are psychologists Daniel Kahneman and Amos Tversky. Kahneman and Tversky assert that the clustering illusion is caused by the representativeness heuristic, a cognitive shortcut whereby a small sample of data is assumed to be representative of the entire population from which it is derived. The human brain wants to see patterns and trends in data since they’re easier to comprehend and extrapolate conclusions from. In other words, if there seems to be a non-random pattern in a small subset of data, people tend to believe that the entire sample also contains that non-random pattern. This is often untrue, giving rise to the clustering illusion. Many people underestimate the amount of variability present in random samples and mistakenly conclude that a non-random pattern exists.

#### So What?

The clustering illusion is dangerous for individuals whose jobs rely on pattern detection and large samples of data. For example, economists and investors must be wary of the clustering illusion when determining where to invest their money. If a certain company yields high returns in the short-term, it is not necessarily indicative of their long-term performance. Their successes may be clustered into this short timespan, giving the impression that they will continue this pattern in the future. This is, of course, subject to change, so investors must be careful not to fall too deep into the clustering illusion trap.

The clustering illusion has social implications, as well. Say, for example, you are moving to a new city and must decide which neighborhood to live in. You look at crime rates for various areas and find that two of the city’s six main boroughs have more reported robberies than the others. You may be led to believe that crime is localized to these particular areas. However, the total number of thefts may be randomly distributed throughout the area, with no statistically significant difference in the number of reported robberies between each neighborhood. In this case, your decision-making is biased by the clustering illusion. This bias may spill over into your assessments of the residents of these neighborhoods, too, leading you to make incorrect judgments of the dangerousness of certain people and affecting your behavior around them. The lesson here is that it is vital to look at the big picture before drawing conclusions from apparent clusters of data, which may not be representative of the entire sample.

## Think Further

1. What are some other real-life examples of the clustering illusion?
2. Have you ever experienced the clustering illusion? How did you come to realize you were affected by it?
3. How might we overcome the clustering illusion?