Monday, April 9, 2012

clustering illusion

In 2003, the mother of a child with leukemia in the Sacramento area thought it odd that there were several other people with cancer in her neighborhood. She did a survey and found what appeared to be an excessive number of cancers in the area. I can understand the woman’s desire to find something to blame for her child’s illness and I can also understand how the average person might be led to think that there must be something in the local environment that is causing the cancers. However, several things should be considered.

The woman’s boundaries extended to wherever she arbitrarily decided to draw them. She included all kinds of cancers in her survey, not just leukemia. She included people who had lived in the area for various amounts of time, ranging from having been born there to having moved into the area in adulthood.

Epidemiologists tried to explain that when you looked at the numbers, they weren’t that unusual and didn’t warrant investigation into an environmental cause. The data showed no difference in the leukemia rates in her area than in the rest of the Sacramento region. The Sacramento Bee took up her cause and eventually there was an official government analysis of the water supply that found no environmental toxins in the water. Still, the Bee persisted and identified tungsten found in tree rings as the probable culprit, even though tungsten is not a known human carcinogen and the connection between tungsten in trees and cancer in humans is speculative.

What the Bee and their experts were calling "a cancer cluster" is considered an example of the clustering illusion by epidemiologists: the intuition that random events which occur in clusters are not really random events. To some, the occurrence of a number of cancers in a defined space cries out for a causal explanation in terms of some unknown environmental hazard. To others, familiar with the data and knowledgeable of proper statistical analysis, the same number of cancers occurring within the same defined space is expected by the laws of chance.

The Centers for Disease Control investigated 108 cancer clusters between 1961 and 1990. None could be linked with environmental causes. It may seem improbable, but the chances are better than even that a given neighborhood in California will have a statistically significant cluster of cancer cases.

The clustering illusion is due to selective thinking based on a counterintuitive but false assumption regarding statistical odds. For example, it strikes most people as unexpected if heads comes up four times in a row during a series of coin flips. However, in a series of 20 flips, there is a 50% chance of getting four heads in a row. In any short run of coin flips, a wide variety of probabilities are expected, including some runs that seem highly improbable.

Sometimes a subject in an ESP experiment or a dowser might be correct at a higher than chance rate over a limited period of time. However, such results do not indicate that an event is not a chance event. In fact, such results are predictable by the laws of chance. Rather than being signs of non-randomness, they are actually signs of randomness. ESP researchers are especially prone to take streaks of "hits" by their subjects as evidence that psychic power varies from time to time.

A classic study done on the clustering illusion demonstrates just how hardheaded we are when it comes to facing facts that don’t support our beliefs. The study was done by Thomas Gilovich and some colleagues. It centered on the belief in the “hot hand” in basketball. It is commonly believed by basketball players, coaches, and fans that players have “hot streaks” and “cold streaks.” A detailed analysis was done of the Philadelphia 76ers during the 1980-81 season. It failed to show that players hit or miss shots in clusters at anything other than what would be expected by chance. Gilovich et al. also analyzed free throws by the Boston Celtics over two seasons and found that when a player made his first shot, he made the second shot 75% of the time and when he missed the first shot he made the second shot 75% of the time. Basketball players do shoot in streaks, but within the bounds of chance. It is an illusion that players are ‘hot’ or ‘cold’. When presented with this evidence, believers in the “hot hand” are likely to reject it because they “know better” from experience.

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