A study of new diagnosis of kidney cancer across the United States’ counties reveals that the counties in which the incidence of kidney cancer is lowest are rural, sparsely populated counties in the Midwest. The counties in which the incidence of kidney cancer is highest are also rural, sparsely populated counties in the Midwest. Even though one might think that something about the location of the counties explains these facts, the key factor is actually that rural counties have small populations.
The descriptions of the counties with both the highest and lower kidney cancer incidence reveals our immediate and automatic search for causality. When we read the first fact, we instantly work to explain why rural, sparsely populated counties have low incidence of kidney cancer—that is, until Kahneman reveals that those same counties have the highest incidence.
System 1 is inept when faced with “merely statistical” facts, which change probabilities of certain outcomes but do not cause them to happen. Kahneman asks readers to imagine a large urn filled with marbles. Half the marbles are red, and half are white. Two people—Jack and Jill—each draw marbles. Jack draws four marbles each time, Jill draws seven marbles each time. They both record each time they observe a homogeneous sample—all red or all white. Jack will observe these extreme outcomes much more often than Jill (12.5% of the time versus 1.56% of the time). It is a statistical fact that samples of four marbles yield extreme results more often than samples of seven marbles do.
The moral of this chapter is that because of System 1’s ongoing quest to make sense of the world, we have a very difficult time accepting randomness when there are facts that might help us explain causality and construct a story. Kahneman tries to counteract this impulse by demonstrating mathematically (though still through constructing a story) how smaller samples simply yield more extreme results.
This purely statistical fact explains the statistics of kidney cancer in rural areas. Extreme outcomes (both high and low) are more likely to be found in small than large samples. There is no causal explanation: small populations do not cause nor prevent cancer. This principle makes some sense to people: we have long known that the results of large samples deserve more trust than small samples.
Even though we have learned that large sample sizes are important and more accurate, we still have a difficult time understanding why on the most basic level, revealed by our inability to identify the correct explanation for the cancer incidence example.
Kahneman and Tversky’s work in the early 1970s began with an exploration of whether people who have no training in statistics are good “intuitive statisticians.” This is particularly important in the field of psychology because it is crucial in research to choose a sample size that can accurately prove one’s hypothesis. The risk of error for a given sample size can also be calculated fairly simply.
The difficulty that people have with understanding statistics does not merely lead them to attribute incorrect explanations to different scenarios, as Kahneman explores throughout the chapter. The misunderstanding of statistical principles can have a large effect on people’s time, work, and money.
Kahneman had read shortly before his work with Tversky that psychologists commonly chose samples that exposed them to a 50% risk of failing to confirm a true hypothesis, and found that he often made those same mistakes by relying on intuition and tradition. The pair developed a questionnaire that described a research situation and asked researchers to choose the sample size. Kahneman saw that the mistakes he had made were shared by a large majority of the respondents.
Kahneman’s and other psychologists’ errors have echoes with some of the errors explored in earlier chapters. Even though the psychologists could avoid their errors with slightly more effort, they instead rely on their intuition to judge sample size and as a result end up making errors that could change the outcome of their research.
Kahneman next presents a statement: “In a telephone poll of 300 seniors, 60% support the president.” The summary of this poll is “elderly support president.” Unless people are professionals, they may not react differently to a sample of 300 vs. 3,000. When reliability is obviously low, we discredit the message. But it’s difficult to distinguish between degrees of belief. We usually believe smaller sample sizes because we are prone to exaggerate the consistency and coherence of what we see.
Again, as Kahneman wrote in earlier chapters, we have a difficult time understanding the significance of numbers in a given context. We know that a sample size of 3,000 is better than a sample of 150, but it is likely that we would believe the information in both studies. The story that the study creates is more resonant to us than the “degree of belief” it carries.
Our preference towards causes exposes us to serious mistakes in evaluating randomness. Kahneman proposes a scenario: looking at the sex of six babies born in sequence at a hospital. The sequences BBBGGG, GGGGGG, and BGBBGB are equally likely, though our intuition biases us into thinking that BGBBGB is more likely. We do not expect to see regularity produced by a random process.
In addition to discounting sample size, we are biased towards believing causality over randomness. When we detect what appears to be a rule (like six girls being born in a row), we reject the idea that the process is random—even though we know that there is always equal probability between the birth of a boy and the birth of a girl.
Kahneman soon applied this principle in his own work. When the Yom Kippur War broke out in Israel in 1973, Kahneman was working in the Israeli Air Force. At first the air war was going quite badly for Israel because of the performance of Egyptian ground-to-air missiles. In two squadrons that flew from the same base, one of them lost four planes while the other lost none. An inquiry was conducted in the hopes of finding out what the unfortunate squadron did wrong. But Kahneman saw that with no operational differences between the two, the command should accept that the different outcomes were due to blind luck.
Like the sequence of six girls being born in a row, the fact that one squadron lost four planes and the other lost none seemed to imply that something within the unlucky squadron must have caused their losses. It follows the same principle: when we observe patterns, we reject that the idea that there is randomness or luck involved. We prefer to form a story that can help us avoid similar issues in the future.
The illusion of causality has many forms: it makes us think that there is a “hot hand” in basketball, that a certain investment adviser is unusually skilled, or that a CEO is particularly talented at making acquisition deals. Often, we misclassify random events as systematic.
Kahneman finishes the chapter by providing an example that mirrors the one about cancer incidence. Research has shown that the most successful schools were, on average, small schools. The Gates foundation then made a $1.7 billion investment in the creation of small schools. This makes intuitive sense: small schools give more personal attention and encouragement to students. But the facts are wrong: if the studies had looked at the worst schools, they also tend to be smaller than average.
Kahneman’s final example is also perhaps its most shocking. Both the researchers in this story and the executives at the Gates foundation made the same mistake in ignoring the fact that smaller samples provide more extreme results. But this example in particular shows the consequences of those mistakes: 1.7 billion dollars to build schools that might not, in fact, be better.
We pay more attention to the content of messages than to information about reliability, and statistics produce many observations that ask for causal explanations but in fact do not have causal explanations. Many facts of the world are simply due to chance.
Kahneman’s conclusion supports a major thematic idea: that we vastly prefer objective stories over subjective numbers, both when we ignore sample sizes and when we assume causation.