A Field Guide to Lies: Critical Thinking in the Information Age Read Online Free

Democratic candidate, John Kerry, won nine of the eleven wealthiest states. However, 62 percent of those with annual incomes over $200,000 voted for Bush, whereas only 36 percent of voters with annual incomes of $15,000 or less voted for Bush.
    As an example of the exception fallacy, you may have read that Volvos are among the most reliable automobiles and soyou decide to buy one. On your way to the dealership, you pass a Volvo mechanic and find a parking lot full of Volvos in need of repair. If you change your mind about buying a Volvo based on seeing this, you’re using a relatively small number of exceptional cases to form an inference about the entire group. No one was claiming that Volvos never need repair, only that they’re less likely to in the aggregate. (Hence the ubiquitous cautionary note in advertising that “individual performance may vary.”) Note also that you’re being unduly influenced by this in another way: The one place that Volvos needing repair will be is at a Volvo mechanic. Your “base rate” has shifted, and you cannot consider this a random sample.
    Now that you’re an expert on averages, you shouldn’t fall for the famous misunderstanding that people tended not to live as long a hundred years ago as they do today. You’ve probably read that life expectancy has steadily increased in modern times. For those born in 1850,the average life expectancy for males and females was thirty-eight and forty years respectively, and for those born in 1990 it is seventy-two and seventy-nine. There’s a tendency to think, then, that in the 1800s there just weren’t that many fifty- and sixty-year-olds walking around because people didn’t live that long. But in fact, people did live that long—it’s just that infant and childhood mortality was so high that it skewed the average. If you could make it past twenty, you could live a long life back then. Indeed, in 1850 a fifty-year-old white female could expect to live to be 73.5, and a sixty-year-old could expect to live to be seventy-seven. Life expectancy has certainly increased for fifty- and sixty-year-olds today, by about ten years compared to 1850, largely due to better health care.But as with the examples above of a room full of people with wildly different incomes, the changing averages for life expectancy at birth over the last 175 years reflect significant differences in the two samples: There were many more infant deaths back then pulling down the average.
    Here is a brain-twister: The average child usually doesn’t come fromthe average family. Why? Because of shifting baselines. (I’m using “average” in this discussion instead of “mean” out of respect for a wonderful paper on this topic by James Jenkins and Terrell Tuten, who used it in their title.)
    Now, suppose you read that the average number of children per family in a suburban community is three. You might conclude then that the average child must have two siblings. But this would be wrong. This same logical problem applies if we ask whether the average college student attends the average-sized college, if the average employee earns the average salary, or if the average tree comes from the average forest. What?
    All these cases involve a shift of the baseline, or sample group we’re studying. When we calculate the average number of children per family, we’re sampling families. A very large family and a small family each count as one family, of course. When we calculate the average (mean) number of siblings, we’re sampling children. Each child in the large family gets counted once, so that the number of siblings each of them has weighs heavily on the average for sibling number. In other words, a family with ten children counts only one time in the average family statistic, but counts ten times inthe average number of siblings statistic.
    Suppose in one neighborhood of this hypothetical communitythere are thirty families. Four families have no children, six families have one