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Date of publication: 2017-08-29 21:16

The alternative is to make guesses from the knowledge of individual cases, and this is likely to be very misleading. The trouble is that we are likely to only know of a few cases personally, and they might not be very representative of the overall situation. For example, someone might know one person who was killed in a car crash despite wearing a seatbelt and nobody who was killed without one, and therefore falsely assume the seatbelt was detrimental. However, if we look at a large number of traffic accidents, statistics show that seatbelts make driving substantially safer, and this information is a much better guide to what is likely to happen to us.

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Sports announcers always want to inject as much excitement as possible into the games they announce, so they will find any way they can to make what happens into some kind of a record. We often hear things like "That give him the team record for most yards gained from scrimmage by a running back in the first quarter." Players on other teams may have gained more, players who weren't running backs might have gained more, players may have gained more in other quarters, and players who weren't starting from scrimmage (as when returning kicks) may have gained more. Other players presumably have the records for all of these. With so many qualifiers available, sportscasters can concoct some impressive facts for almost any game we watch.

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One way that statistics can be made to sound more impressive is by putting qualifications on them that might not seem important, but really are. One example is the statement that "The brown bear is the largest land predator in the world." I presume this is true, but it's safe to assume that the words "land" and "predator" wouldn't have been included if they didn't rule out other animals. The word "predator" rules out elephants, which are bigger but aren't predators, while "land" rules out various kinds of whales which are bigger predators but don't live on land. The two qualifiers together create a category in which the brown bear comes out first.

Nevertheless, recognizing that statistics people present to us are frequently flawed doesn't imply that we can depend on anecdotes about individual cases or a few our own experiences. These are likely to be atypical of what happens in the world at large. Instead we should withhold judgment until we can get more reliable information about what is really going on.

Even when statistics are technically accurate, particular statistical facts can be very misleading. I once heard a statistic that the rate of teenage pregnancy in a conservative religious group was higher than the national average. This seemed surprising until it became apparent that the reason wasn't a high percentage of unwed mothers - it was a high percentage of women who got married while still in their teens.

Most often, statistics are obtained by taking a sample from a larger group and assuming the whole group has the same characteristics as the sample. For example, if we ask 655 people who they are going to vote for in the next election, and 55 of them say they will vote for Murphy, we might assume that about 55% of all the voters will vote for Murphy. This is very useful, since we can't possibly ask all the voters, but it has some important limitations.

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