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## Car Accident Statistics

Here we discuss an example illustrating how people sometimes come to wrong conclusions when interpreting statistical data.

In a study of car accidents it was observed that, among the total number of accidents considered in the study, in 200 cases a driver was talking on a cell phone, and in another 200 cases a driver was listening to music or to the radio. The researchers concluded that listening to the radio and music is as distracting as talking on the phone. What is wrong with this conclusion?

This conclusion doesn't take into account the number of people who listen to music as opposed to the number who talk on the phone. Imagine, for example, that only 200 people in the US talk on the phone while driving. That means that all of them get into accidents. In this hypothetical case we can say that talking on the phone is extremely distracting - a person is destined to be in an accident. Also, the conclusion doesn't take into account the time spent on each activity.

Let's call the "distraction level" of an activity the probability of getting into a car accident while driving and performing this activity for one hour. Our Distraction Estimator below uses the fact that the number of car accidents involving talking on the phone is the same as the number involving listening to the radio or to music; it estimates which of these two activities is the more distracting, based on the percentage of time an average driver spends on each activity. You can enter different percentages yourself and see the effect on the Distraction Level.

Distraction Estimator

Below is another Distraction Estimator that estimates the same thing in a different way, using inputs that you may find easier to guesstimate. It starts by assuming that listeners and talkers spend the same amount of time on the road on average as non-listeners and non-talkers. It may be that this is not the case. For instance, it could well be that people who drive a lot are more easily bored by their time on the road and are more inclined to listen to something. For this reason you can also enter your guess of the ratio of the average time spent on the road for listeners to the time spent by non-listeners. For instance, if you think people who listen to the radio or to music spend, on average, twice as much time on the road as people who don't turn on their radio or music player, then you enter 2.

Extended Distraction Estimator

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