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Misinterpretation of Probabilities

Single-event probabilities can lead to miscommunication because people tend to fill in different reference classes. This type of miscommunication happens frequently with mundane statements such as those made in weather reports:
Example: ‘There is a 20 percent chance that it will rain tomorrow’.
Some people think that it will rain 20 percent of the time, others that it will rain in 20 percent of the area, and still others that it will rain on 20 percent of the days that are like tomorrow. Although the third option is the intended message, approximately two thirds of the people will interpret this statement incorrectly.

Conditional probabilities

Information in the form of conditional probabilities is often misinterpreted. Sometimes it is difficult to make inferences on the basis of probabilities.
Example: The statement ‘If a woman has breast cancer, the probability that she will test positive on a screening mammogram is 90%’ is often confused with the statement ‘If a woman tests positive on a screening mammogram, the probability that she has breast cancer is 90%’.

Relative risks

One of the most common means of describing clinical benefits in the world of medicine and public health is the relative risk reduction. Since relative risks are larger numbers than absolute risks, results presented in this manner appear to be greater than the same results presented as absolute risk reductions.
Presenting benefits as absolute as absolute benefits or in terms of the number needed to treat to save one life are two simple examples of ways to make results more understandable.

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