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Unusual Events

If the research question being studied involves unusual events, the mean or median is not adequate as a summary statistic.


1. If you are deciding what capacity air conditioner you need, the average yearly (or even average summer) temperature will not give you guidance in choosing an air conditioner that will keep your house cool on the hottest days. For this purpose, it would be much more helpful to know the highest temperature you might encounter, or how many days you can expect to be above a certain temperature.

2. Traffic safety interventions typically are aimed at high speed situations. So the average speed is not as useful as, say, the 85th percentile of speed.

3. Pregnancy interventions are often aimed at reducing the incidence of low birth weight babies. Neither the mean nor the median birth weight in a population gives you information about low birth weight babies, so neither the mean nor the median is a suitable summary statistic in this situation. However, percentage of births in the low weight category might be a suitable summary statistic. ("Low weight" might be defined as weight in a range know to be associated with greater risk of health problems, or it might be defined as weight below a certain percentile of a reference population of newborns.)

4. If two medications for lowering blood pressure have been compared in a well-designed, carefully carried out randomized clinical trial, and the average drop in blood pressure for Drug A is more than that for Drug B, we cannot conclude just from this information alone that Drug A is better than Drug B. We also need to consider the incidence of undesirable side effects. One might be that for some patients, Drug A lowers blood pressure to dangerously low levels. Or it might be the case that for some patients, Drug A actually increases blood pressure. Thus in this situation, we need to consider extreme events in both directions.

Unusual events such as earthquakes and extreme behavior in the stock market can have large effects, so are important to consider. They have come to be called "Black Swan Events," a term coined in the 2007 book The Black Swan1, by risk analyst Nassim Nicholas Taleb.

Many techniques have been developed for studying unusual events; however, these techniques are not usually mentioned in introductory courses in statistics. And, like other statistical techniques, they are not "one-size-fits-all." Some references are given below.2,3

1.   Taleb, N. N. (2007) The Black Swan: The Impact of the Highly Improbable, Random House. See also the "Special Section: Reviews of The Black Swan" in The American Statistician, Vol. 61, No. 3, August 2007, pp. 189 - 200, and the review by David Aldous. Taleb's earler book, Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets (Random House, 2001) may also be of interest.

2. For extreme events, references include:

3. For questions involving quantiles (percentiles), quantile regression may be useful.

Last updated June 19, 2015