Paradoxes Of Probability And Other Statistical Strangeness

Statistics and probability can sometimes yield mind bending results. Shutterstock

Kristy Hamilton 13/04/2017, 22:52

The Conversation

Statistics is a useful tool for understanding the patterns in the world around us. But our intuition often lets us down when it comes to interpreting those patterns. In this series we look at some of the common mistakes we make and how to avoid them when thinking about statistics, probability and risk. The Conversation


You don’t have to wait long to see a headline proclaiming that some food or behaviour is associated with either an increased or a decreased health risk, or often both. How can it be that seemingly rigorous scientific studies can produce opposite conclusions?

Nowadays, researchers can access a wealth of software packages that can readily analyse data and output the results of complex statistical tests. While these are powerful resources, they also open the door to people without a full statistical understanding to misunderstand some of the subtleties within a dataset and to draw wildly incorrect conclusions.

Here are a few common statistical fallacies and paradoxes and how they can lead to results that are counterintuitive and, in many cases, simply wrong.


Simpson’s paradox

What is it?

This is where trends that appear within different groups disappear when data for those groups are combined. When this happens, the overall trend might even appear to be the opposite of the trends in each group.

One example of this paradox is where a treatment can be detrimental in all groups of patients, yet can appear beneficial overall once the groups are combined.

How does it happen?

This can happen when the sizes of the groups are uneven. A trial with careless (or unscrupulous) selection of the numbers of patients could conclude that a harmful treatment appears beneficial.

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