In the first episode of 2024, the podcast continues with a direct paradox. What is the Simpson paradox? How can it influence meaningful data analysis? And how can you avoid falling for it?
Simpson's paradox describes the situation in which a statistical evaluation of an entire population produces a different result than an analogous analysis of the individual subpopulations. For example, it may be the case that the average income in all educational levels of a population decreases, while the average income of the entire population increases.
So how exactly can this apparent contradiction be resolved? As a statistician and fan of data analysis, why do we have to deal with this at all? Where does this paradox occur in the real world and how can we avoid succumbing to this misleading intuition?
Our blogging statisticians Dr. Sascha Feth and Dr. Jochen Fiedler discuss all these questions with host Esther Packullat in the new podcast episode »Misleading Intuition in Statistics – the Simpson Paradox«. The team focuses on practical examples that bring the paradox and its meaning to life in practice. At the same time, they warn against superficial or even deliberately misleading analyses, as the paradox is also suitable for targeted manipulation. Because here, too, the following applies: don't trust any statistics that you don't...understand very well!
50 people take part in a test on each of two days. On the first day, ten women and 40 men, on day two the exact opposite: 40 women and ten men. Now five out of ten women fail on the first day (i.e. 50 percent) and twelve out of 40 women fail on day two (30 percent). In total, 17 out of 50 fail (34 percent). For men, 16 out of 40 (40 percent) fail first and then two out of ten (20 percent). In total, 18 out of 50 fail (36 percent). Overall, men therefore have the higher failure rate (36 percent compared to 34 percent), while the failure rate for women was higher on each individual day (first 50 percent to 40 percent, then 30 percent to 20 percent).
Have you discovered an equally misleading phenomenon that you would like us to discuss or a statistic in the media and would like us to discuss it in the »Streuspanne«? Or have you noticed a mathematical number game or thought experiment? Then please get in touch with us.
The podcast is only available in German.
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What does a seesaw and income have to do with the Simpson paradox? Listen here!
Fraunhofer Institute for Industrial Mathematics ITWM