What are some commonly misunderstood statistics

Three pitfalls when interpreting statistics

Dr. Thomas Petersen

In the daily newspaper “Die Welt” an article appeared in September last year with the headline “Smartphones make seniors eight years younger.” A study has shown that older people are more intellectually efficient today than they were a decade ago, which can be attributed to the use of smartphones be. The proof: Seniors who deal with communication technology are mentally fitter than those who keep their hands off it.

This article deserves a place of honor in social science textbooks because it combines two of the three most common misinterpretations that lead to statistical information from market and social research being misunderstood.

On the one hand, the editor fell for a so-called "sham correlation": When two things are statistically related, one tends to interpret them as cause and effect. But that can be a mistake: In the last decade, the number of people who own a smartphone has increased and, at the same time, the mental fitness of the elderly has increased. It quickly becomes the interpretation that smartphones are smart. But it could just as well be said that dishwashers promote mental fitness. Their use has also increased. In fact, the growing efficiency is due to older advances in medicine. It has nothing to do with smartphones.

But doesn't that leave the finding that older people who use modern cell phones are more mentally fitter than those who don't? Here lies the second mistake: confusing cause and effect. You just have to swap both in your mind as a trial and then the supposed sensation turns into the banal message that intellectually active people are also more willing to get involved with new technology. The pioneer of survey research Elmo Roper would have said: "So you mean, because the crickets are chirping, does the sun go down?"

Finally, the third common mistake is the method of misleading the viewer with correct numbers by choosing the wrong scale for them. There is also an example of this from the newspaper “Die Welt”. Last year she published an article with the headline "Chart of doom prophesies stock market crash." The accompanying chart shows the development of the Dow Jones Index in the years 1928 to 1930 and 2012 to 2014 in comparison. The agreement was fascinating: the line that showed the development from 2012 to 2014 was practically congruent with the line that showed the data from 1928 to 1929 until shortly before »Black Friday«. Accordingly, the graphic suggested, a huge stock market collapse should follow in the coming days.

Practically no one noticed that the lines were congruent only because different scales had been selected for them. In fact, the index had doubled in just under two years from 1928, while it had only increased by about a fifth from 2012. Investors who knew how to read the graphics could save themselves the panic.

Once you have seen through the logic, you will be amazed at how widespread such misinterpretations are, not least in market research and advertising. With a little practice, however, you can easily recognize the warning signs, for example when impressive growth rates are reported, but not about the initial level of growth, or when a manufacturer of sports nutrition advertises the health of its customers. You can see that it is worthwhile to deal with at least some basic rules of statistical logic, especially when business decisions are to be based on statistical data. The prejudice is correct: you can actually prove almost anything with statistics - but only to the naive observer.

Born in Hamburg in 1968. Studied journalism, ancient history and prehistory at the University of Mainz from 1987 to 1992. 1993 Magister. 2001 PhD. 2010 habilitation. 1990 to 1992 journalist at Südwestfunk in Mainz. Since 1993 research assistant at the Institute for Demoscopy Allensbach, since 1999 project manager. Since 1995/1996 teaching positions at various universities, including University of Mainz, TU Dresden, University of Technology and Economics Berlin. 2007/2008 representation of the professorship for methodological and historical foundations of political science at the University of Hamburg. Past President of the World Association for Public Opinion Research (WAPOR).

Research focus: methods of demoscopy, field experiments, visual communication, political communication, election research, market and social research, theory of public opinion.

Does the shape of the graphic shown correspond to the informative value of the data? Are the labels and scales correct? Is all the information necessary for a complete understanding included? Graphic visualizations for data presentation are not always useful. Sometimes the good old-fashioned table remains the best form of presenting data.

Developed from daily practice in dealing with statistical figures and their implementation in graphics and diagrams, the brochure shown on the right (2nd edition from 2011) points out sources of error and shows how things could be done better.

The examples appeared for the first time in the January 2006 to December 2007 editions of the Baden-Württemberg Statistical Monthly Bulletin. The author of the articles is Wolfgang Walla, who was head of the department and at the same time editor of the monthly statistical magazine until his retirement.

Order number: 8020 11001

The publication is available for free download as a PDF file on the Internet at www.statistik-bw.de/Service/Veroeff/Querschnittsver!F6ffnahmungen/802011001.bs.