How could I improve my statistical thinking?

Method & Didactics School year 10-13

Maren Sauer

Risk literacy

Gerd Gigerenzer's plea for statistical education

In April this year, DLF-Nova broadcast a lecture that can be understood as a welcome plea from a teacher's perspective - as a plea for a society that recognizes and strengthens the content of math lessons in their practical and political significance and thus allows a meta-level of teaching: Gerd Gigerenzer, psychologist, director emeritus at the Max Planck Institute for Human Development (Berlin) and one of the authors of the so-called “Unstatistics of the Month” explained the relevance of an early training in “statistical thinking” with plenty of anecdotes.

"Have the courage to know"

... this motto of Kant fails grandiose in the breadth of today's society, according to Gerd Gigerenzer. The psychologist is primarily concerned with “dealing with risk and uncertainty” - as the title of his lecture tells us. He seems to regard the competent handling and interpretation of statistics and probabilities as the basis for a realistic (opportunity and) risk assessment as an absolute prerequisite for democratic coexistence.

Many research projects that Gerd Gigerenzer carried out in the past illustrate, however, that there could be a lack of “using one's own understanding” (Kant) and that instead, foreign interpretations or everyday theories prevail:

“If you go on the internet and look at tomorrow's weather and you read, 'The probability that it will rain tomorrow is 30%.” What does that mean? We did a survey in many cities around the world and asked people. [...] Most Berliners are of the opinion: a 30% chance of rain means that it will rain 30% of the time tomorrow. So seven to eight hours. Others say it means 30% of the area will rain tomorrow. So probably not where I live. […] A woman in Athens said to us: 'I know what a 30% chance of rain means. Namely, three meteorologists think it's raining and seven don't. ‘This example illustrates the following: We are surrounded by probabilities and percentages. We think we'd understand. But if you look closely, everyone understands something different. "

The lecturer advocates a lesson that teaches "mathematics of uncertainty" by constantly questioning both numbers and interpretations and allowing uncertainties as a result.

"Every 11 minutes ..."

Inadequate and therefore underage math skills are accepted even in elitist circles today, and are actually a means for a basis of understanding closeness between largely unknown people. And industry and politics know how to deliberately use this broad self-image of inability to exert influence.

Gerd Gigerenzer clarifies a pink and red dream: “Every eleven minutes a single falls in love through Parship. Sounds good? You pay for it and then you wait eleven minutes ... Or maybe another eleven? That would be great news if Parship only had a hundred members! Start thinking. Six fall in love every hour. Now let's assume that we are out and about 24 hours a day, looking for partners. So 24 times six is ​​144. Then we do the search for a partner 365 days - it comes out around 50,000. Allegedly Parship has between four and five million ... - let's say if they only had a million of premium members. So if 50,000 fall in love out of a million in one year - it's 5%. So 95% don't fall in love. In the year. [...] So if you want a good chance of falling in love like this, then you've got to wait more than ten years. Maybe you should try the conventional method. "

Do you know the relative risk?

While this is “only” about misleading advertising promises, other of his examples show that media with selective presentations or inappropriate articulation of basically harmless statistics stir up panic: “Recently, Focus-Online brought the news: 'Fatal shark attacks around 100 % increased. 'You are now on vacation in the Mediterranean. Are you still letting your children into the water? […] What will they do then? The answer is: thinking. Well - that's a relative risk. In the previous year, the absolute number of people killed by sharks was six worldwide. There is almost no animal that kills fewer people than sharks. And that year it rose to twelve. […] The likelihood that you will be killed in your car if you drive to the beach is much higher than that of a shark. So if you're worried about your life, it's not about the sharks. "

"Collective number blindness" is particularly common when dealing with relative and absolute probabilities, which the above example also requires. The proclamation of “100%” in the title appears to be overpowering and all-encompassing, because you learned: 100% is a whole. However, this only applies to an absolute probability. The fact that a change in probabilities, on the other hand, requires a starting or “basic value” and, in case of doubt, a quick calculation of the rule of three, is often ignored in everyday life.

For this reason, Gerd Gigerenzer advocates a consistent explanation by means of absolute frequencies - for example 3% becomes 3 out of 100 people and an increase of 100% results in 6 out of 100 people. Absolute frequencies contain an imagery that probabilities cannot offer. This could be a step towards "honest communication", which would become even more important in times of fake news.

Plea for (early!) Statistical education

Of course, the understanding of statistics must be promoted across society and especially in professions in which a lot depends on understanding numbers, for example among medical professionals. According to Gerd Gigerenzer, even mathematics lessons should be understood in a certain way in an enlightening way and should therefore be taken into account: “You could learn such examples in school. And children are happy when they learn what their parents don't understand. Then they can go home and say, 'Dad? Do you know what a 30% chance of rain means? ‘And then you can see that you can learn something useful in school!"

To listen to

Lecture G. Gigerenzer: Dealing with Risk and Uncertainty - How to Make the Right Decisions

For further reading

The "unstatistics of the month" regularly questions published figures and their interpretations

Teaching mathematics 197: Basic statistical education

teaching math 194: use math!?!

Stochastics blog: prenatal diagnostics

Method & Didactics School year 10-13