How can statistics be manipulated?
Definition lies with statistics
So that you can arm yourself against the charlatans of statistics, we show you popular tricks and tricks. Keep in mind: Despite their sometimes bad reputation, statistics have a lot of argumentative weight. In the words of the German statistician Elisabeth Noelle-Neumann: “For me, statistics are the means of information for the mature. Those who can deal with it are less easy to manipulate. The sentence "You can prove anything with statistics" only applies to the comfortable who do not feel like looking closely. "
A (fictitious) study records the age at which people in this occupational group die on average for various occupations. The result of the study is surprising. While pilots and professional footballers die on average under the age of 60, teachers and medical professionals live significantly longer. What is the reason? Dangerous working conditions, too much stress on the football field, too many aircraft accidents? No. The reason is that occupational groups are compared here that do not allow a direct comparison, because a third variable (besides occupation and age) interferes with the investigation: the average age. Real professional footballers have only been around since the 1960s and the aviation industry has grown rapidly in recent years. Accordingly, there are on average many more young pilots and professional footballers than young teachers and doctors. If footballers or pilots die young due to an accident or illness, these cases are more significant than in the other two occupational groups because there are fewer cases in their occupational group who die in old age.
Clothes make the man and digits make numbers - the more precise the numbers, the more we trust them. This trick was known in ancient Greece: Herodotus wrote after the Persian War that the enemy army consisted of exactly 5,283,220 men. The historian lied uncontrollably (there were probably around 15,000), but made an informed impression and the victory of the Greeks delighted and shone in a glorious light. The English theologian John Lightfoot also knew about the power of precision: "Heaven and earth and everything that goes with them were created by the Triune God together and at the same time: On Sunday, October 21, 4004 BC, 9 a.m.". With this accuracy, who can still doubt the date of the creation of the world?
But “sham accuracy” as a means of persuasion is not only reserved for antiquity: If today an economic report says that 1,450,000,000 overtime hours were worked in Germany every year, this figure should also be treated with caution. Based on around 40 million employees in Germany, this would be exactly 36.25 hours of overtime per person per year. But it is just as likely to be 33, 34, 38 or 40 hours per person. It would therefore be fair to say that the number of overtime hours in Germany is estimated to be between one and two billion.
"I'm a little skeptical of statistics," said Franklin D. Roosevelt, the 32nd President of the United States. “Because according to statistics, a millionaire and a poor guy each have half a million.” If a statistician adds the wealth of a millionaire and the poor and divides the sum by two, he calculates two half-millionaires. Sounds exaggerated, but it hits a statistical problem. In statistics, the average is called the arithmetic mean, or the shorter mean.
Whenever extreme values occur in a group, the mean value should be treated with caution - especially if the group is not particularly large. But doesn't this always balance out over the large number? Let's take a small Swabian town with 10,000 households as an example: On average, this small town has a household income of 42,000 euros per household per year (it is an affluent region). In the coming year the König family will move to the village - thanks to a trading empire, the annual income of this household is 200 million euros a year. Statistically, the small town no longer earns 420 million euros a year (10,000 households times 42,000 euros), but 620 million euros. The average household now has 62,000 euros available - at least in the statistics. Extreme numbers have a strong effect on the mean, even in large groups.
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