Deceiving People with Statistics
We are surrounded by all kinds of irrelevant and misleading information produced by poorly presented numbers when we are to come to a decision. Statistics as a discipline provides us tools to evaluate our options properly and to ensure the rationality of our decision, however misusing statistics is also a very powerful way to distort reality and deceive people. All it takes is to use the power of the language, attach irrelevant facts or illustrate numbers such that they prove something else than the actual facts.
First off, consider the example below.
Correlations presented as causations
Given article talks about a study, that researchers at Oxford Brookes University discovered that after two weeks, 85% of people involved in the study had lost more than four pounds in weight.
How the article is presented in the newspaper suggests a causal relationship. That is, eating cereals twice a day causes losing weight.
However we cannot talk about causation here, there is at most a correlation. Meaning that if people who eat cereals twice a day lose weight, it does not mean that eating cereals is the reason that they lose weight. There must be another variable, like being health-conscious, that affects both sides of the equation. Health-conscious people eat cereals twice a day because they think it is healthier. Similarly, health-conscious people are careful about their diet overall, that is they work out, drink a lot of water and avoid high-calorie desserts, so they lose weight.
Plus there is not always another variable around! See the example below. There is a correlation between the number of people drowned by falling into a pool and the number of films Nicolas Cage appeared in. Of course, these two statements do not cause each other in any way possible, plus there cannot be another variable that affect both of them.
Multi-dimensional Lies
Another good example of deceiving people with statistics is to represent numbers with pictures and figures. Very good examples of this are given in Darrel Huff’s classic, How to Lie with Statistics.
Let’s say we want to compare the average weekly income of workers in Paris and Milan. A simple bar chart to represent the facts can be given as follows. For the sake of the example, let’s say the weekly average income of a worker in Milan is 200 Euros and in Paris 400 Euros.
If you were to use it in your newspaper or report, and if your point is to prove that workers in Paris are way richer than the ones in Milan, a bar chart is not such an appealing way to represent the facts, right? Let’s try another way.
In this case, we used an eye-catchy and illustrative way to represent the facts, however, the facts are not the actual facts anymore.
The money bag that represents the workers in Paris is twice as high as the money bag of workers in Milan, however, it is also twice as wide. This means that the money bag of Paris is around 4 times larger than the bag of Milan. Even worse than that, your brain feels the money bags as 3-dimensional objects therefore it will try to estimate and compare their volumes. Since the big money bag is twice as larger as the small money bag in all dimensions, that makes a ratio of 1:8! We were comparing 200 Euros with 400 Euros in the beginning, however if 200 Euros fit in the small money bag then there must be at least 1600 Euros in the money bag of the worker in Paris.
Cut-out Graphs
For the next deceiving example, we’ll be visiting some actual data on the number of women in the parliaments of some countries. The chart below shows how many women took seats in Argentinean, Spanish and Swedish parliaments in the last elections.
Pretty close numbers, right? Now check the illustration below. Supposedly, in the second bar of South Africa, there are way more women in the parliament than the second Spanish parliament.
However, apart from the impression it gives, it is the same numbers and the same graph. We just cut out half of the chart and the number of women in the parliaments significantly differs now!
The story does not finish up even when you show the full picture. What does the number of women in the parliament tell you? We cannot distinguish if in Sweden there are 152 out of 5000 seats taken by women or 150 out of 152. Let’s say, you were to comment on how developed these countries are by evaluating how many seats do women have in their parliament, you should better check the percentage of women in that parliament.
The chart below shows the rate of women in the parliament of the given countries.
Now we have another picture with a little help of the scissors (half of the graph is cut off again). Compared to the previous figures that in South Africa there are more seats occupied by women, now it feels like, right, of course there are more women in the Swedish parliament!
Is it the case? I don’t think so. If you check the real numbers below, in reality, the percentages are quite close to each other!
And if you enjoy this topic, please consider reading the book ‘How to Lie with Statistics’ by Darrel Huff.
