Let me start by making my point clear: numbers (so the statistics) do not lie, they simply cannot! Lying is "the act of saying or writing something that is not true, in order to deceive someone, deliberately”. Numbers, do not speak, as far as we are concerned, so they cannot lie!
So, why do I want to talk about how statistics lie while they literally do not? Simply, because I wanted to catch your attention? Partially yes, but also because they still can trick us, to cause us to believe something untrue. This is what we may call an “unintentional lie”, even though for using such a term you could get criticized as it is an oxymoron.
Let me explain such tricks with a simple example: If you read in a respectable newspaper that
the average salary in Paris is about 2500 euro per month (net, after taxes and all)
the average salary in Paris is higher than any other city in France
your brain may, unintentionally, trick you by making you assume that “Woow! One would prefer to live in Paris than province”, knowing that this 2500 euro is far more than the average salary in the rest of France. But is your assumption true? Certainly not. There are lots of rich people working and living in Paris, like well-known doctors, lawyers, and artists who earn your annual salary just in a month, while there are others living with SMIC (minimum wages) and even less!
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| https://www.courrierinternational.com/sujet/df |
In fact, the average salary tricks our brain and gives us the illusion of knowing the income of an average man/woman working in Paris while, somewhere in our brain, we have confused the average salary of the whole of Paris (of rich and poor families) with the average a person can get in Paris! In order to get a more complete overview, things like the variation between salaries (variance or standard deviation in statistics) and also the living cost of a Parisian should come into play.
So, at the end of the day, it is not the statistics to blame, but us, and our brain. We use statistics to compare and to decide, as the statistics summarize complicated comparison (with lots of factors) into one or two numbers which are easy to understand and to interpret, like the mean (average), and this can mislead us sometimes, as we saw in that example.
This scary “bug” in our understanding of statistics has not been detected only recently; in fact, it has been so infamous that in 1954, Darrell Huff, an American writer, published a best-seller book titled “How to Lie with Statistics” which illustrated simple but important misuses of statistics for the general public. In his book, he explains in a simple language how plots and numbers can do us a bad trick!
If this problem has been known for since a long time ago, politicians and the people of business were those who benefit it more. They use it almost every day to deceive us into buying our vote, our support or to suck our money!
For example, when Colgate tells you that
- 80% of dentists recommend Colgate’s toothbrush
they do not lie about the 80% itself, but they do not tell us the setting of the survey: that each dentist could recommend more than one product and Colgate could succeed to get the recommendation from 80% of the surveyed dentists while another brand might have gotten 100% support! And this seemingly unimportant detail will change the whole meaning of the message, doesn’t it?
But things can be more complicated than these quite simple examples: Recently, an article by The Guardian titled “Are female leaders more successful at managing the coronavirus crisis?” got viral in the social network.
This article describes what women leaders, in Germany, New Zealand, Taiwan and some other countries have done to take the pandemic under the control, and emphasizes on the empathy that they showed towards the society. At one point, the authors claim that
“ … women have managed the coronavirus crisis with aplomb. Plenty of countries with male leaders – Vietnam, the Czech Republic, Greece, Australia – have also done well. But few with female leaders have done badly.”
They do not come into an obvious conclusion; however, the reader may easily assume that the women leader did a better job in handling this crisis. The immediate impression coming out of the article is likely to be a positive answer to the question posed in the title: “Yes! Female leaders are more successful in managing the coronavirus crisis.” This is also compatible with the interpretation of a large part of social media from this article.
When I read the article, the first thing which came to my mind was the measure by which they decided which country did a good or bad job during this crisis. They did not mention any, even if they really had! My next concern was that the article was flawed in different directions to start with:
- How can one disregard all the differences between countries, such as the quality and quantity of health care facilities, namely ICU beds per capita, number of tourists visiting the country (in particular from China) and also the role of other parties involved in managing a health crisis, like the Ministry of Health?
- If we assume that country X under the leadership of Mr. Y did a bad job, it seems very unlikely that just by replacing him with Madam W we get a very different outcome, isn’t it? So, probably in the best case, we cannot show anything better than a correlation between having a women leader and well-managing coronavirus. And who does not know that:
Then, I wondered to make such a comparison on my own, just a simplified study to see if what they tried to promote can be roughly justified based on the existing data. Here are some of my assumptions:
- I rely on the data from Our World in Data. Whether or not they are trustable in a country or not is not what I can reject or validate, but to be on the safe side, I prefer not to take the data from China into account.
- I consider the “number of confirmed cases per capita” as the measure to compare the countries: the smaller it is, the better the country could control the spread of the virus. If we do not consider the population of a country, we may reach very counter-intuitive conclusions: A small country whose all inhabitants got contaminated would perform superior to a big country which could limit the cases to 6% of the population!
- One should be aware that the total number of confirmed cases (per capita or in total) is smaller than the total number of contaminated people, as lots of countries (with men or women leaders) did not do massive testing, unlike South Korea.
- Some countries, like Sweden, took the herd immunity approach which is, simply speaking, letting virus contaminate the population to create immunity as fast as possible. Whether or not it was a better approach, it is no point in considering these countries into account for this study.
Here is the map for all counties based on the measure I chose:
As one can see in the first glance, the whole western part of Europe is quite dark, while south-east Asia is almost white. And in Oceania, Australia and New Zealand have a similar color To be more precise, we select a couple of countries from North America, Western Europe, Asia and Oceania and try to see if there is any difference between countries based on the gender of their leader:
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| Women-led countries |
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Excluding Taiwan, it seems that there is no big difference between the countries I have selected. In fact, for women-led countries, we get the average 2496 while for men-led countries this value is smaller 2066! I also compute the quantiles of the data in R and I get:
This confirms my initial guess that for women-led countries Taiwan was quite an exception (we call it an outlier in statistics) and may even get ignored.
So, did men even do better (on average)?
To be honest no! At least, it cannot be justified based on the sample I chose. To confirm it, I do a famous statistical test, the so-called Mann-Whitney-Wilcoxon Test which tells how much the two groups are different and if the difference we observe is significant or it is simply due to chance. In my case, it is the latter which holds:
Why is it so? Because the p-value is large! If p-value was small enough (usually less than 0.01) I could say that the difference between these two groups is significant, but now it tells me that there is 70.21% chance that I could observe the same difference between groups even if everything was based on the chance!
What can we conclude from all these?
You may get disappointed, but I would say NOTHING! Some women-led countries (like Taiwan) did a great job, while some others like Iceland did a terrible job! And, based on the measure I chose, men-led countries did a similar job as women-led ones. The statistical test does not confirm any significant difference between these two groups. So, a statistician may not agree with the authors in saying that female leaders had a better performance during this crisis.
For me, it is sad and surprising that after this article being published, instead of getting criticized, it was promoted mostly with positive feedbacks such that others tried similar misleading arguments, like Christiane Amanpour, a CNN's journalist as well as a very recent article in New York Times:
Whatever is their intention of promoting all these deceptive contents, the simple truth is that they are far from being true. It will not help to defend women’s right, achieving gender equality or anything like that. On the one hand, it may damage all genuine attempts of people who work hard towards these holy objectives. On the other hand, it is morally wrong to feed the public with wrong information and “analyses”. Such a wrongful practice will result after a sufficient amount of time, in them to accept these invalid claims as non-refutable facts! In the next article, I will touch, quite carefully and from the statistical point of view, one of these topics: the gender pay gap!
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