How to save yourself using a bit of logic and statistics

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Logical versus emotional motives. Perceptions versus observed numbers. We are always facing a fight between two sides of the same coin. When we feel anxious, scared, or worried, we look for certainty. Several examples arise in day-life activities.

When I was a young adult, I suffered for a while from severe anxiety problems. It took a long time, and I had to deal with several personal issues before getting rid of them once and for all. However, at that time, something unexpected came to my help. I went back to school and started studying statistics. My anxiety was always linked to some “catastrophic-thinking.” At the start of the day, I imagined that something terrible would happen, every morning, every day. After my first semester in Statistics, I had become familiar with the ideas of random variables, samples, and observational study. One morning I got up, I started the day, and I decided to write down my morning fears in a notebook. In the evening, I had to record if anything happened in the real world. After two months of observation, the catastrophes of my fears had zero frequencies.

Among my many fears, traveling by airplane was not included. Still, I met several people traveling who were scared to death of flying. Once I was sitting next to a lovely, terrified person, we overcame her fears by chatting from Rome to New York; however, “chatting for almost seven hours” is not a general solution for dealing with this specific fear. Then let us see if, again, statistics help. First of all, let us consider the chance of death by taking a commercial flight. These days it is smaller than one in a million. According to the site, this probability (per flight) is actually one in seven million. Given that we assume flights are independent of each other, this probability is not influenced by whether you fly once every three years or every day of the year. But fears are irrational; they are strong emotions and may take control of our minds easily. To conquer them, we need more evidence in favor of flying. We can try to compute how many days it may take, on average, to succumb to a fatal flight accident. Let us consider a flight attendant that flies, on average, every day for his/her entire life (we distribute multiple daily flights over days). We would expect only one death in every nineteen thousand years. Well, this is why there are so many aging flight attendants around.

When it comes to comparing real risks to fears, we can rely on statistics with great confidence. For example, from U.S. National Safety Council Injury Facts website, we can retrieve a table with the estimated odds in the US of dying from a given cause. The leading cause is heart disease, followed by cancer. The least probable causes are traveling by airplane and traveling by train.

Table from (see website for more information for how estimates were obtained).

Nowadays, we are facing an epidemic that has changed our way of living. Face masks, social distancing, smart-working are new aspects of our current lives. Along with alerts and warnings on correct behaviors, we read newspaper titles and get scared to death (sometimes I think I’ll die of a heart attack before covid-19 gets to me). In Italy, as I’m writing (mid-February 2021), fear of the new English/British virus’ variant is spreading. Titles such as “A storm is coming! We need more restrictions against the English variant!” (in Italian) are increasingly common. The writer is a well-known and extraordinary scientist, a physicist. All the ingredients to make the fear-cake rise are there. Imagine! Every person reading the news will likely be scared, and their anxiety will grow “exponentially.” Again, statistics and numbers come to help us.

There is a rather interesting article about a study by the Italian National Health Institute  (INHI, in Italian) on the English virus variant. I read the details and found that the conclusions were drawn using 852 samples at the national level on a two-day time window. Of these samples, 152 showed the variant, and the estimated regional prevalence ranges between 0 and 59%. The study claims that the national prevalence is 17.8% with a (correct) warning: “This value constitutes a weighted average that takes into account the cases notified in the Regions / PPAA in the two days of the survey and not an estimate on national data.” The mutated virus is already present over almost the entire national territory. The INHI report contains several other warnings: 

  • Among the possible limitations of the study, the following points should be mentioned: 
    • The sampling method could be inhomogeneous among the various Regions / PPAA. 
    • Some regions did not use a pre-screening for S-gene target failure preliminary for the subsequent sequencing. 
    • No data are currently available relating to the age groups of the cases selected for the survey,the possible belonging to outbreaks, and geo-localization (potentially useful for evaluating geographic representativeness with greater accuracy). 
    • Some differences between Regions could, in part, be explained by the different methodologies used for the selection of samples or the use of different technologies. 
    • In some regions, the small number of samples may not allow the detection of rare events.

Is there enough evidence in favor of the “coming storm?” Honestly, as a statistician, I don’t think so. Media reports, too often, do not appropriately weigh the statistical warnings in scientific studies. There is little incentive to report the uncertainties; vague headlines don’t sell. Suppose the speaker is a prestigious, well-known scientist or a government institution (as in the latter case). In that case, there is no reason why doubts come to the top of a listener’s head. Therefore, it is also incumbent on the statistical community to bring those doubts to the surface, presenting results in a way that the uncertainties cannot be easily ignored.

Moreover, the current epidemic is associated with an “infodemic,” a large amount of information from many sources, especially spread online through social networks and video-sharing platforms. Disinformation and malinformation have recently grown significantly, often as a result of tailored commercial or political campaigns on the web. Non-statisticians sometimes analyze data with models that do not correctly describe the phenomenon of interest. This overload of information and misinformation also plays a crucial role in our perception of the epidemic’s evolution. For example, estimating an epidemic outbreak’s growth over time using an exponential model is likely incorrect. Epidemics usually start with an exponential growth that, however, slows down quickly. A logistic-type curve is usually more correct.

With this in mind, since the beginning of the COVID-19 pandemic, I read the catastrophic Italian newspaper titles, and then I write them in a notebook, and I wait. One year into the pandemic, although tragedy stroked too many of us, although we had an excess death of 84000 individuals (up to November 2020), and we are crying our beloved deaths (I personally lost more than a friend this year), the frequency of catastrophic events described by many journalists, is zero.

Indeed, some statistics, and some rational thinking, can help us enormously to face difficult times. 

Read more from StatGroup-19 here.


All posts are written by authors in their personal capacity and in no way represent the view of the organisations, universities, governments, or agencies where they are employed or with which they are associated, or the views of the International Statistical Institute (ISI).

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