Churchill is credited with the bon mot: “Don’t trust any statistics that you haven’t faked yourself!” Whoever said that, it is certainly wise advice and it is more relevant than ever. For months we have been confronted with alarming statistics regarding Corona. How credible are they? Here is a case study from another profession.
Can it be said that there is a race whose members are superior to the rest of the species in terms of grace and intelligence? If it’s as obvious as it is in this case, then it must be allowed. We’re talking about the beagle, the likeable four-legged friend with floppy ears.
You don’t just meet him walking in the park, but also at airports, where he’s on an important mission: fighting the war on drugs. He often wears a uniform jacket that makes it clear that this is not a stray street dog, but an official.
His job is to check incoming luggage for prohibited substances and then dictate his findings to an assistant, whom he keeps on a leash. He is extremely accurate, but he is not infallible either. It can happen that he barks massively at a harmless children’s backpack, but “overlooks” a sports bag full of hash.
We call the first type of error a “false positive = FP” i.e. when a clean piece of luggage is incorrectly identified as a drug suitcase. The other mistake is a “false negative = FN” i.e. when he declares baggage with drugs as clean.
During his training, our Beagle – let’s call him Buddy – was able to drastically reduce its error rate. Nevertheless, mistakes still happen in everyday work, an average of 20 percent of the FN type and 5 percent of the FP type. What are the consequences?
Let us assume that the customs authorities today simply want to gain an overview of the statistical frequency of drug smuggling. You don’t want to arrest anyone, but you want to get an idea how serious the problem is. To do this, Buddy is allowed to examine a load of 200 suitcases from Venezuela. The result: he sounds the alarm 15 times!
What does that mean now? His FN quota is 20%, so out of 200 suitcases, has he overlooked 40 that are positive? And the 5% FP – did he bark wrong 10 times at completely harmless suitcases? You have to know that in order to be able to compile reliable statistics.
Nothing easier than a wrong statistic.
So Buddy barked 15 times out of the 200 suitcases. I have worked out what that means for you: there are probably 6 suitcases with drugs.
With his 20 percent FN he overlooked one of the 6 drug cases; but he barked properly five times. And with the remaining 194 clean suitcases, he accidentally barked 10 times because of his 5 percent FP.
Barked five times correctly plus ten times barked incorrectly positive results in a total of 15.
The result 6 is still extremely uncertain, it is by no means set in stone, it is just the most likely value. 3 or 10 would also be possible, although less likely than 6.
That is terribly inaccurate, of course, and you may be asking Buddy to retire when his nose is so bad. But stop! Your judgment is only justified if we use Buddy for statistical research. In individual cases, his service is worth its weight in gold. The owners of the five positive suitcases that Buddy identified correctly plus those of the ten clean suitcases that Buddy was wrong about would now be called to customs, where their luggage would then be examined more intensively.
The ten clean passengers could now continue their journey unmolested, but the five crooks would spend the next days and nights quite uncomfortably. Yes, and one of them would have gotten away.
So Buddy is definitely suitable for individual studies, but not for statistical statements. That would only be possible if the percentage of false positives were significantly smaller than the percentage of drug dealers among the passengers. But that is not the case.
It could now be that the customs officials want to dramatize the drug situation in order to get more money from the government. To do this, they have Buddy and his colleagues examine more and more suitcases every day and then spread alarming messages: “Sad record: drug dogs identify over a thousand pieces of luggage containing drugs in one day.”
Error in the test tube
With the story of Buddy, I am trying to add clarity to the interpretation of the ubiquitous pandemic statistics, namely the computational and logical aspects, not the clinical ones.
With Corona there is also the problem of FP and FN tests. In order to present this harmlessly and apolitically, I have moved the problem to a different location – the mathematics remains the same and can be transferred to the Corona world without medical expertise. If we are told that thousands have tested positive, then this number must not be put into the world without naming the total number of tests and the assumed FP rate in the same breath. Anything else would be misleading.
In individual cases, however, the false positive “patient” will then go to the doctor and, after a detailed examination, will send him home as healthy. The genuinely positive person is treated accordingly by the doctor or referred to hospital. Yes, and the false negative will also see a doctor a few days later if the symptoms drive him there.
A statistical statement, or even a testing of the entire population, would only make sense if the percentage of infected people was significantly higher than the percentage of false positive tests. And that’s not the case – fortunately.
But here is a simple statistic that you can rely on: the average lifespan of a person in our part of the world is around 80 years, and that is around 1,000 months. That’s good news. It follows that an average of one thousandth of the population dies every month. This is the bad news.
Since the beginning of March, i.e. for around 7.5 months, in Canada there were statistically around
7.5 x 37,000,000 / 1000 = 247,500 deaths.
In that time, about 9000 people died of Corona, around one thirtieth of the number mentioned above. So people are thirty times more likely to die from something other than Corona.
Currently, the risk of losing your life due to Corona is even lower, because most of the corona deaths occurred in April and May. So if you forgot your mask going to the supermarket, it doesn’t have to be your last purchase, at least not for health reasons.