Statistics are great. They can tell us tons of useful stuff about what is happening in the world. They can tell us lots of fun facts. They can be used to educate and inform. But, do you know what else statistics are good for? They are great tools for deceiving people.
Percentages are particularly useful tools for deception and they are not hard to use. I can teach you how to do it in three easy steps and then you too can use percentages to trick people into believing whatever flawed arguments you want to concoct!
Step 1: Come up with a percentage. Often you can just look them up, but if you can’t find a percentage that is relevant to a topic that interests you, then you can always create your own. Percentages are just proportions multiplied by 100 with a fancy little % symbol at the end. So, all you have to do is take two quantities: a denominator, which usually represents some sort of total (like number of people in a population), and a numerator, which usually represents a subset of that total (like number of people with a certain characteristic). If you then divide the numerator by the denominator and multiply by 100, you have a percentage. Ok. That was the hard part. Now for the easy part.
Step 2: Use the percentage in a conversation. Just use the percentage in a conversation or argument. When you do this, make sure that you don’t really explain what the percentage means. That way its meaning is left up for interpretation, preferably whatever interpretation supports your argument. And that brings us to the last step.
Step 3: Don’t explain what the denominator is. This part is super important. If you explain what the denominator is, then people might actually understand what the percentage means and be able to determine whether it is actually relevant to the conversation. But, if you leave that information out, then no one can refute your percentage (since they can’t know for sure what you meant), and you are free to imply all kinds of things based on that percentage.
This is all a bit abstract, so let us look at a wonderful example of “lying with percentages” that I have seen multiple sources use on social media in the last couple of weeks. Actually, technically it’s not lying (that is the beauty of it), but it is dishonest and definitely can fool people!
We will start with the percentages and then I will walk you through the process of obtaining those percentages, so you can create your own just like them. Here is a technically true, but extremely misleading statement:
“Did you know that COVID-19 has a 99.96% survival rate? Did you know that its hospitalization rate is only 0.11%? Makes you wonder what all the fuss is all about!”
Boom! Argument over. People are overreacting to COVID-19 and you have the statistics to prove it. Sure those statistics are deceiving, but they are not wrong.
Ok, so how did we come up with that gem:
Step 1: To get the “survival rate” for COVID-19 you could take the number of people in the US, around 330 million, as the denominator and the number of people in the US who have not died from COVID-19, which is around 330 million minus the 135 thousand deaths, as the numerator. You divide them and multiply by 100 to get the percentage:
(330,000,000-135,000)/330,000,000*100=99.96%.
Never mind the fact that is not usually how people define survival rates. It is a type of survival rate, and this one supports your argument.
The hospitalization rate is similar. The CDC claims that there are 107.2 cumulative hospitalizations with COVID-19 for every 100,000 people in the US. So, the hospitalization rate is:
107.2/100,000*100=0.11%.
Step 2: Now just use that trump card the next time you are involved in a discussion about masks or social distancing and you can “prove” that all those cowards are making a big deal out of nothing.
Step 3: Whatever you do, do NOT mention the fact that the denominator was the total population rather than the number of people who were actually sick. That way people can think that you are saying that if they get the coronavirus then they have a 99.96% chance of surviving, when the survival rate for people who test positive for COVID is around 96% (See PPS at the end for further discussion about this). This goes for the hospitalization rate as well. If you don’t mention that the denominator is the US population, people might think you are saying that the chances a person with COVID will be hospitalized is around 0.11% when the reality is that the chances are much higher (around 10% if you use confirmed cases for the denominator).
The wonderful thing about keeping the meaning of percentages ambiguous is that it allows you to deftly avoid having to face the inconvenient implications of those percentages. For example, it allows you to claim a survival rate of 99.96% and then argue that we should embrace herd immunity as a strategy and hint that it won't be so bad without revealing the highly problematic consequences of such a strategy. There are serious flaws with that argument, for example:
1. The 99.96% figure can only go down since the denominator is constant. So, as the total deaths rise, that percentage will decrease.
2. To get to herd immunity, we will need around 70% of the population to become immune. The number of confirmed COVID-19 cases currently constitutes just over 1% of the population (although antibody studies suggest that the true number of cases may be around 11x higher). So that means we need somewhere between 7 and 70 times as many cases to obtain herd immunity.
3. If the current mortality rates hold then reaching herd immunity would involve 800,000 to 9 million additional deaths and 2.1 million to 24.4 million additional hospitalizations.
The good news is that if you keep things fuzzy and avoid providing context, then most people won’t notice those unfortunate details!
Anyway, I hope you found this illustration helpful. Now you too can use percentages to win any argument even if the evidence is not on your side. Remember: Winners don’t worry about civility or integrity, they do whatever it takes even if it means playing dirty, getting under their opponents skin, and torturing the data until it confesses.
Note: In case it was not obvious, this post was intended to be satirical. Please don’t lie with percentages. Please provide context when citing statistics. And please be respectful of each other. There are more important things than winning an argument!
PS. The title of this post was inspired by the book, How to lie with statistics by Darrell Huff.
PPS. The case fatality rate is currently 4%. This means that the ratio of deaths to positive tests is around 0.04. However, that is not really what most people care about. What people really want to know is: If I get sick what is the chance that I will die? This is a much harder question. For one, it depends on who you are. Your age and any underlying conditions have a big effect on that risk. And, even if you ignore all that and just think about the average person you run into another issue: we do not know the denominator! How many people have actually been infected? It is almost certainly somewhere between the roughly 3.5 million positive tests and the 330 million total people. Antibody tests suggest that it should be substantially higher than 3.5 million and much lower than 330 million. Most experts think the mortality rate is somewhere between 0.5% and 1% which would be consistent with having 3 to 7 undocumented cases for every confirmed case.