Statistics: A great way to lie!
By: A. Jama
Tags: Market Research, Data Science, Statistics, Bias, Fallacy

The current global pandemic has made some things clear about the whole world: we are a collection of armchair warriors, who, armed with Wikipedia and the Internet, think we know everything. Everyone in 2020 is an epidemiologist and/or a statistician.

The speed with which most countries adapted radical (and at times unwarranted) policies was impressive. I mean, who, in 2019, could have predicted a global lockdown in Spring 2020? If anything, many of us might have thought such a thing would be impossible because we are technologically capable of dealing with these threats in this age (remember the 2014 Ebola scare?).

But this unprecedented situation also means we are desperate for some understanding of what is going on and what we should do. So once there is some sort of consensus (lockdown, in this case), there appears to be low tolerance for deviance from the party line.

Sweden is a good case in point: it is (or was) taking heat for not imposing a total lockdown and people were citing all kinds of number as evidence of the Swedish state’s failure (lockdown in most cases is a political, not a scientific, decision).

Every time I see these convincing-appearing sensationalist pieces, I must keep reminding myself of a famous quote: “There are three kinds of lies: lies, damned lies, and statistics.”

I want to highlight the importance of understanding statistics for what they are by using two examples.

First is a good personal example of a very misleading claim. I was by far the most popular kid in my class in high school! In the school student council elections, I got voted in by 70% of my classmates.

Or do you remember this campaign by Colgate: 80% of dentists recommend Colgate!

What Colgate thinks its toothpaste can do.

Are these claims verifiably true? Yes!

Is it the whole truth or even relevant truth? Nope.

Context is KING!

Let me break down both above stories and put them in context.

Starting with the personal one, there was a bit of manipulation involved on my part. Each class of the IB section of school got to send two representatives to the student council for 2 years. That year, I pushed for giving each student two votes so we could have a say in both selections and even rank our choices but the top two overall would win.

Come election day, I received votes from 13 classmates or 68%. That is a fact. But can that fact justify the claim that I was the most popular?

I only got 3 first-choice votes (16%) and 10 second-choice votes (53%). The other winner received 6 first-choice votes (32%) and only one second-choice vote (5%). I think it would be fair to say he was more popular but, statistically speaking, my 70% beat his 37%. There were yet others who had more first-choice votes than I did.

Then there is the fact that the sum is not 100% which makes the 68% far less important or impressive. 70% of my classmates does not equal 70% of the votes. There were 36 votes cast of which I only received 13 (36%).

This brings me to Colgate and their statistical lie. 80% of dental practitioners did recommend Colgate. BUT they also simultaneously recommended other brands, meaning here too, the sum is not 100%. They phoned some dentists and asked them to recommend some toothpaste brands. You can see how it went from the table below.

It is clear that 4/5 dentist recommend Colgate. But 4/5 also recommend Brand A toothpaste.

Their poster implied that 80% prefer Colgate exclusively which is absolutely not true. They tried to argue in court that they were factually correct and never intended to imply that. But it was concluded that it counted as manipulation as that was in fact the intuitive interpretation made by most people (things usually sum up to 100%) and which was also the impression Colgate presumably wanted to give to the public.

How impressive would a billboard with the slogan “80% of dentists think Colgate is also OK” be?

The adjusted Colgate campaign poster.

To sum it up

Even though we know of these biases and fallacies thanks to extensive research, it still takes some mental training to always be contextualising these types of numbers. I work with data professionally, I have studied behavioural economics and psychology, and yet I cannot stop myself from thinking “80% of dentists recommend Colgate” every time I’m in front of the toothpaste shelf in the supermarket.

A major problem is that these statistics are not only misleading on their own, either. They contribute to other decision-making biases and errors, such as the availability heuristic, which eventually impact our outlook on life, how we make both silly and important decisions, and affect what we hold to be truths.

In a follow up, I will summarize the most common statistical fallacies so keep a look out. And thanks for reading!