80% of Heart Attack Victims Have High Cholesterol
-Lipitor Television Ad
If you had high cholesterol, would you start feeling worried? Lipitor is lying. Not in a factual sense, but in an emotional one. This is an example of a great statistical lie. One that we have a hard time understanding on the surface, but which demands to be clarified. The world has too much fear already and we don’t need pharmaceutical companies abusing our understanding of statistics to create more fear driven consumption. So lets walk through this.
This quote causes our fear center goes off because we start thinking that 80% of those with high cholesterol have heart attacks. But that’s not what this statistic says. What does this statistic tell you if you have high cholesterol?
There is not enough information about the rest of data. The one critical piece of information that is missing is the number of people with high cholesterol who never have a heart attack. To help explain why, lets convert this from statistics into real people and figure out what the true risk of heart attack is if you have high cholesterol.
Suppose the following (these are not hyper accurate, but are reasonable approximations based on a quick survey):
- 30% of the population has high cholesterol
- .2% of the population have heart attacks every year (765,000/300,000,000)
- 80% of heart attack victims have high cholesterol
So if we have a sample of 10,000 people:
- 3000 have high cholesterol
- 7000 have normal cholesterol
- 20 have heart attacks
- 16 of these have high cholesterol
- 4 of these have normal cholesterol
The overall risk of having a heart attack if you have high cholesterol is 16/3000 or 0.5%!!! Imagine if they had used the real statistic in their advertisement:
0.5% of High Cholesterol Sufferers have heart attacks
Not nearly as compelling.
So besides inane advertising that is simply fear mongering, why does this matter? It matters because this fallacy comes up in many other settings as well. The formal name of this fallacy is the Base Rate Fallacy or the Prosecutors Fallacy. The latter because similar statistical lies are used to convict people based on “what are the chances that…” type of arguments.
Moreover, as I’ve stated before, our knowledge is becoming increasingly fragmented. We have no way to run our own study about a particular medical diagnosis or how often a car breaks down. We are at the mercy of whoever provides us with the information. Being aware of how statistics are used can help us be more vigilant in thinking about what is true.
[Personal Note: I don’t have high cholesterol, nor am I a doctor, but I play one on TV 🙂 (reference to yet another frailty in our ability to discern truth)]