The Fallacy of Free Extrapolation

While Penn and Jimmy chat, watch Teller.

Watch only Teller. Even if you do not see the rabbit, see if you can detect the moment when the rabbit went into the hat.

Now, watch me while I attempt to trick you. Be on guard, because I'm about to throw lots of distracting patter your way.

Children can easily injure themselves while playing or exploring, and a fractured forearm is a common childhood event. For every twenty children who fell out of trees in my town last year, three children broke their arms. Three divided by twenty is fifteen hundredths. That's 15%. I can take that known quantity, 15%, and extrapolate the rate of broken arms for the children in my town. I can--with strong statistical confidence--now report that 15% of the five hundred children who live in my small town suffered a broken arm last year, which is seventy-five children. While there may be some slight statistical variance, we are now confident that approximately seventy-five children broke their arms in my town this past year. When I was an ICU nurse, I sometimes floated to the ER, and I've comforted children with broken arms. I've assisted with putting casts on children, so I have a lot of experience with broken arms. This is something that I understand professionally. 

If I just tricked you, if you are not far too smart for me, I just used the Fallacy of Free Extrapolation to misdirect and mislead you. I attempted to persuade you that the group of children who fall from trees is so much like the group of all children that the same rate of broken arms should apply to both groups.

Let me try again, but this time I'll clean up my story and show you the exact moment of misdirection, when the rabbit goes into the hat.

For every twenty children who fell out of trees in my town last year, three children broke their arms. Five hundred children live in my small town. Therefore, 75 children in my town broke their arms last year.

Even in my short version, if your brain was following along, if you were expecting to trust me, if you were expecting to believe me, and even when I did not throw a lot of misdirection your way, I might have caught you at therefore.

So, did you catch the moment when Teller put the rabbit into the hat? And did you catch me when I tried to trick you into thinking that the group of children who fall from trees is just like the group of all children, only a few of whom have fallen from trees in the last year?

Let's try another one.

Twenty percent of the children who come to our clinic with sore throats have strep throat. Therefore, twenty percent of the children in my state have strep throat. 

Just like I tried to make you think that the rate of broken arms among all kids should be just like the rate of broken arms among kids who fall from trees, I'm now attempting to make you believe that the rate of strep throat among all kids should be just like the rate of strep throat among kids who have sore throats.

But you wouldn't fall for that, right?

Keep the Fallacy of Free Extrapolation in mind as you watch the following brief clip.

Is the group of people who have qualified for testing for COVID-19 in California just like the group of all people who live in California? Stop for a minute and imagine what things are likely to be different between the group of Californians who have headed for Urgent Care to be tested for COVID-19 and the group of all Californians. How would the two groups be alike? How would they probably be different? Which group would have a greater percentage of people who did not feel well? Which group was more likely to experience a high fever? Which group was more likely to purchase and use cough medicine? Which group was more likely to test positive for COVID-19?

When your mind is prepared to follow along and believe, your mind can become very susceptible to misdirection, and you can be easily persuaded to accept and believe a fallacy. In the clip above, I chose the most concise example of this fallacy from Dan Erickson's recent video, but he committed the same fallacy numerous times, and it was invalid every time. He didn't only make this fallacious claim for his county and state. He also used the same fallacy for New York, for Spain, for Sweden, and for Norway. Worse, he used this fallacy to invent his own mortality rates for each location.

FALSE:

We have 33,865 COVID cases out of a total of 280,900 total tests. That's 12% of Californians were positive for COVID.

TRUE:

We have 33,865 COVID cases out of a total of 280,900 total tests. So, 12% of Californians who were sick enough to qualify for testing were positive for COVID.

See the difference? He went on to say, "What is materializing in the state of California is 12% positives.... We have 39.5 million people.... That equates to about 4.7 million cases throughout the State of California."

And it doesn't. The next time you hear a claim like that, just remember that the group of Californians who qualified for COVID-19 testing probably looked something like this.

But most people in the State of California haven't needed or wanted to be tested for COVID-19. Yes, some people in California didn't feel well, didn't look well, and needed to be tested for COVID-19. But many people in California have felt well this past month and a lot of them looked something like this.

Beware the Fallacy of Free Extrapolation. Unless a big group is very similar to the small group concerning the specific issue you are measuring, you can't extrapolate the data from the small group to draw conclusions for the big group.

I'd like to say more about Dan Erickson's video another day.

Stay safe and keep others safe!

Valerie