An exercise in critical thinking
Today I start out with a challenge for you. Can you spot the logical errors in the following hypothetical news story?
A scientific study followed 10 million people in US who purchased a pillow from the My Pillow Company. It found that within one month of receiving their pillow, 11,248 people died and 91,130 were hospitalized. Over 100 were diagnosed with Bell’s Palsy, a paralysis of the facial muscles, 12,904 had a miscarriage, and 1,250 developed a blot clot from which 201 of those people died. These numbers are greater than ALL the side-effects of all the vaccines in the entire world combined. Demands for government action from some consumer groups have been ignored or muffled, due to massive government-wide “covers up”.
A fallacy is a mistaken belief or misleading conclusion based on faulty reasoning. Did you spot the faulty reasoning in the hypothetical news story? What is the misleading conclusion(s), and what errors in logic (there are more than one) lead to that conclusion?
Just to be clear, there was no such scientific study of My Pillow that I know of; however, if there had been one, their numbers would likely be similar (within a small cushion).
Once you’ve identified the logical errors, replace “pillow” with “COVID-19 vaccination shot” and repeat the exercise. Were the logical errors that you found the same or different?
Analysis of the fallacy
On the surface it seems absurd that a pillow could cause all that death and disease. But, you should be careful not to let your preconceived beliefs taint your analysis of the data. We all have a strong “confirmation bias”. Our first inclination is to explain or rationalize why a pillow has nothing to do with those outcomes. This is not the same as critically analyzing whether the data, accompanying argument, or analysis logically supports the stated conclusions.
The hypothetical news story states that 11,248 people died within one month of receiving their pillow. Do you think it is possible they might have died in that same time period had not received their pillow? Or perhaps the inverse situation is true. There were 9,988,752 people who did not die. Is it possible some of them would have died if they not received their pillow? It is impossible to determine if these counterfactual questions are actually true, but it is possible to determine whether they are statistically supported. A starting point is to estimate the “base rate” — how many people you would expect to die among people who don’t receive a My Pillow in that month1. The number 11,248 is pretty much meaningless by itself. What you actually need to know is how the observed count compares to the base rate2. This is the first logical error — the story provides the wrong data for the desired conclusion, and omits the data needed to support the conclusion.
The story compares these case numbers to side-effects from vaccines. This is our second logical error, comparing apples to oranges. “Side-effects from vaccines” would include only increases over the base rates, whereas the total numbers stated in the story includes the base rate plus any increases.
The story implicitly concludes that the pillow causes the adverse outcomes, which uncovers a third logic error: inferring causation improperly. Strictly speaking, the article never explicitly states that the results are causal (i.e., is doesn’t use phrases like “as a result of”, “causes”, or “follows from”), but by including a comparison to something else that is causal it communicates that the adverse outcomes are caused by the pillow. Even if the story had presented data that 1,000 people more than expected by the base rate died during that month, that alone still does not prove a causal connection. The difference might be attributable to random fluctuation or to a compounding variable (e.g., people with pre-existing health issue are more likely to order the pillow). However, it might warrant a closer examination.
I define The Deadly Pillow Fallacy as follows: an unsound argument that uses observed rates of an event to draw a causal conclusion, when it argument actually requires a comparison of the observed rates to a base rate. In addition, it makes an unwarranted claim of causation, either implicitly or explicitly. By cuddling up to this fallacy, you buy into the tenet that “no evidence of correlation implies causation”.
Deadly Pillow Fallacy in action
Today I watched a “news” story video that a relative sent me that used the Deadly Pillow Fallacy to misguide viewers. In fact, seeing the fallacy in action inspired me to write this blog post. Before reviewing the substance, I’ll provide some brief background.
The Vaccine Adverse Event Reporting System (VAERS) is a system and website managed by the US CDC and FDA to track adverse medical events that occur after a vaccine has been given. If, hypothetically, a population receives a placebo3, a certain fraction of recipients would die and be reported to VAERS. Others would be hospitalized, have heart attacks, or be diagnosed with a new disease and be reported. A placebo would provide a “base level” of adverse events, since by definition it does not cause any adverse outcomes. A safe vaccine with no side-effects4 would be expected to have similar rates. The system is useful for spotting possible issues since it enables the CDC and FDA to spot cases where the number of incidents is significantly higher than the base rate, which would then merit deeper scientific investigation. The key thing to remember is that its data are the number of incidents reported, not the number of incidents caused by a vaccine.
Below I’ll provide a verbatim transcription taken from the “news” story I watched today. The host provided no background on VAERS prior to the part transcribed below. Worse, take note of how the host embellishes the VAERS numbers with language (like “directly from” and “as a result of”) that grossly misrepresent the actual meaning of the numbers. Can you spot the similarities to the My Pillow example story? Are you able to recognize the deadly pillow fallacy?
“According to the VAERS web site, a US government site which tracks adverse reactions to vaccines, nearly 6 thousand people HAVE DIED as a result of taking this vaccine. Some 20 thousand more have been hospitalized, nearly two thousand others have come down with Bell’s Palsy, a paralysis of the facial muscles, and 44 thousand people have checked themselves into urgent care. That’s not to mention the 59 hundred life threatening reactions people have had DIRECTLY from receiving the vaccine, including 22 hundred people who suffered HEART ATTACKS as a result of getting the injection. And this is ALL government data. According to VARS over 650 women have suffered miscarriages as a result of the vaccine. And some 45 hundred people are now disabled, some permanently. These numbers are greater than ALL the other side-effects of all the other vaccines in the entire world combined.”
You should now recognize that the numbers cited in this news story are not the numbers the host needs for his argument. He shows numbers of events reported no VARS rather than cases attributable to the vaccine. As far as the viewer an tell from this, the vaccine might be causing a decrease in the case rates! He has simply not provided the relevant information to draw any conclusion either way.
Now that you understand what VAERS is, you hopefully realize that the speaker’s embellishments like “as a result of” and “directly from” explicitly misrepresent what the numbers actually mean, and hence (unlike the pillow story) contains explicit lies. By comparing VAERS case numbers to cases from other vaccines, it employs an apples to oranges comparison in order to obtain an absurd conclusion. He communicates (both implicitly as well as explicitly) that the conclusions are causal, hence completing the gamut of logic errors for a trifecta Deadly Pillow Fallacy.
As you watch news stories, especially from less main-stream media sources, see if you can spot additional instances of the Deadly Pillow Fallacy. In terms of difficulty, the Deadly Pillow Fallacy ranks as one of the softest. Although I can’t support it with evidence, I conjecture that learning to recognize it may help you to sleep more soundly.
 You can use a very quick “back-of-the-envelope” analysis to obtain a rough idea. The human lifespan is about 25,000 days. If the 10M people are selected randomly across all age and health demographics, you’d see about 10M/25K = 400 deaths per day on average. Since the study monitored them for 30 days, that would be base rate of 12,000 deaths.
 To do it right, you actually need a probability distribution for the number of people expected to die under the assumption that the pillow has no influence on whether someone dies. Ideally you would tailor the distribution to the same age and health demographics as the participants in the study. Without a full distribution, you don’t have a principled way to know whether an observed different between the base rate and the observed numbers is meaningful (statistically significant).
 You can’t tell the health providers and participants that it is a placebo, since that would discourage them from reporting adverse effects.
 When given to a population with the same age and health characteristics.