I was about 22 years old, just graduated college, and moved to Boulder, Colorado to live "the good life." In the city of Boulder, there is a park called Chautauqua Park with very impressive rock formations known as the Flatirons. The Flatirons, as the name suggests, is a flat rock structure with about a 60-degree incline. While still in my invincibility phase, I thought it would be a good idea to climb the Flatirons—alone and without any equipment, experience, or common sense. About an hour into my ascent I was about 100 yards up, or about 30 storeys. I stopped for a break and looked down. A panic came over me and for the first time in my life I felt as if I was going to die. At this point in the story, you would most likely hear the amazing element which might include a god, angel, a voice of support from a loved one who has passed away, or some other aspect of the supernatural that can be credited for the survival of the protagonist. While it might be obvious to many that the lack of clear natural solutions (e.g., a cell phone or other people) to the problem at hand encourage even the most skeptical of people to reach out for supernatural help in an act of desperation, it is less obvious that it is the survivors that live to tell their amazing stories of supernatural assistance, not the people who didn't make it out alive. This is known as survivor or survivorship bias.
What makes a good "saved by the supernatural" story fascinating is not just the supernatural elements, but the claims that it was the supernatural that deserved the credit for the survival of the person with the experience. To the non-statistical thinker (which is virtually all of us), 80% of people who have survived life-threatening situations having stories of supernatural intervention would seem like very strong evidence of a supernatural force that can intervene and save a life. But if we take the survivorship bias into consideration, we arrive at a much less fascinating truth.
Let's use the example of automobile accidents, since we have relatively good data on these. According to the National Highway Traffic Safety Administration, roughly 32,000 people die each year on the roads in the United States. The number of people involved in fatal accidents is roughly double that amount, meaning that about half of the people survive, and half die. Let's say that 80% of people involved in a fatal accident reach out for supernatural help. Given an even distribution among survivors and non-survivors this would mean that 25,600 people who reach out for supernatural help die and 25,600 who reach out for supernatural help live to tell about it. Now we need to add in the 20% of survivors who did not reach out for supernatural help that lived: 6,400. So what we end up with is a group of 32,000 survivors, 80% of whom appear to have been saved by supernatural intervention. Of course, dead men don't tell tales, so we forget about the 80% of those who died and reached out for supernatural help and didn't get it. Because of the survivorship bias, we have a radically biased sample that leads to a fallacious conclusion.
How do we know that the number of people who reach out for supernatural help can be evenly distributed? For example, perhaps all those who reach out to the right god get help, but those who died never reached out to the right god. Although we can't ask those who had died what they were thinking when they died, we can look at statistical data and make some strong inferences. Here is what we do know: after adjusting for other factors we do know that people die at roughly the same rate no matter what their religion or system of belief. If Muslims were to out survive Christians, Jews, atheists, and those who are just "spiritual," then that would warrant more study into the Muslim belief system. However, there is no evidence that any one group be it Muslims, Christians, Jews, or atheists have a significantly different survivorship rate than any other.
The survivorship bias is used by scammers and con artists who take advantage of the "statistically ignorant" public. One common scam is something I call the "prophetic investor." The scammer will send an e-mail to a very large group of people (say 10 million) with a claim that they have a perfect track record for picking winning investments. But they tell you not to take their word for it, let them prove it you by picking a stock a day for 7 days in a row that increases in value. Then, they say when you are convinced, call them and invest with them. Here's how the scam works:
Day 1: Five different stocks are chosen, and each stock is sent to 2 million people as the winning pick. Let's say three of those stocks make money, and two don't. The 4 million people that received the stock pick that lost money are removed from the list (kind of like dying).
Day 2: Another 5 stocks are chosen. This time, each stock is only sent to the "survivors," about 1.2 million people each get a new pick. Out of that group, perhaps just two stocks are winners. That means that 2.4 million people got the winning stock: two days in a row! You can see where this is headed...
Day 7: After the final day of sending, about 100,000 "survivors" remain on the list. These are people who have been sent the winning picks 7 days in a row and are convinced that the "investor" must be legitimate. After all, what are the chances that anyone would pick 7 winning stocks in a row with that much confidence?
Whether someone is selling you investment services or a religion, think about the survivorship bias and how you might be jumping to an inaccurate conclusion.
In case you were wondering, I didn't call upon the supernatural when I found myself facing what I believed was my imminent death 30 storeys up. Although, at the time, I did believe in a god and was far less skeptical as I am today, I was heavily into self-help and I remember convincing myself that I could get down since I got myself up there. Of course, as we now know, that is not strong evidence for the effectiveness of self-help because we don't know how many people who drew upon the same source of motivation in similar predicaments didn't come out alive. I'm just glad I wasn't part of that group.
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