I don't know if your assessment of the study is valid (it seems a little simplistic to think that they wouldn't account for this to be honest), but what you des

I don't know if your assessment of the study is valid (it seems a little simplistic to think that they wouldn't account for this to be honest), but what you describe is classic Survivorship Bias. Here's an entertaining video from Derren Brown that shows how to use this technique to convince people you have psychic powers: https://www.youtube.com/watch?v=9R5OWh7luL4 https://www.youtube.com/watch?v=9R5OWh7luL4 Edit: also see the comment about the Miracle Man scam in this thread.