For once, a pretty good article on medium. A nice primer to how to and how not to interpret statistical results.
An example of this mistake happening time and time again is when there is a (statistically significant) discovery in carcinogens i.e. something that causes cancer. A 2015 Guardian article said:
“Bacon, ham and sausages rank alongside cigarettes as a major cause of cancer, the World Health Organisation has said, placing cured and processed meats in the same category as asbestos, alcohol, arsenic and tobacco.”
This is straight up misinformation. Indeed, bacon, ham and sausages are in the same category as asbestos, alcohol, arsenic and tobacco. However, the categories do not denote the scale of the effect of the carcinogens, rather, how confident the World Health Organisation is that these items are carcinogens i.e. statistical significance.