I have a study with a sample size of one that concludes that people shouldn't drink milk tea because of the intense gas pain that follows. You should see my p value. It's glorious.
Interestingly enough, there is a design that still works with a single person... But it requires a bunch of time points. In other words, you can prove milk tea is bad for you in particular by drinking it enough times and having terrible gas and/or diarrhea to improve that p value.
You naturally can't extrapolate that to others in the population but at least you'll definitively prove you probably have lactose intolorance!
I'm so glad I didn't see that. I hate just now easy it is for things to get published and, worse, draw media attention.
Although if I had to guess, it isn't the sample size and sds so much as drawing stupid conclusions from correlations without using controls for things that actually lead to depression and addiction. (Like the wine is good for you studies that ignore the benefits of wealth, ugh)
The wine is good for you did not ignore the benefits of wealth.
It first ignored the fact that the initial study was of Japanese doctors and maybe having a medical education made you more likely to adopt healthier practices.
The next study ignored wealth.
The next study ignored education and wealth.
It proceeds to be bad study after bad study until 20 or so years after the first study when someone thought "what if the non-drinking crowd included people who were alcoholics and people who had to stop drinking because of health problems?" Turns out when you only focus on non-drinkers who never regularly drank and compared them with wine drinkers the wine drinking crowd has a lot more health issues.
I work in the wine business and I laugh every time I see a new study to see what they ignored to conclude wine was a health food
Wine as a health food is such wishful thinking, haha. I have the privilege of learning some advanced statistical methods in grad school and so many of those issues are easily accounted for with better data and models.