For central limit theorem to hold, the random variables must be (independently and identically dustributed) i.i.d.
How do we know our samples are i.i.d.? We can only show if they are not
Was 14 and on a Friday boss gave me some money to go find a book on C. He would take care of the expense form. I read the book over the weekend, and he had me writing code on Monday. (The book had a diamond on the cover and didn't turn out to have the popularity of K&R). He told me to find example code and copy and paste it. I wrote a terminal emulator and a manufacturing quotation database (he provided me with greenleaf libraries). They both ran fast. All that accomplished and I didn't know pointers well enough to be able to teach them. This was in '86. I also had a full collection of Byte Magazine which was motivating. It is so less nerve-wracking writing code today, knowing what to do if there are bugs in the language or libraries.
For central limit theorem to hold, the random variables must be (independently and identically dustributed) i.i.d. How do we know our samples are i.i.d.? We can only show if they are not
Add to that https://en.m.wikipedia.org/wiki/Why_Most_Published_Research_...
We've got to do better or science will stagnate