I have a science background, but stats has always been a weak point for me. The tests I’m thinking of specifically are Fisher’s Exact Test, Barnard’s Test, and Boschloo’s test, but I’d like to understand the concept generally. Fisher’s is generally the go-to standard for my field, but from my understanding, Barnard’s is *sometimes* more powerful than Fisher’s, and Boschloo’s is *”uniformly”* more powerful than Fisher’s. To my not-understanding brain, that sounds like Boschloo’s should have long since made Fisher’s obsolete, so I’m looking for clarification on what “power” actually means, as well as why something like Barnard’s could be more powerful in some cases but not in others.
In: Mathematics
There’s a popular metaphor going around:
You send a child down into the basement to look for a particular tool. The child comes back and reports the tool is not there. What are the odds that the child is correct?
If the basement is well lit and well organized, the tool is large, and the child looked for a long time, then the odds are pretty good that the child is right and the tool is not there.
If the basement is dark and cluttered, the tool is small, and the child only took a very quick look, the odds are pretty good that the child is wrong and the tool *is* down there.
When the basement is dark and cluttered and the tool is small, the child needs to look for a much longer time before you can conclude that the tools is not there.
In this metaphor, the tool is the correlation we’re looking for. The clutter is the amount of noise in the data. The size of the tool is how strong the correlation is, and the child’s statement that the tool is not there is the null hypothesis.
The time spent looking is the amount of data collected. You want to collect data until you’re reasonably sure (typically 95% sure) that the child was correct.
(I think I got part of that backward, but I don’t know which part.)
Latest Answers