Family-wise-error, what is the family? In the last 4 hours I have been trying to wrap my head around the Error 1 Inflation that, citing wikipedia, happens, when we perfom multiple independent tests on the same dataset. The probability that one of these results ends up with a Type 1 error when not caring about adjusting the significance level is: $1−(0.95)^{t}$. What I do not understand is, why doesnt this apply to all tests that are done and why the "same dataset", when I do a test today, and another one on a completely different question tomorow, the probability that one of these is higher also rises. I know this has been asked before, but none of the answers really helped me.
Thank you
Is there a rule of thumb to decide which tests fall into the "same bin"? Is the same dataset really important?
I have just read this article: http://daniellakens.blogspot.com/2020/03/whats-family-in-family-wise-error.html and I think I wasnt aware of a huge part of this whole debate. When considering a situation, where the result is true if only of the hypothesis is true, It is absolutely clear to me that we need to consider FWE being an issue. But if we that 3 individual claims on their own, is it okay not to adjust?


What I do not understand is, why doesnt this apply to all tests that are done

You understand it correctly. It also applies when we do multiple tests with different datasets.
This is why significance levels are sometimes very low. See for instance the history behind 5-sigma (Origin of "5$\sigma$" threshold for accepting evidence in particle physics?).
