when the whisker bars overlap I know that means that there is no significant difference between the variables, but why is that? I don’t really understand why we can deduce that from the overlap
It’s because whiskers bars show a range. We are more confident in our predictions when we have a range instead of a single answer.
Let’s say X was between 65 and 75
and Let’s say Y was between 70 and 80
And you were asked is Y more than X? Now logically and using intuition you might say Yes because the some numbers of Y are bigger than X’s highest.
But statistics does not allow for us to say that. We have to treat all values equally plausible. So because there is overlap in X and Y we cannot confidently say Y is bigger than X.
thank you! that makes sense