The world is a pretty complex place. ANOVAs and other univariate statistical models are super useful…until they’re not. Sometimes we have data or questions that are more complicated than our univariate friends can answer, sometimes we have…drumroll please…
Well, you’ve proved me wrong! I expected the mean wouldn’t be affected, because it’s a linear combination of the two group means.
The changing number of sampling points really is paraxodical to human intuition (like most things in statistics).
What statistics are susceptible to Simpson’s Paradox? That’s an interesting question you raise, Matthijs Cox. I think you’re mistaken though: the arithmetic mean is definitely among them, just like the median. You can see that illustrated below with my example data: