These two effects explain a lot of the stupid decisions that come out of "data driven" processes. It is common for data to suggest the opposite of the truth.
Actually, I think the best takeaway from phenomena like these is that just doing statistics on a set of data can't tell you "the truth". If you don't understand the actual causal factors in play, your knowledge is very limited, no matter how much data you have or how many different ways you slice the statistics.
For example, in the UC Berkeley case described in the Simpson's Paradox article, the data actually doesn't tell you anything useful about "bias" in the sense of "something people are doing that they should do differently to make the admissions process fairer". It doesn't even tell you where to look for possible "bias" without knowing more about the admissions process: it is controlled primarily by departments or by the university as a whole?
I would argue that ultimately, all your knowledge and understanding comes from "doing statistics on data". Maybe the statistics is done by sloppy slurpy things in the brain instead of in R, and maybe it's actually mathematically unsound most of the time, but it's still some sort of statistics.
For example, the GHZ experiment [1] can rule out local hidden variable models and confirm QM predictions with no statistics at all: the two different models make contradictory predictions with no continuous variation between them.
"For specific combinations of orientations, perfect (rather than statistical) correlations between the three polarizations are predicted by both local hidden variable theory (aka "local realism") and by quantum mechanical theory, and the predictions may be contradictory."
"Perfect" correlations means, as the parenthetical comment shows, "doesn't require statistics to check".
> the GHZ experiment [1] can rule out local hidden variable models and confirm QM predictions with no statistics at all
However, one needs to use statistics to even show GHZ works. That does sound contradictory to me. The correlations you get in experiments are never perfect and in this case they can be pretty far from perfect.
Not for the particular cases described in the quote I gave. For a complete verification of all the GHZ theorem's predictions, yes, you need to do statistics, because some of those predictions are probabilistic.
> The correlations you get in experiments are never perfect
In some cases, like the ones described in the quote I gave, it isn't a matter of correlations. You have contradictory results predicted by two different models, each prediction being 100% certain according to the model. You don't need any statistics to test that: just do one single run and see which way it comes out.
The answer to questions like that can't be found in the data. You have to go look at how the university admission process actually works, and what roles the university vs. the individual departments play in it.
It may be true in some cases, but I think the "Any" is disproven by the existence of proper scoring rules.