Of course they can, unless you magically exclude all statistics that made a bad assumption on independence.
I plot all the daily high temperatures and the presence of the ice cream cart and it turns out the ice cream cart causes warmer highs! Solid statistics.
Turns out the guy that has the ice cream cart has a weather app on his phone though and doesn’t come out on forecasted cold days.
Is that the fault of statistics though, or the non-statistical implication of causation that was tacked on the end of the statistical detection of correlation? Statistics is pretty explicit that it can't tell you about causality, right?
Of course they can, unless you magically exclude all statistics that made a bad assumption on independence.
I plot all the daily high temperatures and the presence of the ice cream cart and it turns out the ice cream cart causes warmer highs! Solid statistics.
Turns out the guy that has the ice cream cart has a weather app on his phone though and doesn’t come out on forecasted cold days.