but pragmatically speaking... you can't?

I'm not sure what you mean. People work on these problems all the time in social and psychological sciences and we're at a time when neuroscience has been working to dispel some notions and support others.

i'm saying using the tools/data that we have available right now, you can't? cause it seems like you were making it so no matter what the stats regaurding homophobia and mental illness were, they'd still be explainable by the idea that homophobia causes mental illness. which seems a bit... unscientific.

I'm not sure where you get that impression.

alright.. so i'll ask this way.. is there a statistical result that you would say doesn't fit with the idea that homophobia causes the increased amount of mental illness in homosexuals?

one where just based on the statistics, it would seem to contradict this idea?

I"m confused. I thought your thought experiment was to presume that it was the case and ask if you could get at it at all. The tools are probably available, and the data might be too (depending on how sophisticated of a meta-analysis you could come up with). The real bottleneck is likely funding. There's probably not enough people that care to fund or work on it.

My negative point about statistics is that taking two observables and correlating them isn't enough (pirates and global warming anybody?). On the positive side, there are lots of advanced statistical methods (Bayesian methods, reverse inference) that would greatly supplement a simple correlation. Most psychologists and sociologists don't use them and have a poor understanding of how to interpret the null hypothesis in the first place. And no one of these methods would be enough alone, you'd need to synthesize positive results from several methods in a meaningful way.

well... my thought experiment was more prodding for a way to reach that conclusion through practical means like examining statistics... not doing the kind of in depth studies you were talking about. so since you resorted to such methods, i assumed that you were saying stats alone couldn't ever validate such a conclusion.

That's technically true when you say "stats alone" and that's true for any mathematics. Mathematics is often self consistent, and within its axioms you can prove things as true or false about numbers. But once you start qualifying those numbers and interpreting what they mean, then you introduce the possibility of improper framing and misinterpretation. Super simple example, but 1+1=2 is unquestionably true (we invented all those symbols such that the statement would be true).

When you start qualifying, you can come to false ststements, like 1 apple + 1 rock = 2 vegetables is not true despite 1+1=2 being true. Thus is an obvious example - it gets a lot more difficult to parse with abstract definitions (as in sociology and psychology) and probabilistic statements.

Here's a read you may find interesting:

"The Unreasonable Effectiveness of Mathematics in the Natural Sciences"
https://www.dartmouth.edu/~matc/Math...ng/Wigner.html

Found this relevant post in r/dataisbeautiful:

Spurious Correlations