Is this a valid approach?

I asked this in another thread, but unfortunately I still don't know whether it's possible to do this or not. I'll keep my question/example as brief as possible:

Is it a valid approach to look at a sample size of 1,000,000 men and conclude that if "body height" and "number of women attracted to them" are correlated, that there must be a real correlation between those two?

The assumption would have to be (imho) that we can look at these two metrics and how they are correlated *and assume that all other factors that might influence "number of women attracted to them" dont play a role, because the sample size is big enough*.

I'm really just wondering about the part in * *.



TS Contributor
You can say there is a correlation, even with a much smaller sample size. A correlation is merely an apparent relationship between two variables.

However, what you cannot say (and what I suspect you want to say) is that there is "cause and effect" - increasing body height increases the number of women attracted to them - because you conducted an observational study, and did not perform a controlled experiment where you manipulated body height, kept everything else constant, and observed a change in the dependent variable (number of women attracted to them).
thx. So I assume that studies such as tall men earn more (based on the hypothesis that they're perceived as more "alpha maleish" / respected more by their bosses) than short men are completely irrelevant as there's a correlation, but it's simply an observational study..and conducting a controlled experiment is not possible at all?


TS Contributor
They're not irrelevant - there is some value in being able to say that there is an apparent relationship between two variables, especially if a sound theory and hypothesis is developed before collecting the data. But it's not as "strong" as a controlled experiment and being able to show cause and effect.

Whenever you cannot directly manipulate one or more variables (and keep all other variables constant or highly controlled) and observe the change in the dependent variable, by definition you cannot do a controlled experiment.
In the taller men earn a higher income couldnt I look at it like this:

height = A, income = B.

So there are 3 possibilities if theres a correlation:

1) height has an effect on income
2) income has an effect on height
3) There's a third variable C which causes A and B

Apparently a change in income wont change height (this would actually be possible to test..or we can just assume most men do earn more money the older they get but they dont grow taller the older they get (after a certain age of course)).

It seems very unlikely that there's a variable that would cause a higher income and being taller..a common denominator between those variables...thus we could assume that height has an effect on income (though its more of an idea than a proof).

Wait..I just realized..possibly kids of wealthy families could earn more money and have access to better/healthier nutrition which could be a variable c...or..or...but these seem to be rather unlikely if were looking at an industrialized country...though possibly intelligence could be a common denominator that leads to higher income and healthier nutrition, which might cause an "advantage" in height, too....but at least it seems as if these things shouldnt have a very big effect, thus if the effect was more than minimal we could at least assume that height affects income? (but I think it is rather minimal hehe)
They're not irrelevant - there is some value in being able to say that there is an apparent relationship between two variables, especially if a sound theory and hypothesis is developed before collecting the data.
I just realized that sometimes being able to detect a correlation w/o looking for a causation can be insightful, too. For example if we look at IQ tests (I mean those at a psychologist's not the online ones that overestimate people's intelligence to feed into their ego so they do the marketing for them) it might be insightful to know that people with a high score on such a test do very often excel on the job.

I guess its almost obvious to state that the high score on the IQ test wouldnt cause them to do very well on the job (though it might help as they believe theyre smart and should do well on the job ;)) at least not as the only factor...but the correlation would still give some valuable insights.

P.S.: It was just an example, I think IQ tests are an oversimplification and only correlate to a certain degree with real life intelligence.