True Correlation


What is the difference between correlation and true correlation?

Is true correlation is always zero. Ref : Reading 9, Ex-8


True correlation (rho) means the actual (and usually unknown) correlation value in the population (between two variables, for example). It’s the same idea as someone referring to the “true mean” when they are talking about the parameter mu.

Typically people say correlation when referring to a correlation that was estimated from a sample, usually called rho-hat. The “hat” is the same symbol you see over other parameter estimates (it just means estimated). They’re talking about an estimate of the true value.

The true correlation is not always zero (it just depends what correlation you’re referring to). However, let’s say you are looking at the correlation between A and B. If it is truly zero, you may take different samples that yield correlation estimates around zero, but this doesn’t mean the true value has changed from zero.

Or r. (In line with sample means and standard deviations using Roman letters instead of Greek letters.)

Thats true, and I think it depends where you look (but not that it matters, as long as you understand what it means). It isn’t uncommon to see estimated regression coefficients as beta(i)-hat rather than b(i). I do frequently see correlation estimates labeled as r, though.

The CFA curriculum tends to use Greek letters for population parameters and Roman letters for sample statistics.

I, too, have seen statistics texts with rho-hat, alpha-hat, beta-hat, and so on.

Thanks for the reply. Though I am still confuse, but don’t know what to ask further.

True correlation means in actual the population correlation between two variables. It can be any value. If I am not align with your explanations please help.


Did I make a statement that was unclear, and if so, which statement(s) could be more clear? If not, I would be happy to take another shot at it.

Let me know how I (or someone else) can help!

This is correct if you include the bold.