Sorry if this is trivial - I'm arguing with someone on Facebook who is claiming that r-squared values, or correlation coefficients represents "chance" or "probability". I've never heard of this.(adsbygoogle = window.adsbygoogle || []).push({});

I just need a simple yes or no answer along with a short explanation why it is or isn't probability.

He says:

"It is the probability that there is a connection between two different things.

A Correlation Probability of 1 means that these two things ALWAYS occur together, even if there is absolutely no causal links between them.

A Correlation Probability of ½ (or .5, or 50%) means that the two things are connected 50% of the time. Or, roughly what we would see in "Chance" for most things, depending upon what two things we are looking at."

I say:

"I think you have something wrong here. I don't know what a correlation probability is and I'm struggling to find it online. The ".55" value and other correlations in the literature are correlation coefficients, they are r-squared values calculated using a least squares regression analysis. R-squared estimates the fraction of the variance in IQ scores that is explained by % genetic relation - it has nothing to do with chance.

Chance of randomness is given by the p value, calculated by a t test on the same data. The chance of randomness depends on the data sets you're attempting to correlate and the variances of the data points. I still don't actually understand where you've gotten 50% from."

He says:

"An R-Squared IS a PROBABILITY (Describing the Chance/Probability that two variables are correlated)."

Is r-squared the same thing as probability? I've not learned it that way, I've learned it *only* as how much variance in one thing explains variance in another.

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# B Does a correlation coefficient represent probability?

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