Say I have a continuous variable that for some reason needs to be binned into a dichotomous variable. In such a case, I pick some cutoff point and encode everything above that cutoff as 1 and everything below as 0.
Now I run a Pearson's point biserial correlation with both versions of that variable. Generally I'll expect a fairly high correlation, but still below 1.
Why is this and how should I interpret it?