I prefer the z-score formula for r for a number of reasons.
The name of the thing makes more sense (the first moment of the product of
z-scores, product-moment). Although this isn't obvious to students at first,
many appreciate this little bit of trivia.
The interpretation is more direct for two-variable regression, and ties
correlation and regression together nicely. If x is 1 standard deviation above
the mean, y is predicted to be r standard deviations above the mean--with a
perfect correlation, y is predicted to be as far above the mean as x and with
zero correlation, the mean of y is the best guess.
It provides another way of explaining regression to the mean, and the effect of
measurement error on regression to the mean.
This method for explaining regression to the mean also works well with design
issues, like the use of "matching" in non-equivalent control group designs.
"James D. Dougan" wrote:
> But - why use the z-score formula for r? The old covariance formula is far
> more intuitive than the z-score formula. Yes - you can easily show how the
> product of z-scores works the same way as covariance, but students really
> don't grasp z-scores very well to begin with and it is hard for them to get
> the translation back from z to covariance.
>
> My guess is that texts want to use the z-score formulation for r because
> it makes a smoother transation into multiple regression. But (sigh) I
> don't think multiple regression really belongs in a 200-level intro stat
> course....
