I believe the "dumbbell" effect you are referring to is Simpson's paradox: http://en.wikipedia.org/wiki/Simpson's_paradox http://en.wikipedia.org/wiki/Simpson's

I believe the "dumbbell" effect you are referring to is Simpson's paradox: http://en.wikipedia.org/wiki/Simpson's_paradox http://en.wikipedia.org/wiki/Simpson's_paradox As you point out obviously you can see it in a 2D scatter plot, but you have to select the correct two variables.