A study in the Journal of Biomechanics found an arm swing increased jump height by an average of 3.386 inches compared to not using an arm swing.
A study in the Journal of Strength and Conditioning Research found the addition of the arm swing causes greater benefit to men than women. The researchers speculated this was because of increased upper body strength.
Train the upper body for strength with push-pull exercises (Bench Press, Rows, Pull-Ups and overhead presses).
You can also train for the arm swing action by performing Med Ball Slams and Med Ball Overhead Throws.