A study shows that, apart from its effects on those for whom we pray, the act of praying for someone else can bring calm to the person praying.
You might be inclined to say, "Duh" to that. But I find the amount of research being done on prayer by social science and medical researchers these days interesting. Both Dale Matthews and Larry Dossey, themselves physicians, have written extensively on research into the connections between prayer and healing.
Presumably any quiet activity that takes a person's mind off of whatever has been frustrating or angering them would bring a degree of calm, including prayer.
But it's interesting that the calming activity in question isn't prayer for one's self, but prayer for others.
At the beginning of his best-selling book, The Purpose Driven Life, Rick Warren hits readers with a bracing assertion, rooted in the teaching of the Bible: "It's not about you."
Prayer for others--what Christians call intercessory prayer--is one way people can embrace the fact that they as individuals aren't centers of the universe and that instead of praying to complain about others--a legitimate Biblical form of prayer known as imprecatory prayer and found in the Psalms, by the way--peace comes when we choose to allow God, through out prayers, to use us as channels of grace and help to others. It's not about us!
So, I would theorize that one reason those, in this study who prayed for others were calmed is that intercessory prayer moves toward the kind of compassionate regard for others that Jesus commands in the great commandment. I hope that more research is done along these specific lines.