Unarmed Damage

I was wondering if race plays a role in the amount of damage that an unarmed attack does. I noticed that my character (a Nord), after picking a bar fight, dealt (seemingly) less damage per hit to my opponent than when my cousin's character (an Argonian) fought the same exact NPC. We were both the same level at the time. I have not played ANY Elder Scrolls games before and Skyrim is my entrance into the franchise. Thanks!