Do you not see the difference between "active military" and deployed troops?

Of course, but I can't find statistics for that per country per capita.

I would be very surprised if countries like New Zealand and Australia do not have more deployed troops per capita than America does.

Not counting the Navy, the US has at least double the per-capita rate of deployed troops. But that's misleading too, because most of New Zealand's deployments aren't hostile; a US soldier is far more likely to see combat than an NZ soldier.

Can you back that up with links to stats please.

Well to start with New Zealand, can you name a country it has invaded?

New Zealand has many troops in the "war against terror".