Checking your unit stats in Age of Empires 3

IIRC there's a tab (along the left side of the action card) when you have the unit selected that you can switch between their actions and their stats; it's fairly subtle.

Holding the ALT key while a unit is selected will display the stat sheet. Most of the figures and symbols are fairly self-explanatory, but for clarification you can hover the mouse cursor over any value and it will tell you in more detail what it means.

Bear in mind that the stat sheet shows the unit's stats in its current configuration - so if your unit is in Stealth mode, or a ranged unit is in Melee mode, this will be reflected. It also means that you'll need to switch Artillery to attack mode before you can see their attacking stats.