The mirror test is a good example. To recognize yourself in mirror, you need to understand that you are a person. Not many animals recognize themselves: apes, some ravens, elephants dolphins... all usual suspects known to be intellegnt.
Give them a mirror and once they figure it out they spend the next hour making faces and checking out their own ass. Mark their face and they'll try to clean it in the mirror.
Then ants.
Ants seem to get mirrors too. So either ants are self conscious or the test is no good.