There are four attributes:
Each covers a different set of aptitudes and talents, discussed on their own pages. Each is the most important attribute...depending on what you want to do.
In order of speed, they are, from fastest to slowest under the ideal condition for their use:
In many cases, these conditions won't apply, in which case the GM must engage in some interpretation.
Nabiki and Ranma are throwing down with each other, probably for some stupid reason. Nabiki is first in Psyche, Ranma is first in Strength. They are about fifteen feet away from each other. Nabiki decides to cast a spell, Ranma decides to kick Nabiki in the head. Checking the casting time, the GM rules Ranma gets his kick in before Nabiki finishes her spell, and sends her flying into a wall. Her spell is wrecked.
Nabiki feigns unconsciousness, deciding to use her superior psyche in a psychic attack once he comes close enough for her to try to touch him. Ranma falls for it (Her Psyche is superior to his by a landslide, it's easy for her to trick him like this. If Ranma tried to trick Nabiki, she'd likely be able to sense the deception with her top ranked Psyche).
Ranma bends over to make sure she isn't dead, and when he touches her, she tries to invade his mind. Unfortunately, Strength is faster if you're touching the person than Psyche is, when Psychic Contact has yet to be established. So Ranma pulls away from her before she can finish initiating the psychic conflict. She tries to grab his foot, but his superior strength easily lets him play keep away. He dances back and pulls a sword off the wall so he can fight her without allowing her to touch him and risking mind control. His fourth in warfare beats her seventh, after all.
Nabiki grabs another sword and they start fencing while she tries to find some way to get psychic contact. She fights defensively, then tries to pull a trump and trump out. But she's within range of Ranma's weapon, and warfare is fastest when you're within weapon reach. He knocks the trump away before she can activate it.
Nabiki finally remembers her own shapechanging. She takes on her demon form, which is armored. She attacks all out, taking several wounds from Ranma in order to get close enough to stare into his eyes. Psychic contact is intitiated. Ranma now faces a difficult choice; he can focus his attention on resisting her assault, or he can hope that he can knock her out before she controls his mind by focusing on the physical combat. He goes that route. Unfortunately for him, Psyche (once contact is established) is faster than Strength, which means she can clobber him with her first rank Psyche faster than he can clobber her with his Strength or Warfare. Ranma ends up as her flunky boy. If Ranma had fought more carefully and not locked eyes with her (which he could easily do with his large Warfare and Strength advantages), she could never have attacked his mind without him being able to disrupt the contact with a nice hard punch, due to the relative speeds.
Warfare has a combat advantage over Strength (assuming the person using Warfare has an actual weapon handy). X points of Warfare will beat X points of Strength in direct confrontation, unless the Strength oriented person has a higher Warfare than the first person. In which case, he'd probably be using a weapon instead of Strength anyway. Still, Strength does involve unarmed combat skills as well as raw physical power, and so it is possible for a person whose points in Strength sufficiently exceed the other person's Warfare to block all the Warfare person's assaults and start pummeling them into the ground.
Alternately, if your Strength beats their Strength, but doesn't sufficiently beat their Warfare, you can risk taking a few blows and then close in to grapple, which is pure Strength vs. Strength. This can work well, but if their Warfare beats yours by enough, you may simply get cut to ribbons in the process, or maybe not even succeed at all.
Power Words like 'Neural Disrupt' are a very useful accessory when trying to pull that stunt.