The +1/2 Level Modifier

When does the +1/2 level modifier apply?

PHB pg#27
Gaining Levels: Level Modifier
“…everything that’s based on your level becomes one-half better – your attacks, defenses, initiative, and ability checks.”

PHB pg#279
Attack Modifiers
“An attack modifier is a bonus or penalty that applies to your attack roll. Add the modifier to your base attack bonus when you make an attack.”

PHB pg#26
Making Checks: Ability Checks
“Sometimes you’re not making an attack or a skill check, but trying to accomplish a task that doesn’t fall into either category. You make an ability check.”

Based on the above I'd say that it does not apply to damage or any other variable listed as the result of a power. For example the Paladin can Lay on Hands a number of times per day equal to his Wisdom modifier. So a Paladin with a 17 Wisdom can use Lay on Hands 3 times/day regardless of his level. But if his wisdom increases from 17 to 18 then he will be able to use Lay on Hands 4 times/day.

Do you agree or disagree with my interpretation?