There isn't one
There is no specific rule that states how Large+ creatures interact with area effects. Notably, Areas falls under Effects, and neither uses words that would lock-in a particular ruling such as "any portion of a creature's space" or similar.
Some effects occupy an area of a specified shape and size. [...] Many area effects describe only the effects on creatures in the area.
Anything you do in the game has an effect. [...] Many spells, magic items, and feats create specific effects, and your character will be subject to effects caused by monsters, hazards, the environment, and other characters.
Rules on Spell Areas don't make it any more clear, only provide some guidance on applying area effects that also have a range.
From the other side of things, Size, Space, and Reach provides no guidance regarding applying effects; neither the word area nor effect even show up in the section (which makes some sense because it was written under the Movement in Encounters header).
Rule of Thumb
I have always, and all of my groups have always, considered that an area effect affects Large+ creatures fully if even one square is shared unless circumstances dictate otherwise. For example, clipping the corner of a Large creature's space with fireball would deal full damage and not provide any bonus to the reflex save. However, dropping an obscuring mist onto their corner would not usually make them concealed, or conceal others from them, in the direction they are standing out of it.
This ruling makes sense to my groups for a couple reasons. Firstly, it is reliable; you don't have to ask the GM about every area spell you want to toss out. Secondly, it is most in line with the idea that the effect affects an "area" and that area has a creature in it (albeit not that whole creature); other rulings would cause further questions and confusion about "if the Large creature can be in its other 3 squares, why is that square part of it at all?" and "I have cover because my foot is behind the wall".