Lars Anderson began 2008 in the California League. Lancaster is a great place to hit, and he ended up having a fine season there, hitting .317/.408/.513 with 13 homers, 46 walks, and 64 strikeouts in 306 at-bats. But he did a lot of damage at home, and some were a bit skeptical about how this would transition to higher levels.
The Sox promoted Anderson to Double-A Portland in July and he didn't skip a beat, hitting .316/.436/.526 in 41 games, obviously proving he could hit outside of Lancaster and against better pitching. Indeed, his production was actually more impressive at the higher level: his OPS was +22 percent compared to league for Lancaster, but +29 percent compared to league for Portland. He did have a notable home/road split in Double-A, hitting .348/.482/.530 at home (1.012 OPS) and .284/.388/.522 on the road (.910 OPS), granted a .910 OPS was still just fine.
The only major flaw I can see in the Double-A numbers is his platoon split: .225/.367/.375 against lefties, .355/.465/.591 against right-handers. Obviously he has work do to against left-handed pitching. His strikeout rate crept up over once per game in Double-A, though his walk rate remained high and I'm not worried about his plate discipline. Scouting reports about Anderson late in the year were overwhelmingly positive.
In short, Anderson's Double-A transition was very successful. He still has some things to work on, notably his performance against southpaws, and he needs to put the finishing touches on his strike zone judgment. It's also still a bit unclear if he will be a 20-25 homer guy or a 30+ homer guy at maturity. But there's no doubt he's one of the elite hitting prospects in the game.