Does Winning Conference Tournament Lead to NCAA Tournament Success?

There was a post on Tigerboard.com discussing a quote by Bill Self where he said "We really don't care about that; the NCAA Tourney is what really matters." I responded to that post responded that 7 out of the last 10 champions were Tourney Champs. First, as with any NCAA Tournament stat, I decided to verify it and found out that the answer was 6 out of 10.

2010 Duke Yes
2009 North Carolina No
2008 Kansas Yes
2007 Florida Yes
2006 Florida Yes
2005 North Carolina No
2004 Connecticut Yes
2003 Syracuse No
2002 Maryland No
2001 Duke Yes

I went a bit further to see if winning the conference tournament was correlated with getting to the final four. I found that out of the last 40 final four teams, 18 have won their conference tournament and 22 have been at-large teams. During 4 of those years, an at-large team made the final four the same year the tourney champ from the same conference made the final four. Those teams were:

2001: Maryland - At-L; Duke - Tourney Champ
2002: Kansas - At-L; Oklahoma - Tourney Champ
2005: Michigan St - At-L; Illinois - Tourney Champ
2006: LSU - At-L; Florida - Tourney Champ

So adjusting for these years, that leaves 18 at-larges and 18 tourney champs. In conclusion, winning the conference tournament has no correlation on whether a team will make it to the final four or not.