Taken from Whatculture:

While O Brother, Where Art Thou? was eventually credited as an adaptation of The Odyssey (the first Coens script to adapt an existing source), it was a different quest to return home that served as Joel and Ethan’s original inspiration, one that provides another slice of sepia-toned 1930s Americana. “We were thinking of it more as The Wizard Of Oz,” Joel revealed on the movie’s 15th anniversary on 2015, “We wanted the tag on the movie to be: ‘There’s no place like home.’” Even after the story moved more toward picking up on the episodic beats of Homer’s classical epic poem, there still remains a few residual elements of Oz in the film as released. The scene in which our three bumbling heroes disguise themselves as Klansmen to rescue Tommy from a lynching, for example, is an homage to the similar rescue of Dorothy from the Witch’s castle by her trio of bumbling sidekicks in the children’s fantasy classic. The Klan even march in formation with low rhythmic chanting just like the Wicked Witch’s guards.