According to Thomas Bayes, the analysis isn't quite wrong. Comment reproduced for your convenience:

Based on the census tables that he cites, here’s what I see for 2005 (in 2005 dollars):

All men: $31,725

White men: $32,179 * Soltas says $31,725, which is the median for all men.

White, not hispanic men: $35,345

Conard says $35,200 for white men, which is very close to the number for white, not hispanic. The number he uses for white women is $19,600. The Census data that Soltas cited shows $19,451.

Based on this quick comparison, I’m not sure that Soltas has discredited Conard’s analysis.