A 30-something percent gap is plausible, a claimed 78-percent gap (in either direction) is preposterous on its face — nobody would work in the private sector at all if that were true.
“The study found that federal government workers earned an average of $84,153 in 2014, compared to the private sector’s average of $56,350. Cato based its findings on figures from the U.S. Bureau of Economic Analysis (BEA).”