antithetical vs wrongheaded

antithetical

adj
  • Pertaining to antithesis, or opposition of words and sentiments; containing, or of the nature of, antithesis; contrasted. 

wrongheaded

adj
  • Having an obstinately (persistently, stubbornly) perverse/erroneous opinion or judgement. 

How often have the words antithetical and wrongheaded occurred in a corpus of books? (source: Google Ngram Viewer )