Alex Tabarrok drew attention a couple of weeks ago to this study: disagreement with the consensus on controversial topics corresponds with worse understanding of non-controversial knowledge, like that we breathe oxygen from plants or that electrons are smaller than atoms.
The authors then correlate respondents’ scores on the objective (uncontroversial) knowledge with their opposition to the scientific consensus on topics like vaccination, nuclear power, and homeopathy. The result is striking: people who are most opposed to the consensus (7, the far right of the horizontal axis in the figure below) score lower on objective knowledge but express higher subjective confidence. In other words, anti-consensus respondents are the most confidently wrong—the gap between what they know and what they think they know is widest.