In 2013, the University of Bristol psychologist Stephan Lewandowsky and colleagues published two papers containing a provocative claim: A tendency to endorse conspiracy theories, they suggested, makes people more likely to challenge various aspects of science, too. Across the two papers, they linked conspiratorial beliefs to science rejection on no less than five issues: climate change, vaccines, genetically modified organisms, and the ties between HIV and AIDS and smoking and lung cancer.

Since then, the research has been widely discussed and criticized — particularly the conclusion about climate science rejection — and now, the intensity of the debate seems set to go up yet another notch. The reason is that the journal Psychological Science has just published two papers on the matter: one, a statistical critique of the Lewandowsky papers, and the other a response from Lewandowsky and his co-authors (also discussed in a blog post here).

The critique, by Ruth Dixon and Jonathan Jones of Oxford University, charges that the most publicized conclusion of the prior studies, that believing in conspiracy theories is linked to climate change skepticism, is “not supported by the data.” Lewandowsky and his team, meanwhile, say that Dixon and Jones have undertaken an “atheoretical and highly circumscribed reanalysis,” and they stand by their results.

[Related: Fifty percent of Americans believe in some conspiracy theory. Here’s why.]

The claim of a link between climate change skepticism and conspiracy theories — which Lewandowsky and his colleagues measure with a questionnaire that asks about whether the moon landings were faked, whether Princess Diana’s death was an accident, whether Lee Harvey Oswald acted alone in assassinating JFK, and much more — has been very widely discussed and debated in the blogosphere and beyond.

The dispute aired in the new papers is extremely technical. (Just to give you a taste of it, Dixon and Jones write at one point that they’re using “non-parametric local regression” to show the problem with Lewandowsky’s results.) However,  some obvious conclusions can be drawn.

While almost all of the attention has been directed to the finding of a link between conspiratorial beliefs and the denial of climate change, in both cases, the original papers in question did much more than that. The authors admit that the correlation that they found was relatively small, and that other factors play a much bigger role in driving people to be skeptical of climate change — namely, holding “free market” and conservative beliefs.

Thus, the debate here would really seem to be between one camp who thinks that conspiratorial thinking has no role in climate change skepticism, and one camp who thinks it has a minor role. That’s important to keep in mind.

Moreover, Lewandowsky et al also showed that conspiratorial thinking plays a much bigger role in other kinds of science denial, and this conclusion is not disputed by Dixon and Jones. In one of the 2013 papers, for instance, Lewandowsky found a very large correlation for this type of psychological research (for stats nerds, > .5) between conspiracist ideas and skepticism of vaccinations.

Thus, even as a new debate is sure to rage due to this new statistical critique, one key conclusion seems indisputable: Conspiratorial thinking feeds into some forms of science denial — but in many cases, it’s not nearly as important as considering people’s ideology, or worldview.

Update: This post has been updated to remove a reference to debates over replication of results in psychology, as the argument here is more about reanalysis of data than full replication of experiments.

Read more:

Why the moon landing couldn’t have been faked

How a group of conspiracy theorists could derail the debate over climate policy

Meet the crunchy, chemical-hating anti-vaccine conspiracy theorists. From 100 years ago.

Why there are so many kooky conspiracy theories about oil