Right-wing media thrives on Facebook. Whether it rules is more complicated.

Untangling the influence of right-wing media is hard, especially with limited data.

A few years ago, New York Times columnist Kevin Roose decided he wanted to get a better look at what was happening on Facebook. Because Facebook does not offer much data about activity on its platform, Roose turned to a Facebook-owned tool called CrowdTangle, which lets journalists and researchers see which public posts are getting the highest levels of engagement. It seemed revealing at first glance.

“I started collecting this data without any kind of agenda. I was...