Category errors and identity salience

From Witches Now Outnumber Presbyterians In The United States by Jonathan Turley.

According to a report from the Christian Post, the number of witches and wiccans has increased dramatically since the 1990s. Indeed, the figures is taken from studies from a Trinity College and the Pew Research Center that found that there are at least 1.5 million witches in the United States. That would put them 100,000 over the 1.4 million mainline Presbyterians in the country.

The Pew Research Center reported in 2014 that 0.4% of the population — 1 to 1.5 million Americans — “identify as Wicca or Pagan.”

Most of these Americans view themselves as pre-Christian in their faith with a close connection to the Earth and natural forces.

A great example of the care you have to have with surveys (covered in my post, Statistical subsidiarity, and with particular reference Scott Alexander's 4% Lizardmen factor.

In this instance, I suspect they are not controlling for definitional constancy leading to a category error. Your religious affiliation is likely not to have the same saliency as a likely optional identity (on average.) In this instance, when answering a Pew question on your religion, if you respond that you are Presbyterian, that is consistent with some internal definition presumably having something to do with belonging to a congregation, attending with some frequency and self-identification as Presbyterian to others.

If you are responding to a question about religious beliefs (as opposed to religion) you do not necessarily have the same definitional constancy. I suspect that there are very few self-identified witches who belong to a coven, attend with some regularity, and who also self-identify as a witch to others in the same manner as a Presbyterian responds.

The outward and visible signs of being a Presbyterian are different than the outward and visible signs of being a witch. Indeed, even if one personally self-identifies as a witch, my suspicion is that the centrality of that identification is far smaller and weaker than the centrality of being a Presbyterian is to a Presbyterian.

Its like asking one person whether they are a Presbyterian and asking another person whether they believe in karma. The two categories are marginally related but they are different categories with different salience.