I've been reading several papers on conspiracism recently, and a common thing they do is demonstrate a correlation (or not) between two variables. For example they might demonstrate a correlation between a person's "need for uniqueness" (as measured by answering some standard questions), and a person's Generic Conspiracy Belief score. So we get results like (Lantian 2017):

https://mindmodeling.org/cogsci2017/papers/0436/paper0436.pdf

So my question here is how to interpret these numbers. I'm assuming r is the correlation coefficient "Pearson's r". This is a kind of "goodness of fit" measurement, which shows how closely the distribution of values fits a line through them (found via linear regression).

Sounds reasonable, however in it seems to be a measure of the

I suppose, now I've rubber ducked my confusion, that the magnitude is somewhat irrelevant as its automatically going to be scaled relative to other factors. Like if you've got a r=1 then that means that this is the only relevant factor. r = .13 means there are other more significant uncorrelated factors or random variation (i.e. factors that have a proportionally larger effect) because those factors would spread the y values out, and decrease r.

There seems to be some subjective language used. Here we've got two studies, one says:

"was associated with" for a r=.17

The other says:

"link was very weak (r = –.13), "

Now can you really go from .13 to .17 (ignoring the sign) as from "very weak link" to "associated with"? I suppose they are not that different, and written by people with different native languages, but the gist of one paper seems to be making the correlation (.17) but with the other paper they conclude there's no real correlation (.13).

Is it fair for the popular press to say "researchers find Conspiracy Belief linked to need for uniqueness" and also "researchers find Conspiracy Belief not linked to low intelligence"?

Also, how do they get this amount of variance?

"Thus, Gf predicted only a negligible amount of variance (2%) in conspiracy belief."

Is that 2% from the r=-.13 only? Or other values from the data like p = .08? What's the math to arrive at 2% in that paper. "2% of the variation" seems more understandable than the r value, so would be a better number to use if I understood where it came from. And could you also calculate it for the other paper?

but also:

We first tested our main prediction, thatpeople with aIn line with this hypothesis

higher need for uniqueness should have a higher level of

belief in conspiracy theories.

and with our preliminary work,we found that a higher needThe test of the quadratic effect of belief in conspiracy

for uniqueness (measured by the Self-Attributed Need for

Uniqueness scale) was associated with higher belief in

conspiracy theories (measured with the Generic Conspiracist

Beliefs scale), r(206) = .17, 95% CI [.03, .30],

p = .015.

theories on need for uniqueness was not significant,

t(205) < 1. The linear association was replicated with the

single-item measure of belief in conspiracies, r(206) = .18,

95%CI [.04, .30], p = .011, and the quadratic effect was still

not significant, t(205) < 1.

https://mindmodeling.org/cogsci2017/papers/0436/paper0436.pdf

(Gf is standardised "reasoning ability", or "fluid intelligence")In line with our expectations, the correlation between the Conspiracy Belief and Irrational Belief factors was strong, r = .72, p < .001. However, the negative link between the Conspiracy Belief and Gf was very weak (r = –.13),and despite our large sample it was not statistically significant (p = .08). Thus,Gf predicted only a negligible amount of variance (2%)in conspiracy belief. However, as expected, there was a negative correlation between Gf and Irrational Belief, r = –.31, p < .001. In addition, the open-minded cognitive style showed the substantial negative correlation with Conspiracy Belief and Irrational Beliefs. Thus cognitive style was a much stronger predictor of conspiracy and irrational beliefs than Gf.

So my question here is how to interpret these numbers. I'm assuming r is the correlation coefficient "Pearson's r". This is a kind of "goodness of fit" measurement, which shows how closely the distribution of values fits a line through them (found via linear regression).

Sounds reasonable, however in it seems to be a measure of the

*quality*of the correlation, and not the

*magnitude*. Sure, it shows that people have more need for uniqueness then they are more likely to be conspiracy minded. But it does not show how much?

I suppose, now I've rubber ducked my confusion, that the magnitude is somewhat irrelevant as its automatically going to be scaled relative to other factors. Like if you've got a r=1 then that means that this is the only relevant factor. r = .13 means there are other more significant uncorrelated factors or random variation (i.e. factors that have a proportionally larger effect) because those factors would spread the y values out, and decrease r.

There seems to be some subjective language used. Here we've got two studies, one says:

"was associated with" for a r=.17

The other says:

"link was very weak (r = –.13), "

Now can you really go from .13 to .17 (ignoring the sign) as from "very weak link" to "associated with"? I suppose they are not that different, and written by people with different native languages, but the gist of one paper seems to be making the correlation (.17) but with the other paper they conclude there's no real correlation (.13).

Is it fair for the popular press to say "researchers find Conspiracy Belief linked to need for uniqueness" and also "researchers find Conspiracy Belief not linked to low intelligence"?

Also, how do they get this amount of variance?

"Thus, Gf predicted only a negligible amount of variance (2%) in conspiracy belief."

Is that 2% from the r=-.13 only? Or other values from the data like p = .08? What's the math to arrive at 2% in that paper. "2% of the variation" seems more understandable than the r value, so would be a better number to use if I understood where it came from. And could you also calculate it for the other paper?