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From The smart move: we learn more by trusting than by not trusting | Aeon Ideas:

We find the same pattern in other domains. People who trust the media more are more knowledgeable about politics and the news. The more people trust science, the more scientifically literate they are. Even if this evidence remains correlational, it makes sense that people who trust more should get better at figuring out whom to trust. In trust as in everything else, practice makes perfect.

What does the bolded phrase mean? Does it mean that even if the evidence isn't causal, the next phrase still makes sense? And what is the "evidence" they are referring to?

Meta: Does this question belong here or ELL?

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    $\begingroup$ "While we cannot prove causality, it's reasonable to expect these two things to go hand in hand". $\endgroup$ – Flater Apr 19 at 10:05
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  1. Both the cited finding that, "People who trust the media more are more knowledgeable about politics and the news" and the cited finding that, "The more people trust science, the more scientifically literate they are", are results found in observational data. It is well established that it is difficult to infer causality from observational data. As a result, these are referred to as correlational. That is, it has not been established that trusting the media causes people to become more knowledgeable of these topics; likewise we don't know that trust in science causes people to become more scientifically literate. For example, it could be that being more educated leads to both greater knowledge and trust in the media, and it could just as easily be that being more scientifically literate causes people to trust science more.

  2. The following claim ("people who trust more should get better at figuring out whom to trust") does not logically follow from the prior claims. As a result, the causal status of the prior claims is not that important in supporting its truth. Instead, it seems to be an appeal to intuition.

  3. The "evidence" is the two findings that had just been cited.

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  • $\begingroup$ Great explanation. Roughly, it sounds like if we base our assumption on the conclusions inferred from correlation, then the best we can produce is intuition, as an opposite to deduction when we have causation. $\endgroup$ – surlac Apr 19 at 4:36
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    $\begingroup$ @surlac, I wouldn't equate deduction in logic w/ causal inference in statistics, and induction in logic w/ correlation in statistics. That doesn't really hold. $\endgroup$ – gung - Reinstate Monica Apr 19 at 5:38
  • $\begingroup$ Ob. xkcd: xkcd.com/552 $\endgroup$ – Eric Towers Apr 19 at 23:16
  • $\begingroup$ @gung-ReinstateMonica, I see. I still think inference plays certain role, but probably more in the context of inferring causation from correlation. $\endgroup$ – surlac Apr 26 at 5:04
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It means, that changing one of those variables may, as well as may not, lead to changing the other. We can not apriori say which is how much likely.

Imagine, that you can force somebody to increase the knowledge about science. If evidence is correlational it may or may not result in changing the trust. If there existed causal evidence, that knowledge causes trust, it is highly likely, that interventionally changing (for example by motivating to learn) knowledge of a person will have the effect of changing the trust.

Also the other way. Imagine, that you can change somebody's trust. If evidence is correlational, changing somebody's trust to science, may, or may not, result in gaining knowledge. Causal evidence make such effect much more likely.

The reasons for such distinctions are many.

One of them is that correlation do not distinguish direction. There is possibility, that only knowledge causes trust, but not the other way. Also, there is possibility, that first people gain trust, then knowledge. Also, there is possibility, that the relation is bicausal: when someone gains some knowledge, gains some trust, but trust then motivates to gain even more knowledge, which leads to even higher rust.

The other is, that maybe such relation do not exist directly, but it is caused by third variable. For example studying in college. If person goes to college such person both gain knowledge, and is persuaded, that science make sense, because meets a lot of people, who trust science, and make a living of it. Unless we make special analysis, which may take such things into consideration, we do not know for sure if causal relation exists at all.

The third example is that maybe people, which are analysed, and such correlational evidence is derived are selected in a way, that "makes" correlation without any relation between them. For example if we make such analysis on the group of people, who are successful scientist, assuming, that success requires both knowledge and trust in what they are doing, such correlation may appear, but changing one of the variables will not result in any reaction from the other.

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  • $\begingroup$ Interesting perspective. Sounds like chicken or the egg causality dilemma, with a bicausal relation. $\endgroup$ – surlac Apr 19 at 4:44
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Evidence being "correlational" (more often called "observational") means that this was passive observational evidence of a statistical association between things, without any controlled experimentation. For example, consider the claim that "[t]he more people trust science, the more scientifically literate they are." Presumably the authors are referring to some passive observational evidence that trust in science was correlated with scientific literacy amongst the observational group. Presumably this evidence did not involve any experimental intervention to manipulate one of these variables and then observe the later effect (or lack of effect) on the other.

An alternative way to acquire evidence about this matter would be to conduct a randomised controlled trial (RCT) where researchers intervene in some way to affect one of the variables under study and then observe whether there is any change in the other variable over a period of time. (Usually the intervention is only for one group in the study, and another group is left as a "control" group.) For example, researchers might conduct some intervention that they think will exogenously increase the "trust in science" of the treatment group (without improving their scientific literacy) and then measure the later "scientific literacy" for both groups to see if their intervention has had any effect.

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Trust in Science -> Scientific Literacy is observationally equivalent with Scientific Literacy -> Trust in Science. Similarly, Education -> Trust in Science & Education -> Scientific Literacy is also observationally equivalent with Trust in Science -> Scientific Literacy. So when they say "even if this evidence remains correlational" they're saying they can't rule out these alternative explanations which could induce the same correlation without there being a causal relationship where Trust in Science -> Scientific Literacy. The next phrase is then a claim that despite being unable to rule out reverse causality or omitted variable bias based on the correlation, nevertheless it makes sense that there would be a causal relationship where Trust in Science -> Scientific Literacy.

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  • $\begingroup$ So is it correct that the whole sentence can be summarized as "it makes sense that there would be a causal relationship where Trust in Science -> Scientific Literacy, even though don't have enough data to prove it"? $\endgroup$ – Ooker Apr 19 at 3:17
  • $\begingroup$ There is no proof that there is causal relationship between trust -> literacy exists, it's only observation that two patterns occur. Thus the sentence in your comment @Ooker needs to have a proof that there is correlation exists. So in the math terms, correlation is necessary for causation. but not sufficient. $\endgroup$ – surlac Apr 26 at 4:53
  • $\begingroup$ @surlac I understand that. I just want to understand why the author says "it makes sense" even when there is no proof of causation. Do they mean that in case we do have the proof for causation, the result shouldn't surprise us because it matches with our intuition? $\endgroup$ – Ooker Apr 26 at 6:04
  • $\begingroup$ I think the conclusion is based on large corpus of observational studies, which author tries to point out by going through observations and showing how one variable is correlated with another, even though the only way to establish causation is through an experiment. $\endgroup$ – surlac May 4 at 5:06
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What does the bolded phrase mean?

  • I agree with you that it means the evidence isn't causal. In other words, no causal inference was tested so they only note the correlation in the survey data.

Does it mean that even if the evidence isn't causal, the next phrase still makes sense?

  • Yes. Even if the relationship isn't causal, only an experimental correlation, we are still going to attribute causation to the correlation.

And what is the "evidence" they are referring to?

  • I think it is the evidence from the previous paragraph:

Yamagishi and his colleagues demonstrated the learning advantages of being trusting. Their experiments were similar to trust games, but the participants could interact with each other before making the decision to transfer money (or not) to the other. The most trusting participants were better at figuring out who would be trustworthy, or to whom they should transfer money.

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    $\begingroup$ "Even if the relationship isn't causal, only an experimental correlation, we are still going to attribute causation to the correlation." This is a bad practice, right? So why does the author say it (the causation) still makes sense? (Hopefully the author understands that correlation doesn't imply causation.) $\endgroup$ – Ooker Apr 19 at 3:28
  • $\begingroup$ I agree that it is a bad practice in isolation. You have to judge if the other evidence is enough to make you believe in the causation. $\endgroup$ – R Carnell Apr 19 at 3:35

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