Sorry I'm a bit late to the party. Haven't read all the posts so don't know if this study has been mentioned. According to this study, children who are exposed to religion have difficulty distinguishing possible from impossible.
According to the study, children raised with little religious background may be incapable of identifying a story in which God does something as "religious". It's hard to tell, because rather than report all classifications of all stories by all groups in study 1, they focused on whether stories were classified as "real" when they were, when they were "religious", and when they were "fantastical". The authors don't do tell us that secular children were more likely to judge religious stories as "pretend", but as that isn't one of their categories it seems more than a little odd.
However, they did provide more for the classification scheme broken down into 5 categories: reality, impossibility, religion, pictorial, and uninformative. The stories differed very little, mainly in that the "fantastical" stories used the word "magical' and the "religion" one used the word God while the "reality" used neither. Oddly enough, scores were pretty similar except in one category: "religion". The non-religious group's responses were almost equal among 4 of the categories (basically none of any groups' responses were ever classified as "pictorial", making the classification schema questionable). Now, if I'm 5 and I know something about religion (I've been taught prayers and told stories about the Bible, for example), and someone tells me a story that involves God and asks me about it I'm probably going to notice that because it involves God it's religious. What's a good way to test that? Take children who non-religious and see if they are more or less identical in how their responses were classified when it comes to the religion stories. Guess what? They were. Non-religious children's explanations were slightly more likely to be classified as religion given religious stories than they were to be classified "impossibility", slightly more likely to be classified as "impossibility" than "reality", and slightly more likely to be classified "reality" than "uninformative".
Take the same story as the "reality" one, insert God, and children familiar with religion identify it as religious.
Do this with the non-religious children, and they are more likely than all other groups to explain it as "reality" rather than "religion".
This could have been a much better study had they not assumed that Barrett's work (and those like him) entails something it doesn't: namely, that a natural tendency in children to religious-like explanations means that there won't be differences among children with and without religious backgrounds in terms of their tendency to explain "stories" as religious (or reality, fantastical, etc.).
As for Study 2 (the second experiment in the same published study), we find "The results also undermine the hypothesis that religious children take a reference to magic to be an indirect reference to a miracle. In fact, religious as well as secular children were more likely, not less likely, to judge the story protagonist as pretend if the story included a reference to magic."
So, when you remove religion for the equation, and voila: "it is important to note that there were almost no religious justifications in Study 2, even by the religious children."
So what they really found was that when children with some religious background (in "Study 1" there were four groups, three of which were religious on some level) when presented with a vignette that refers to God are likely to think it religious, while non-religious children are more likely to think it is reality. Astounding!
I.e. a child who is taught Jesus rose from the dead is susceptible to believing things that are purely fantastical but UNRELATED to religion
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None of the stimuli involved Jesus.