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This question currently has 2 votes to close. Hopefully I'm not asking this question prematurely, but are we to consider all future applied mathematics questions off-topic or on-topic?

I see where the linked question indeed has some relevance to skepticism-- statistics are a huge part of the research from which we derive our conclusions about reality. However, as I mentioned in the comments on that question, I think it more closely fits in the scope of stats.SE. Either that, or this question is possibly too localized for skeptics.SE, due to its mathematically esoteric nature.

Is this indeed the case? Should we consider this question and others like it on- or off-topic?

Edit: I'm trying to think of other examples of mathematical topics which may be relevant to skepticism. The only one which comes to my mind is the Birthday Problem, which really only is relevant because it can be used as a demonstration of the importance of thorough analysis of a claim (the seemingly obvious answer to the problem is incorrect). And still yet, I think it too fits better in stats.SE.

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I think the question goes beyond "Are applied mathematics questions on-topic?" It's really about how does Skeptics.SE fits in the Stack Exchange Network. We cover practically all areas of sciences, just not as deeply as the Stack Exchange site dedicated to that field The question is thus, "Where do we draw the line?"

To answer that, I cite part of my answer to How to deal with medicine questions and the like:

I think we should cover the basic questions on science that are propagated by non-scientists (Al Gore, Jenny McCarthy, mainstream media, etc.) and hearsay ("you get a cold from being cold" and the like), but we leave the real questions to the real pros (i.e. Physics.SE, Biology.SE, Chemistry.SE, etc.).

To answer your question more directly, I agree with you: this question belongs on CrossValidated or on Math.SE. While I believe mathematics questions are on-topic, I think MindDetective's question about Bayesian and frequency probability goes beyond the scope of this site.

The claim that Bayesian statistic are "more sensitive, appropriate, and selective towards genuine findings" isn't something you would hear outside of research. As such, we should consider this question off-topic.

  • Wait, when you say "we leave the real questions to the real pros", then is this site supposed to have no real questions and no real pros? – Pacerier Jun 9 '15 at 20:18
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The scope of the site is not well defined, I would say. If you want experts to come to the site and provide input on skeptical matters then questions should be allowed to vary from the basic to the technical. As a memory researcher, I can provide genuine, quality information about certain topics. By limiting the questions to the kinds of questions that Mythbusters and Wikipedia and Snopes covers, it will likely mean the usefulness overlaps with existing, easy to access sources for answers. I guess the problem for me is labeling something as off-topic simply because it that may not attract an answer is not good enough reason. If the question pertains to real world claims that can benefit with a skeptical eye, then it should at least be allowed a place to be seen, even if no answer is ultimately given. Thus, I feel that my question and the way I asked it was on-topic but the technical nature of it may have limited the responses that could be given.

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    There is nothing wrong with your question. If someone doesn't understand the vocabulary used, then that person has no business answering anyway. The problem is that, at some point, a question goes beyond the realm of mere skepticism. For example, "Is a 0.99995 of higher correlation really necessary for extrapolation of the concentration of [substance]?" is much less about skepticism than chemistry. Your question sits on the thin line between the two. – Borror0 Mar 13 '11 at 18:03
  • That may be a fairer comment. I genuinely intended it be an assessment of the claims of superiority of one type of statistics over another and not about the agreed upon decision points used within each. – MindDetective Mar 13 '11 at 18:26
  • The problem isn't that it might not attract a good answer. However on that point, the number of statisticians who visit CrossValidated is undoubtedly greater than the number who visit here. You are far more likely to get a great answer there, and will certainly expose the question to more scrutiny. My suggestion to move the question was mostly in aid of getting the best answer you can get. – Mark Lapierre Mar 14 '11 at 3:53
  • The main problem I see is that the topic of skepticism, as the critical assessment of dubious or contentious claims, is highly tangential to the crux of the question. The main topic of the question is a comparison of methods of statistical analysis. As such, CrossValidated is a better place for it. I'd consider it on-topic if either the balance were flipped (e.g., it was more about Bem's claim than about the stats used), or if there were no other place to ask about stats (and even then I'd suggest proposing one on Area51). – Mark Lapierre Mar 14 '11 at 3:57
  • Incidentally, you might want to have your say on what the FAQ should contain about the site's scope: meta.skeptics.stackexchange.com/questions/89/… – Mark Lapierre Mar 14 '11 at 3:58
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I think that asking about questions like Bayesianism vs. Frequentist is on topic in the same way that asking about cognitive biases is on topic.

Statistics are essential to reasoning about the world. Whether we should believe in the results of Frequentist statistics or disbelieve is an important question. It's technical but still important.

Challenging common statistical practice is skepticism.

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Although statistics is a very important subject, I think it belongs within the realms of the tools used by skeptics. It could be an appropriate question for meta ("Should we allow backing claims based on Bayesian logic on the same level as classical statistics?"), but not for the main site, where as @Borror0 said, it is off topic.

That said, the question in my opinion could be barely salvageable (I am not sure), if there was some woo claim to debunk without going into mathematical subtleness (e.g. "Is the claim [reference] that Bayesian stats works better than classical stats valid?") - but even then, if you asked the same question directly on Maths.SE, you would certainly get more and better answers.

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