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This post was migrated to mathematics:

https://math.stackexchange.com/questions/2166949/deriving-a-1-alpha100-confidence-interval-for-theta-pivotal-quantity

(Its revision history on CV can be seen here.)

At present I cannot identify any plausible reason why this one is off topic on our site. We have many hundreds, maybe even thousands of questions of precisely this kind; while it uses mathematics (solve an equation), it's directly answering a stats question (how do I find a confidence interval in this case?).

For consistency's sake, I'd like a clear explanation (preferably from each of the people who voted to migrate) of how we can determine that this question is off topic on our site -- what criteria can applied that would put this question over the line?

Getting the policy right here is a serious issue for us -- if we don't identify some criterion that leaves lots of apparently similar questions on topic while this one is not, then many, many questions will need to be closed or migrated.

It looks to me like some of us are in for a very large amount of extra work here (unless we're just going to choose to be deliberately inconsistent, I suppose), and I want to have some clear guidelines to use when doing all that extra work. Right now I have no idea how to conclude this one is off topic.

[If it is in fact in error, I think that those involved should be the ones doing the legwork in redressing the issue -- getting it migrated back. Right or wrong, there's work to be done here.]

I've sought similar criteria before here (and elsewhere) on a number of other (to me) questionable migrations -- it's not like closure where a mistake can be undone with a couple of clicks, we need to be clear about why we're doing it. An example of such an earlier question is here.

[I don't recall having been offered clear criteria on those occasions, though I recall one where at least one or two people offered a level of justification, which overall suggests that there's a problem with some of the voting on migration. Since a migration is hard to undo, we should be prepared to justify why it's off topic.]


Edit (to address an issue in a couple of comments): If a question is on-topic at the source site, the clearly established principle (on many meta.SE threads as well as advice in parts of the help or other documentation relating to migration) is that it shouldn't be migrated; the exception would be where the OP requests it and it's on topic at the destination (in effect, if a question is on topic, askers get to decide where they want their question). As far as I see it, in deciding whether migration is appropriate, that leaves only the question of whether it's on topic here. To me it clearly is, but there's clearly thought to be room for argument (as in the comments).

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  • $\begingroup$ I didn't vote on that, but I can see some ambiguity. I certainly think it should be on topic on Mathematics. It could also be on topic here, IMO, but math might be a better fit. As @Cardinal mentioned in your other meta.CV Q, there are going to be "many questions that fall in grey areas ... Ultimately we want to find the best possible site for each question so that it gets a great answer". $\endgroup$ – gung - Reinstate Monica Mar 2 '17 at 13:31
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    $\begingroup$ As asked the q. was just about solving an equation. Your answer brought in more statistical context, though; I wouldn't have voted to migrate the q. after reading it. $\endgroup$ – Scortchi - Reinstate Monica Mar 2 '17 at 14:11
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    $\begingroup$ @Scortchi the post's title is "Deriving a (1−α)100% confidence interval for θ pivotal quantity", for me that's where the statistical context arises. While it's good to also put that information in the body of the post I don't see it as required to establish statistical context. $\endgroup$ – Glen_b -Reinstate Monica Mar 2 '17 at 14:39
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    $\begingroup$ It was only when I read your answer that I fully appreciated the statistical context so i can see where opinions could differ here. $\endgroup$ – mdewey Mar 2 '17 at 14:57
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    $\begingroup$ @Glen_b: Well, yes; the context is there, but rather scanty - the distribution $\theta$ parametrizes isn't even mentioned - & the question focuses on how to solve $u = \frac{\sqrt{n}(\bar{y}-\theta)}{\sqrt{\theta}}$ for $\theta$. I can see why someone might well have thought "Well if you just need help with the algebra, Maths SE is the best site". $\endgroup$ – Scortchi - Reinstate Monica Mar 2 '17 at 15:03
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    $\begingroup$ I would add stats.stackexchange.com/questions/266151/… as another example for consideration. Although phrased as a request for a "calculation in R," to me it appears to ask a useful statistical question. I can't imagine an answer on SO (whither it was migrated) that didn't also have to work through some statistical and mathematical issues first. $\endgroup$ – whuber Mar 8 '17 at 17:00
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    $\begingroup$ @whuber I see that as a rather more astonishing example, to say the least. Indeed, I had begun a new post about that one (pointing out our on-topic help says " if it needs statistical expertise to understand or answer, ask it here") before I saw your comment. How does that not need considerable statistical expertise to even begin to answer? $\endgroup$ – Glen_b -Reinstate Monica Mar 9 '17 at 1:02
  • $\begingroup$ I remember discussing this in meta a long time ago. At that point, I was in favor of leaving a lot of questions here that others wanted to migrate, esp. to the programming site but sometimes to math. So, do we have a clear policy? It would also be good to distinguish between migrating questions and closing them for being about using a language. I'll follow whatever policy there is, but what is it? $\endgroup$ – Peter Flom - Reinstate Monica Mar 10 '17 at 12:15
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    $\begingroup$ @Peter Asking about the policy is a fair question, and deserves discussion, but at the same time you are dodging the question Glen_b has posed here: "I'd like a clear explanation (preferably from each of the people who voted to migrate) of how we can determine that this question is off topic on our site." What criteria did you apply when deciding to migrate this question? If you would like to discuss this privately, then please join the moderators' chat room. $\endgroup$ – whuber Mar 12 '17 at 15:52
  • $\begingroup$ @whuber Fair enough. I don't think I can exactly articulate what I do, because I am not sure of what the guidelines are supposed to be. What I try to do is to close questions that are about things that look like pure programming questions and that ought to be answerable from package documentation and to migrate questions that are more about programming - usually, these are more complex questions or ones that could apply in several packages or languages. $\endgroup$ – Peter Flom - Reinstate Monica Mar 12 '17 at 21:26
  • $\begingroup$ @whuber Of course, sometimes, I'm wrong. Who isn't? Maybe the standard for migrating a question has to be changed? $\endgroup$ – Peter Flom - Reinstate Monica Mar 12 '17 at 21:27
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    $\begingroup$ Thanks for responding. The problem is I can't see how to relate a substantial number of migration decisions (I've only posted about a few) to what I see as the current standard. Specifically, I can't see how they can be migrated on the basis of two things - 1. don't migrate it if it's on topic here, and - 2. the fairly plain wording of help center which says what's on topic. I don't think those standards changing would solve issue that the decisions frequently don't seem to match the criteria. ...ctd $\endgroup$ – Glen_b -Reinstate Monica Mar 12 '17 at 21:45
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    $\begingroup$ ctd ... if we could see how some of those decisions relate to the criteria, we could then have some way to converge on being consistent with each other. At the very least, when we can communicate about the ones we can't figure out it helps to see where we might need to be clearer about what we're doing and so work at converging on those aspects. $\endgroup$ – Glen_b -Reinstate Monica Mar 12 '17 at 21:46
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    $\begingroup$ I'd like to take this opportunity to state that I appreciate the ongoing work @PeterFlom does to keep the review queues clear. Being rather disagreeable, I have disagreed w/ some of Peter's decisions from time to time, but I agree w/ the bulk of them & I would rather he continue (& I occasionally disagree) than that he stop. The fact is, there are a lot of reviews that need to be done & there really aren't enough experienced, dedicated reviewers. If it weren't for Peter, our review queues would be steadily growing. I hope he continues. $\endgroup$ – gung - Reinstate Monica Mar 13 '17 at 22:49
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    $\begingroup$ Indeed, I think we all appreciate Peter's efforts; no doubt there. $\endgroup$ – Glen_b -Reinstate Monica Mar 13 '17 at 23:01
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The key difference here is that the asker's intention was to get maths help. The asker knew how to compute a confidence interval. They were asking how to solve for $\theta$ in an equation. As you say, it's a lot of work to come up with general rules, but I can see a couple of guidelines that would help you here.

Firstly, think about the type of person who is best suited to answering that question. On the one hand, it's possible that someone who uses statistics often might not know how to solve for $\theta$ in that problem. They might use a solver program instead. Lots of statisticians would be able to solve it, but there's no branch of statistics where that kind of manipulation is fundamental. On the other hand, solving an equation involving surds and powers of $\theta$ is an important skill in mathematics. There are areas of mathematics where an ability to solve a problem like that is a prerequisite. So one criterion might be that a question is only relevant on CrossValidated if the required technique for solving the problem is more important in statistics than in other branches of mathematics.

Secondly, think about what the most likely answer is, and think about how you could generalise that answer. In this case, the asker is asking for an algorithm for solving an equation in one unknown involving surds. That could generalise to other equations involving surds, but it couldn't generalise, for example, to solving for parameters given a boundary of the confidence interval if the equation for that endpoint of the confidence interval doesn't involve surds. The answer is going to be more applicable to other algebra problems than it will be to other confidence interval problems. So again, it belongs with the other algebra questions.

There's a lot of information that's relevant to statistics in Glen_b's answer, but most of that information isn't actually answering the question. He's providing warnings about things the asker might have overlooked. This is useful information, but the asker's intention wasn't to get that information - if it was, the question would have had an explicit "Is this a statistically valid method?" part to it.

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