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Since I'm still quite new to the site, I just wanted to poll what the general consensus is on voting down questions from people with very low rep.

As an example, I don't think the OP from this question really understands the difference between a categorical and a continuous variable. I saw that some had voted the question up, but I personally wanted to vote it down (and did) because I feel the OP didn't understand what he or she was asking.

  1. Do you think this discourages new posters if they have their questions voted down? (Even if perhaps they received answers that are voted up?)

  2. If you answered yes to question 1, is there some approximate metric, duration of account in days, or minimum rep before you believe a question should be voted down?

My motivation is that I really want to encourage my students to ask questions here, but I don't want to raise the noise level with questions that aren't well thought out.

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I do not think we should downvote clear questions that merely reflect some confusion about some aspect of statistics. We should take the opportunity to clarify the confusion so that the OP learns something new and is on the way to become a better statistician.

Summary: Downvote when we see: Spam, unclear questions, irrelevant answers, trolls

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  • $\begingroup$ I'll just add that you can also vote to close (for duplicates, off-topics, meta-questions, subjectives) and flag (for spam and when you think moderator should do something with it, like convert to community wiki). $\endgroup$ – user88 Oct 12 '10 at 17:02
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    $\begingroup$ And even newbies can be expected to react to requests for clarification. So if such requests are ignored for a couple of days, I'll happily downvote or vote for closure. $\endgroup$ – S. Kolassa - Reinstate Monica Oct 14 '10 at 21:09
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I almost never vote down a question that is asked in good conscience to expand knowledge.

That being said, if a question is up-voted excessively, a down-vote can be used to offset. I don't think that should discourage new user. Especially if you follow the golden rule of down-voting: always leave a comment so people understand how they can improve. And equally important: if the OP does improve the question following your comment, switch over to an up-vote to reward the good behavior.

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    $\begingroup$ ... and comments on the reasons for upvoting are always welcome, too! $\endgroup$ – whuber Oct 12 '10 at 21:47
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Ok to vote down newbies?

Yes: when they don't show any research effort, are unclear, or not useful. Evidencing confusion about concepts or making incorrect assertions shouldn't in themselves be considered reasons for down-voting a question.

It's wise to presume that new users are

  • unfamilar with site norms,

  • inexperienced in asking statistical questions,

  • & unaware that they can edit their question;

& therefore to explain in a comment how they can improve their question, if someone else hasn't already done so (that goes not only, of course, but especially, for new users). Those with the close-vote privilege will often prefer to vote to close a question when appropriate rather than down-voting it—an edit will automatically place a closed question in the queue for re-opening, whereas an edit to a down-voted question may well be overlooked (see https://stats.meta.stackexchange.com/a/4574/17230).

Do you think this discourages new posters if they have their questions voted down? (Even if perhaps they received answers that are voted up?)

I'd hope they're only discouraged from asking further poor questions. Constructive, polite, criticism should go a long way to mitigate any disappointment at a first attempt at a question's not being well received.

[...] is there some approximate metric, duration of account in days, or minimum rep before you believe a question should be voted down?

No: most poor questions are asked by new users. Down-voting can flag the post for the attention of other users who may help (e.g. users with over 10k rep. can see a list of recent posts with a negative score at https://stats.stackexchange.com/tools), & I'd like to think it discourages premature attempts—perhaps also by new users—at answers. And it can make the difference between a question's being automatically deleted after thirty days, or hanging around for a year, or even indefinitely (see How does deleting work? What can cause a post to be deleted, and what does that actually mean? What are the criteria for deletion?).

† If this muddles the question to the point of making it unanswerable, it's sometimes good advice for the OP to take a step back & explain the problem at hand without recourse to statistical concepts.

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I think there should be a downvote period of grace for newbies (1 month/week?) until they get familiarised with the website, after that it should be the same as everybody else.

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    $\begingroup$ (-1) A down-vote affects the fate of the question much more than that of the user who asked it - they lose a small amount of rep. that they can recoup by editing the question to improve it, by deleting it if they can't or would rather not edit it, or by asking/answering other questions. I don't see the need for a grace period. $\endgroup$ – Scortchi - Reinstate Monica Apr 7 '17 at 11:29
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    $\begingroup$ @Scortchi As you know, a further fact is that many of the poorest questions come from people with reputation 1: although downvotes are all too visible, the user's reputation is never reduced below 1. $\endgroup$ – Nick Cox Apr 7 '17 at 11:41

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