What fraction of visitors first find the site via Google, other search engines, links from other sites, tips from friends or colleagues, etc.?
I cannot tell you how people first find this site, but I can share some statistics provided I am not too "specific." During the lifetime of this site (including pre-beta and beta phases, up through the beginning of February 2015, four and a half years in),
A strong majority of visits were referred by search engines.
Half of the rest were referred from other sites. Most of these were google.com or stackoverflow.com.
The remainder were direct traffic.
Most of the search engine visits used an unknown search term. The most popular search phrases among those that are known include "statistics stackexchange" and "statistics stack exchange," which perhaps should be considered "direct traffic." But these are a tiny fraction of the new visits.
Here are some related numbers to ponder. Most of them can be gleaned from information readily available to anybody.
As anyone who looks at our main page can tell, we have had 50,000 questions asked. The number of answers posted is almost the same. These are a minuscule fraction of all visits.
I don't have information on the number of comments posted, but would guess there would be several times as many as the number of questions plus answers: perhaps a half million total, just a few percent of all visits. (Some of us average many comments per visit, btw. :-)
The total number of votes (up, down, accepted, etc.) is roughly 1.5% of the number of visits.
The number of edits is less than 10% of the total number of posts--very few posts are edited by the community.
The vast majority of visits therefore involve passive interaction only: no posting or voting of any kind.
Possibly this should be a comment rather than an answer as I do not have access to any site statistics, but judging from traffic levels to questions I have asked or observed, it seems there are several different audiences who come across the content.
I have asked several questions whose viewing figures are low, averaging just a handful of views per day, but almost all those views occurred in a couple of spikes: these occurred when there was activity that promoted the question to the main page for a few hours, or sometimes (e.g. on reporting Welch degrees of freedom) over a couple of days when I put a bounty on. My guess is that most of these viewers were regular SE users, probably registered and occasional contributors on CV.
Questions which make it to the "popular questions" sidebar across SE sites also seem to get a boost in traffic but generally temporary and in the hundreds. I'm guessing the boost mostly comes from SE users who are not CV regulars.
I recently received the "famous question" (10,000 views) for Real life examples of distributions with negative skewness. That came within one year of the question being asked, which judging by other "famous questions" (browse the full list here) is a fairly short but by no means record period of time - some examples take a couple of years to accrue the pageviews. Such traffic is implausible from internally generated traffic and I think it's safe to presume very few readers are registered SE users. In that case it is very likely that the traffic is search engine based: when I search google, that question is 2nd ranked for "negative skew example", 3rd for "skewed distribution example", a front-page result for "skew example" and "negative skew" and has even reached the third page for the very wide search-term "skewed distribution".
This is an indication of the effectiveness of SE at SEO! It also suggests we are writing for different audiences at different times. I think for a lot of the more technical and obscure content our users are basically writing at and for each other. But other content that has a wider and more general audience, which perhaps ought to change the way we approach it. On realising so many people were making use of my question I recently copy-edited it down to make it more useful and readable (~20% reduction in wordcount). While I was tempted to delete some of my initial discussion of examples of symmetric and positively skewed distributions, I realised that since the search engine rank was so high for "skew" and not just "negative skew", for many of the search-engine landers that content might actually have been what they were looking for! Presumably questions like this figuring highly in search results increases awareness of the site but I don't know how this works in terms of conversions to new users.
Other questions have had big spikes in pageviews due to sharing of links on external sites, but at least sharing by our own users seems to only account for a handful of the 369 "famous questions". Compare the publicity badges:
- Announcer - shared a link to a question that was visited by 25 unique IP addresses, 249 awarded
- Booster - shared a link to a question that was visited by 300 unique IP addresses, 12 awarded
- Publicist - shared a link to a question that was visited by 1000 unique IP addresses, 3 awarded
It would also be interesting to know whether such external traffic spikes are temporary. Obviously even CV users could share a "plain" link to the question that doesn't identify them as the referrer, and people who are not registered on CV could not use this option, and none of this is tracked on the badge system. A couple of questions have been reddited for instance.