Is there any quantitative evidence that using social media helps academics disseminate their research results? What about the cost-effectiveness of social media?
My guess is that search engines are much more important than social media, and take less effort?
An article from 2014 "Do highly cited researchers successfully use the web?" suggests that most of the most prolifically cited researchers do not have extensive social presences.
At the same time, studies also show that using the social web can improve hit counts somewhat, which suggests overall that using social media can influence research, but may not have an enormous impact.
Now you'll have to excuse me while I go create a Twitter account for my research group. . . .
I initially left this partial answer as a comment on aeismail's great answer, but it didn't actually fit very well. To compliment his evidence-based answer, I wanted to provide a "use case" for social media.
Why might social media be better than a search engine? Because it provides opportunities for discovery outside of time frames when one is explicitly looking. (In this way, social media functions like alerts from ArXiv that a new paper has been posted to X topic.) Because I have a Zotero (bibliographic manager) plug-in for each browser, any time I come across an interesting article, it is extremely easy to file it away for later if it is a high-quality work that fits into my broad set of interests. When I am putting together a syllabus or literature review, the papers already in my reference manager can be a good starting point for further search.
In an interdisciplinary field, it can be hard to learn about all the relevant new publications. Anecdotally, I follow people (grad school acquaintances, colleagues, researchers I admire) on social media, and I often discover references to research that is germane to me, even if it does not appear in journals or conferences I see regularly. (While some of the relevant work would be posted on ArXiv, many of the papers would not be.) Thus, through social media I'm often helping the hit count, sometimes the citation count.
A search is also tough if the terms one is interested in are broad or vary by field. In those cases, setting up a saved search to look for them may not be useful because many of the results will be false positives, and they will not be filtered for quality. (Plus when I set up automatic searches for anything that produces a large number of results regularly, I usually end up just ignoring them rather than sifting through them.) Thus if I can follow several prolific academics who regularly tweet about their own work and what they're currently reading, this helps me discover interesting work with very low effort.
Also note that most quantitative study designs wouldn't disentangle the effects of social media versus search engines. That is, one of the advantages of a social media post is that many of them are included in web search results. (Analysis of social media's effect on citations will actually under-count social media's impact to the extent that private announcements--like friends-only Facebook posts--are not included.)
I think social media would influence awareness of public to your research rather than citation but I don't know any article about it. from What I experience researchers use social media to reach crowd to find participants, to disseminate knowledge etc. However, I would say it won't hurt your sitations and you might just help public understand your research wich is very important and not researchers do as much as I think necessary. Of course time constrain is big problem.
I can't offer quantitative evidence, beyond "take a look at altmetrics". I can offer anecdote, like most of the other answers ;-) I'll take Twitter as an example here, but I think the same applies to any social media that are viewable by the public, rather than invited people (e.g. "friends").
For journal articles and the like: In my experience Twitter can be a speedy way of letting people know about your latest publication. But would a significant proportion of those people have read it anyway, once their Google Scholar alerts picked it up? Maybe. No way to tell.
For more less specialised outputs (e.g. blog articles) Twitter is a very effective - perhaps the most effective - way of getting readers.
For events such as talks, outreach/knowledge transfer events, some types of workshop, etc., Twitter is effective at getting the information in front of people immediately.
HOWEVER: All this depends on your having followers. And for you to have followers, your account needs to be interesting, useful, entertaining, or a combination of the above. Accounts that are run purely as marketing exercises, especially by individuals rather than institutions, don't really work. So the summary of all this, again just anecdotally in my experience, is that if you have social media accounts that you use regularly - and hence have followers on - then they can be effective channels for dissemination of research. If you do not, then creating an account soley for this purpose is unlikely to work.
