I'd like to add to GuyPowell's words. I think social media is wider.
First - we have to determine it - Social media is an umbrella term that defines the various activities that integrate technology, social interaction, and the construction of words, pictures, videos and audio. This interaction, and the manner in which information is presented, depends on the varied perspectives and "building" of shared meaning among communities, as people share their stories, and understandings. - http://en.wikipedia.org/wiki/Social_media
And finally can we talk about that social media works only in internet or it includes another communications - hearing, neighborhood talking, communications in different social or proffesional groups. The main principle is interaction between people in groups, and it doesn't matter what type of communication (internet/personal/local newspaper) these types can be in personal discuss at the office, bar or by e-mail, or e-forum.
So general position is influence on audience (social, proffesional or relative groups). And as result some following toughts and actions by this groups after discussion. This is the main aim for Social Media Marketing.
Second - we can measure the amplification effects of social media indirectly becouse it's difficult to measure how much and strong influence.
But we can measure increasing of demand on company goods or services. For example some Russian electronic-device company to achive their aims to start promotion of brend hire a lot people and give them big and bright bags with it's logo and they go everywhere with this bags (buses, metro, taxi, walking). Also many agents write in forums, blogs about good quality of this products. If I don't mistake it was Sitronics Company.