I was asked recently for a peer-reviewed piece that demonstrates why stories are better at communicating than data.
It’s all in the context. Data assumes that we all understand the figures and what they mean (and what they don’t mean) and can draw the same consequences and extrapolations from them. A big ask, but occasionally possible where you have an audience with a common background, common training and common intellectual, political and social perspectives on the world. I can’t think of such an audience, but you may be able to.
In short, relying on data assumes that we all have a common context in which the data sit.
I’ve recently taken to recommending Howard Gardner’s "Changing Minds" as a good source. 
[In the interests of transparency, clicking on the picture will take you through to Amazon on Narrate’s associate account – same Amazon price, but a small percentage comes back into Narrate – it pays for this blog.]
I also recommend Emergence: Complexity and Organization, the journal for various complexity-focused organisations. In particular, the 2005 double issue that focused on Complexity and Storytelling.
But for many people that’s not enough. Particularly when they’re evidence and data-focused people like doctors. The argument that’s often put forward instead is that data are irrefutable facts and hence produce change. This article in Fast Company magazine puts the lie to that.
Change or Die
[Dr. Edward Miller, the dean of the medical school and CEO of the hospital at Johns Hopkins University] turned the discussion to patients whose heart disease is so severe that they undergo bypass surgery, a traumatic and expensive procedure that can cost more than $100,000 if complications arise. […] The procedures temporarily relieve chest pains but rarely prevent heart attacks or prolong lives. Around half of the time, the bypass grafts clog up in a few years; the angioplasties, in a few months. […] many patients could avoid the return of pain and the need to repeat the surgery — not to mention arrest the course of their disease before it kills them — by switching to healthier lifestyles. Yet very few do. "If you look at people after coronary-artery bypass grafting two years later, 90% of them have not changed their lifestyle," Miller said. "And that’s been studied over and over and over again. And so we’re missing some link in there. Even though they know they have a very bad disease and they know they should change their lifestyle, for whatever reason, they can’t."
So let’s get this straight. Not only are there mountains of clear, unambiguous data to support change, it’s delivered carefully to people as part of their post-surgery advice by experts whose advice they respect. And it’s life-threatening.
And only one in nine people change in response to life-threatening data.
It’s a great article, but the last word comes from John Kotter, Harvard Business School Professor:
Kotter has hit on a crucial insight. "Behavior change happens mostly by speaking to people’s feelings," he says. "This is true even in organizations that are very focused on analysis and quantitative measurement, even among people who think of themselves as smart in an MBA sense. In highly successful change efforts, people find ways to help others see the problems or solutions in ways that influence emotions, not just thought."