I liked Richard Dawkins' pick of the double-blind experiment. However, the significance of it for the lay person is entirely in why it is necessary. The concept itself is only a consequence. It's nice for people to know what a double-blind experiment is, but it doesn't give them an instant ability to evaluate scientific research. Even double-blind experiments can be flawed, and you wouldn't want people thinking they could trust the validity of a study just because it's double-blind. If consumers and voters started demanding double-blind experiments, advertisers and other liars would have no problem producing misleading results from double-blind studies.

No, the significance of double-blind studies is in why scientists have to go to such extraordinary lengths to escape bias. The ways bias can influence judgment and can be communicated subconsciously between people are pretty amazing, and they justify the skepticism that scientifically literate people take for granted but other people take for unreasonable stubbornness. "My uncle has seen ghosts, my cousin has seen ghosts, and I just told you I saw a ghost. Why don't you believe in ghosts? You just refuse to believe because paranormal phenomena are embarrassing to your narrow scientific worldview."

To help people understand why scientifically literate people think they way they do, we need to tell them stories about how bias affects experiments and leads to bogus results. In his essay about cargo cult science, Richard Feynman tells a great story about an experimenter who discovered an unexpected source of bias in an experimental setup for rats running a maze. That's a perfect example for the general scientific audience, for whom rats running mazes is an icon of objective quantitative science, but the general public needs examples where psychological bias creates results that they personally know to be important and know to be false. Understanding those stories will give them a completely new outlook on the information they take in every day.

Also, the stories need to put people in a serious frame of mind. No matter what their level of ignorance, people have enough meta-cognitive sophistication to worry that if they absorb our scientific skepticism they will miss out on a lot of fun things. They like believing in ghosts. They like believing in aliens. They like believing that there are extraordinary things in the world that are as accessible to them as science and technology are to the nerds. We're trying to rob them of their fun. Sure, they can still play at believing, but it won't be quite as thrilling. (It really is just as fun to watch The X-Files or read Harry Potter when you're scientifically literate, but I don't think they'd believe us if we told them :-) Also, it's a lot less fun to listen to your friends tell stories about how they saw a ghost in the Winchester Mystery House and how they know it was real because the tour guide knew what it looked like without being told because other people had seen the same one. Sigh.)

To get around resistance to the lifeless, booooring scientific worldview, we need something awful to shake people out of that fun frame of mind. Children dying of cancer because of biased studies, something like that. Even better, children getting abducted and molested. TV news shows know how to make people pay attention; let's put their techniques to good use. Unfortunately, my scientific education stopped after my sophomore year of college, so I'll leave it up to others to provide concrete examples ;-)