According to information below, If you wear a helmet motorists might give you less room. Same for "cycling" attire. Might give you more room if you are a woman and/or in non-cycling attire though. Time to replace my helmet with a wig and heels?
"A classic post from Traffic author Tom Vanderbilt on How We Drive, detailing the findings from a UK study on helmet use and motorist behavior, serves as the starting point:
In his study (published as “Drivers overtaking bicyclists: Objective data on the effects of riding position, helmet use, vehicle type and apparent gender,” in the journal Accident Analysis and Prevention), [Ian] Walker outfitted a bike with a device that measured the distance of passing cars. He found, among other things, that drivers tended to pass more closely when he was wearing a helmet than when not (he was struck by vehicles twice, both while wearing a helmet).
New research has identified similar effects. Ollinger writes:
In a Florida DOT commissioned study [PDF] published last month, researchers reached a very similar conclusion. Although the study didn’t specifically address helmet usage, the researchers found that their data was consistent with Walker’s conclusions when it came to how closely drivers passed bicyclists based on the bicyclist’s gender and attire. The study found that on average, drivers passed cyclists more closely when cyclists were dressed in “bicycle attire” and if the cyclist was male. The study was unable to determine the reasons on this passing behavior and the authors of the study speculated that, “it [was] possible that motorists perceived less risk passing riders who were in [a] bicycle outfit.”
The gender factor, at least, appears to be noticeable to the general public. In fact, it has a name: the Mary Poppins Effect."