I'd actually like to see a study on slipping on banana skins. When I was young I heard the phrase and soon after I tested it. Banana skins aren't that slippery unless the medium under it, or the shoe above it is slippery.
Admittedly, this is just my experience, and probably not statistically significant
In my experience, banana peels are quite slippery, especially when they form that 'layer of slime' (when the banana becomes quite ripe) and on a smooth (though not necessarily inherently slippery) surface.
Since you asked for a study, here you go (though I cannot speak for its correctness):
Wow, that is awesome! Thanks for the link. HN delivers again.
For anyone who doesn't want to download the link, the abstract states:
"We measured the frictional coefficient under banana skin on floor material. Force transducer with six degrees
of freedom was set under a flat panel of linoleum. Both frictional force and vertical force were simultaneously
measured during a shoe sole was pushed and rubbed by a foot motion on the panel with banana skin.
Measured frictional coefficient was about 0.07. This was much lower than the value on common materials and
similar one on well lubricated surfaces. By the microscopic observation, it was estimated that polysaccharide
follicular gel played the dominant role in lubricating effect of banana skin after the crush and the change to
homogeneous sol."
The type of banana you get at the grocery store now is called Cavendish. When the slip on banana peel meme was invented, the common banana was the Gros Michel, which has a more slippery skin.
Admittedly, this is just my experience, and probably not statistically significant