Study on likability, weakness, and competence? I heard a podcast about a study (I think it was Radiolab or similar) that found that people are viewed as more likable after they reveal a weakness or a shortcoming, but the effect only occurs if they have established that they are competent. 

What is that study? The podcast said it is influential and well known.

In the podcast, a professor told a story about how when he was a graduate student made a fool of himself in front of his PhD advisor and he joked that he did it on purpose to improve his likebility and she retorted that he hadn't yet established himself as competent. I remember hearing it in late 2014. Any help enormously appreciated!
Thank you all for your responses. I found the answer independently - I was looking for the Pratfall Effect described in Elliot Aronson's 1966 paper "The effect of a pratfall on increasing interpersonal attractiveness" in Psychonomic Science. 

The paper's abstract reads:


  An experiment was performed which demonstrated that the attractiveness
  of a superior person is enhanced if he commits a clumsy blunder; the
  same blunder tends to decrease the the attractiveness of a mediocre
  person. We predicted these results by conjecturing that a superior
  person may be viewed as superhuman and, therefore, distant; a blunder
  tends to humanize him and, consequently, increases his attractiveness.


More information on the Pratfall Effect can be found here: Wikipedia, Psychology Archive 


Aronson, E., Willerman, B., &amp; Floyd, J. (1966). The effect of a pratfall on increasing interpersonal attractiveness. Psychonomic Science, 4(6), 227-228.