(n.) the study of speech impediments
Sometimes things just aren’t fair. Like calling the study of speech defects psellismology.
To be fair, according to the Oxford English Dictionary, that is an “obsolete nonce-word,” coined—along with its derivative psellismologist—in a November 1856 article in Charles Dickens’ periodical Household Words. It might be a nonce-word, albeit never intended to be taken all too seriously, then, but that’s not to say that there isn’t a perfectly sound etymology behind this one. (So no, before you ask, the author of that article didn’t deliberately come up with a word sufferers of speech impediments might find nigh on impenetrable.)
At the root of psellismology is psellism, or psellismus, an earlier English word, borrowed directly from Latin, for an instance of stumbling, stammering, or otherwise indistinct speech. First used in the sixteenth century, the Latin psellismus in turn comes from an earlier Greek term, psellízein, literally meaning “to stammer” or “stutter.” Chances are, that word was onomatopoeic, with that central double-L (an “expressive gemination,” according to the OED) perhaps intended to mimic the stop-start rhythm of a stuttering talker.