|Various strains of stinky Clostridium difficile (Source)|
Clostridium difficile is the bane of hospitals all over the world. This bacterium tends to infect the intestines of people who have been on certain antibiotics. The antibiotics clear out a large chunk of the bacteria normally inhabiting a person's intestines, allowing C. diff (as it's called) to establish a foothold. The bacterium pumps out toxins which cause damage and disrupt the proper movement of food through the intestines (read: lots of diarrhea). In some cases, the large intestine can become super inflamed, a potentially life-threatening situation. If your guts become filled with C. diff, your poop tends to become watery (snot-like) and smell really bad in a distinctive way. It's commonly described in the scientific literature as an odour similar to horse manure, although a quick search through nursing forum threads such as this one mention, among other things, mouldy bread with a dash of skunk, a hot outhouse, rotting chicken, and a fart mixed with hot decaying roadkill.
Although the specific stench of a C. diff poop is reportedly difficult to miss, the one blinded study I found reported a group of 18 nurses were unable to identify poops from patients with C. diff infections based on their odour. That's not a particularly large sample group though, so it might be useful to do another study with more nurses to confirm these results.
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Rao K, Berland D, Young C, Walk ST, Newton DW. 2013. The nose knows not: Poor predictive value of stool sample odor for detection of Clostridium difficile. Clinical Infectious Diseases 56(4):615-616. [Full text]
Sethi S, Nanda R, Chakraborty T. 2013. Clinical application of volatile organic compound analysis for detecting infectious diseases. Clinical Microbiology Reviews 26(3):462-475. [Full text]