I'm not weighting in on the ability of people to detect patterns, but hand washing is a bad example.
Detecting a pattern between 2 things that did happened (everyone but Dave ate pork, and everyone but Dave got sick) is orders of magnitude easier than detecting a pattern between something that did happened (this patient got sick) and something that didn't (everyone washed their hands).
Detecting a pattern between 2 things that did happened (everyone but Dave ate pork, and everyone but Dave got sick) is orders of magnitude easier than detecting a pattern between something that did happened (this patient got sick) and something that didn't (everyone washed their hands).