"You don’t need matrix analysis to know that if you tell everyone to wash their hands, infections will go down." No, but you will need a well designed study or

"You don’t need matrix analysis to know that if you tell everyone to wash their hands, infections will go down." No, but you will need a well designed study or two, maybe a few accidental experiments (situations where a single variable is changed among two randomly selected groups of people), to tell if it's actually true. And it may be that your hypothesis is incorrect. It may be that telling everyone to wash their hands actually makes infections go up in some specific contexts. I can imagine a couple scenarios where that might be the case. One is the false sense of security of the washing hands message leads to a slightly sloppier application of other protocols such as sterilization of tools or cleaning furniture. Or the means of spreading the message its self, say on plastic posters, could be a breeding ground of airborn bacteria. Sure, these are highly improbable, and there's even more I can't imagine, but I wanted to point out that the original hypothesis isn't as airtight as the author intended... if taken literally.